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1. LEO sim ml File Toots Rag E9 E9 F9 6e _ Extrapalatin Simulation info Parameters MM 9 Enable trav mode 1 Advanced Results Ee sumaron Karatian mede Compute periapsis alttude 2 Summary OL puts poectedietime yer initial state Natra Meanparameters Object Characbaristics Type Keplerian sd Mame EXAMPLE space abject i Frame Celestial Mean of Date Mase 1470 kg Reflecting Area 15 Raftactivity coefficient 15 Drag area 15 m7 Drag Coefficient w Constant gt Variable fle Cook Orbit parameters Date boos 07 29TO2 00 00 000 cal a 7052 5 km Atmospharic Drag OG 10 2012 14 04 35 LEO simulation exampla LEO sirn xrnft loadad 3 4 3 Advanced Parameters The advanced default parameters contain recommended values STELA 87 File Took 7 LEO GEO GTO rT AREA TLE Eg lj 8 hal LEO S Run iterations WA Extrapolation Algorthms riteratreg mode EN a Parameters Integrator General zn a Results Atmospheric drag Summary P Enable atrmasphene drag 7 Quadrature ports 3 s3 convergence o threshold 15 10 days Recompute every 1 l steps guration expected yours Solar radiation pressure duration x Enable SAP 5 Quadrature points 11 Third body x Sun perturbations F E Moon per
2. If the user clicks on Uninstall the STELA software will be removed 2 2 3 Install a new version of STELA over an existing one To install a new version of Stela software follow procedure below Copy the modified configuration files e g configuration stela drag coefficient of the already installed version in a backup folder Copy simulation files e g example leo sim 2011 05 05 SMOS sim xml of the already installed version in a backup folder Uninstall STELA nstall the new version of STELA Merge the old configuration files with the new ones the structure of the configuration files may have changed between the previous and new version Copy simulation files in the new example folder don t erase existing simulation example file 2 3 Installation directory The contents of the installation directory are as follows Name E Description Readmetxt txt Fil Contains the STELA version License txt Files The CNES licence in text and PDF License FR p format Directory STELA launchers and icons Contains the configuration files for STELA that may be modified by advanced users don t forget to comment modifications Stela User Manual pdf File Contains the user manual pdf format Contains example files that can be opened by STELA sim xml or i bod mean st tool shap xml Contains all java jar files for STELA and its dependencies Contains resource files
3. Not compliant this status is written in the output results in the output results when the current Protected Region criterion is not fulfilled Compliant this status is written in the output results when the current Protected Region criterion is fulfilled during the simulation duration and when the simulation duration 1s long enough Not Reliable this status replaces both Compliant and Not Compliant status for a GTO simulation It indicates that one single orbit propagation can not give a reliable criterion status due to resonance phenomena see 3 9 2 and Warning 2 Warning 1 the simulation duration must be at least 25 years in order to allow the STELA software to ensure in any case the compliance with Cl and C2 criteria at least 100 years in order to allow the STELA software to ensure in any case the compliance with C2 SC2 C3 SC3 C4 and SC4 criteria Warning 2 for GTO orbits the extrapolation results are very sensitive to the initial conditions date perigee position wrt the sun direction and to the computation parameters area drag and SRP coefficients solar activity due to the sun moon perturbation and to resonance phenomena See Ref 6 A statistical computation using the statistical mode through GUI or in batch mode is to be done in order to obtain relevant results 5 STELA fundamentals Since the first STELA version in 2010 three dynamical models referred to as LEO GEO an
4. 13 30 km Time TT minus LIT 14 67184 Log Date SIUSTZUIS TUUS STEN Lek 2 26 09 2013 15 33 35 Cr ation d une nouvelle sirnulation GTO Ww IMFO The Advanced Parameters view contains the integration step aflag used to enable disable the atmospheric drag force 3 the number of points for the Simpson quadrature used for the modeling of the atmospheric drag force see Algorithm features 4 the number of integration steps where the atmospheric drag force 1s considered to be constant therefore the drag force recomputation occurs every N integration steps a flag used to enable disable the Solar Radiation Pressure SRP perturbation the number of points for the Simpson quadrature used for the modeling of SRP see Algorithm features a flag used to enable disable the Sun perturbations a flag used to enable disable the Moon perturbations the zonal harmonics order of Earth gravity model a flag used to enable disable the Earth potential tesseral perturbation 11 the tesseral harmonics order of Earth gravity model 12 the minimum period used in the tesseral effect computation The tesseral effect 1s taken into account if its effect has a period greater than the given value expressed as a multiple of the integration step 13 the reentry altitude The spacecraft enters the atmosphere when the perigee altitude of its orbit goes bellow this value Ne ov EN pU de ey 14 th
5. Extrapolation 3 y Ji GEOS ees Parameters iterative mode Advanced z F Results pl Exclusion duration 2 100 years Summary Outputs eae acosa e sinl path ge a minus GEO altitude 5 203 km Initial state Object Characteristics Nature Pean paramers T Mame EXAMPLE Space Object Reflecting Area 000 kg Type m Reflectivity coefficient Drag area Drag Coefficient Constant Vanable file Cook Orbit parameters cd Date 1998 01 01700 00 00 000 cal 29 08 2013 15 14 simulation exam le GEO sim xml loaded 3 6 3 Advanced Parameters The advanced default parameters contain recommended values STELA S Fie Tooke 7 EO GEO GT J TS py AREA TLE c T i kal GEO 8 Run iterations VAR X cnes Extrapolation Algorithms riteratree mode Parameters Integrator General LI x Ei 1 7 Atrmpspheric drag Summary Outputs 1 Enable atrmaspherie esl 2 Quadrature points j 1 Algonthm convergence UD k Recompute every 4 1 steps threshold 15 1 km Soler radiation pressure x Enable SAP n Quadrature ponts 11 Third bady z Sun perturbations Mean perturbations Earth perturbatran Zonal order o 7 Enable tesseral perturbation 10 Tesseral order 11 7 Minimum penad 12 5 steps Reentry Reertryalttude 13 30 km Time TT minus LTI 1
6. 1 dey dK1 dix dK1 diy dK1 da dK2 dex dK2 COMMENT dey dK2 dix dK2 diy dK2 dksi dK2 COMMENT Units m rad COMMENT This is a default comment Appendix 1 Using STELA as a library 1 REQUIREMENTS In order to use STELA as a Library you will need An installed version of STELA Software that you can download on the following website http logiciels cnes fr S TELA fr logiciel htm A Java editor Eclipse will be used here as an example e STELAs Javadoc optional you can download it from the previous link 2 INSTALLATION In order to use STELA as a Library you have to take the following steps 2 1 Add the jar n Eclipse right click on the project you want to use STELA Library in along this tutorial it will be called STELATest Open properties select Java Build Path tab Libraries then click the Add external JARs button Go to STELA installation folder default pathway is C Program Files STELA_vX X X Open the lib folder e Select all the jar Ctrl A If you want initialize message you must add all module of Stela Remarque In reality importing all the JAR files shouldnt be necessary like junit jfreechart It depends on the way you are going to use the library Compulsory JARs to use STELA as a library would include stela elib stela etoo stela processing stela commons and the commons math non exhaustive list 2 2 Set up the environment STELA needs
7. Cres USER S GUIDE VERSION 2 5 October 2013 USER s GUIDE The Semi analytic Tool for End of Life Analysis software STELA is a semi analytic orbit propagator 1 STELA purpose 2 Getting Started 2 1 System configuration 2 2 Software installation and removal 2 3 Installation directory 3 Using STELA 3 1 Run STELA software 3 2 STELA main window features 3 3 Open a LEO simulation example 3 4 Parameters of a LEO simulation 3 5 Open a GEO simulation example 3 6 Parameters of a GEO simulation 3 7 Open a GTO simulation example 3 8 Parameters of a GTO simulation 3 9 Results of a simulation 3 10 Output data and Plots 3 11 Tools 4 Assessing Compliance with LEO amp GEO Protected Region criteria 4 Termination criteria 4 2 Protected Region criteria 4 3 Criteria applicability 4 4 Protected regions criteria status 5 STELA fundamentals 5 1 Frames 5 2 Orbital elements 5 3 Time scales 5 4 Propagation models 5 5 Algorithm features for LEO model 5 6 Algorithm features for GEO model 5 7 Algorithm features for GTO model 5 8 Iterative mode for LEO and GEO simulations 5 9 Dispersions used for statistical analysis 5 10 Physical and key parameter values 5 11 Validity domain 5 12 Logbook error list 5 13 TLE conversion 6 Glossary 7 References Appendix Drag coefficient file Appendix A 2 Solar activity file Appendix A 3 Ephemeris file rep 4 5 Sta A
8. STELA uses zero search function using Brent s method This function takes the semi major axis as parameter and returns the difference between the current minimal altitude and the expected one 5 9 Dispersions used for statistical analysis Resonances phenomena encountered in GTO region have very strong effects on the orbit evolution and lifetime A statistical approach 1s needed to handle these effects and properly estimate GTO evolution see SRef 8 The approach selected the Monte Carlo method lies on the principle of dispersing initial nominal parameters such as the mass the orbital elements and so on and analysing the results in a statistical way see 4 2 9 for more information on the results analysis 5 9 1 Date Time Dispersion The user can disperse the day the month or the year of the initial date separately or all together The dispersion may be Uniform or Gaussian The uniform dispersion asks for a minimum and a maximum value The Gaussian dispersion asks for a standard deviation and uses the nominal value entered in the General tab as the mean value Hour dispersion follows the same principle Note that for a Uniform dispersion when entering a negative minimum value or a maximum value greater than 24 it is taken into account as a day change day before for a negative value and after for a value greater than 24 For a Gaussian dispersion mean value is the hour entered in the General tab Note that if the user wants
9. A accomodation constant from 2 4 recommanmded value from 3 610 4 V T and M are computed by STELA T and k are tunable in the stela advanced parameters file not very sensitive the higher this value the higher the C default value 300 K k sensitive the higher this constant the lower the default value 4 5 7 3 2 Mean area The mean area is the area S to be used for drag computation that 1s to say the cross sectional area perpendicular to the velocity direction The user can use the STELA Mean Surface Area tool see Tools to compute it This area 1s constant during the simulation 5 7 3 3 Atmospheric density The atmospheric density model uses in STELA is the empirical model NRLMSISE 00 NRL for US Naval Research Laboratory MSIS for Mass Spectrometer and Incoherent Scatter radar E for the model that extends from Earth ground through exosphere and 00 for the year of release The calculation of density need the knowledge of the date the satellite position the Sun position and data on solar and geomagnetic activities The NRLMSISE 00 model implemented in STELA 1s adapted from the C implementation available on the following Internet site http www brodo de english pub nrlmsise index html Note that the model implemented by Stela uses double precision and has a more precise Pi value than the reference one 5 7 3 4 Solar Activity The solar activity is defined by the geomagnetic activi
10. server class JRE since its startup time 1s neglectable compared to its usual processing time When Stela starts batch or GUI mode server mode is activated if this mode 15 available STELA can be installed for a single user or for a multi users environment according to the system rights available for the user The available system rights vary according to the system credentials for further details or if installing STELA on a multi users environment contact system administrator 2 2 Software Installation and Removal 2 2 1 Install STELA IMPORTANT NOTES e Having a proper Oracle Sun Java Runtime Environment version 1 6 installed is required to run STELA The STELA installer also requires this Ideally the latest version of the JRE should be installed to ensure best GUI compatibility WARNING STELA may not work with IBM JRE or any other JRE than Oracle and it 1s strongly recommended not to use them f a new version is installed in the same folder as the previous one all files will be overwritten User modified files have to be saved previously 2 2 1 1 Install on Windows 1 Double click on the setup file stela install X X X jJar where X X X is the release of STELA The installation program will ask to fill in the following field 2 Information about STELA release are displayed to the user example below is for version 1 2 0 d IzPack Installation of STELA E _ jm xl e Please read the Following informat
11. 0 220 753T334524 5 TST ISIS 65 3758 HIBSTRTSSESS 1 eS LIE 2605 69 LTS 0 1 LS 34453 25544124748 18272 1153242324T1T 2 134548342535328T SSS LATIO B 23587518221563136 Jbl5 Bd 17T23 0P W AA 25102 545 3258104204 1353 37245T75458704 0 TT 1 TIA 0 2582248572115488 2BI5 Bd l TI3 8B Peb dEd 15265 55090123B757T eee 7504 5563T5985892B 2 0171T35642353 54098 2 0235838 71832235 6321 356865 a STELA format called STELA_OEM which uses Modified Julian Days see 5 3 8 F STELA B CDHMEHT CARR ETELE VERSIOU 2 4 0 4 5HAPSHOT CREATION DATE B12 L2 181T15 20 2B B5 B UKTBIMATOIE CARS B HETA STAAT A UBJECT EXAMPLE Ghee OBJECT 10 EXAMPLE apace Bey ect CENTER MEHE EARTH B FRAME BOD EPETER Ur B START TIRE JU15 E 15T23 0 oh s STOP_ TLHE 2813 L1 19192 22 JB 30 B HETA Toe CORED Pedr B CDMMENT Typ z CORED F rmar PUG sec EL XI x3 ES x5 Ib B OCDMMEMT Unite km deg CDHHEMT 070 ceample statistical sieularian sa ARAP 4 18 9 3401 52 55 53H 0 13280E 102959 9g 222 687234524 5 35153115 35 FEBZ 2 48 ba 306553553 1 MeL dESSdEAS 2243 57250 Hi753 450503030571 AJEL 0080191100411 3HMdEH 3E544134748 1B827 115124712873 7 1390563584718 42787 Pp 5 1415758151147887 214B752502715403184 55b a 385bL 4225 b5b19 b181 5522E3 132 04 LIBR FERS AR 3 493B3BDE2EB58 543
12. 7 References SPACE FLIGHT DYNAMICS Volumes 1 et 2 CNES Carrou Cepadues edition 2 Cook G E Satellite Drag Coefficients Planetary and Space Science Vol 13 Oct 1965 pp Un gt 10 11 Morand V Caubet and al Semi analytical implementation of tesseral harmonics perturbations 13 925 946 Koppenwallner Hypersonic Technology Goettingen Technical comments Comment on Special Section New Perspectives on the Satellite Drag Environnements of Earth Mars and Venus Journal of Spacecraft and Rockets Vol 45 No 6 November December 2008 IERS Technical note N 36 IERS CONVENTIONS 2010 Fraysse et al Long term orbit propagation techniques developed in the frame of the French Space Act 22nd ISSFD 2011 Lamy et al Analysis of Geostationary Transfer Orbit long term evolution and lifetime 22nd ISSFD 2011 Le Fevre et al Long term orbit propagation techniques developed in the frame of the French Space Act 5th IAASS Conference 2011 Morand et al Dynamical properties of Geostationary Transfer Orbits over long time scales consequences for mission analysis and lifetime estimation AIAA ASC Conference 2012 Le Fevre et al Compliance of disposal orbits with the French Space Act the good practices and the STELA tool Acta Astronautica Volume 94 Issue 1 January February 2014 Pages 234 245 and IAC 2012 D A Vallado Revisiting Spacetrac
13. Inclination when 1 lt 0 1 1 and 0 180 when i is greater than 180 the usual correction 15 applied Note that these corrections change the distribution form that cannot be considered as purely uniform or Gaussian The user may change the law parameters entered Standard deviation or Delta to end up with a real uniform or Gaussian law 5 10 Physical and key parameter values Here are the physical parameters values used in STELA Earth potential model Grim5_S1 including Harmonics Earth radius Earth flattening e Standard gravitational parameter Geocentric Earth radius for criteria verification and ha and hp computation 6 378 km Astronomical unit UA 1 49598022291E11 m e Solar Radiation Pressure at IUA 0 45605E 5 N m2 e Sun standard gravitational parameter 1 32712440018E20 m3 s 2 kg 1 Moon standard gravitational parameter 4 9027779E12 m3 s 2 kg 1 These parameters are saved in the stela physical parameters file in the configuration files directory Here are other key parameters not to be modified saved in the stela internal parameters properties file in the resources directory GEO margin used in C4 criterion verification h 3 km EO margin used in C2 criterion verification h 2 km GTO margin used in C2 C3 and C4 criteria verification h 10km tnax used in C3 criterion verification 2 years 5 11 Validity domain The following paragraphs describe STELA valid
14. Solar fl10 flux noontime yyyy mm dd No missing Days interpolated Executed by R L Kelley on 02 26 2013 2435839 0 258 63 1956 12 3l 2435840 0 269 17 1957 1 1 2435841 0 279 70 1957 1 2 2435842 0 278 70 1957 1 3 2435843 0 287 80 1957 1 4 2435844 0 290 90 1957 1 5 2435845 0 295 90 1957 1 6 2435846 0 268 50 1957 7 2435847 0 252 00 1957 1 8 2435848 0 236 70 1957 1 9 2435849 0 219 50 1957 110 2435850 0 218 40 1957 1 11 2435851 0 220 50 1957 1 12 JAVA 0L M FAA FA 77 1 17323 ree FEY Pa LE SF Daw I P F L I 4 Appendix A 3 Ephemeris file Examples of STELA ephemeris file are presented hereunder It corresponds to an output data file of STELA The ephemeris can be saved in two different formats a CCSDS compliant format called CCDDS_OEM see ORBIT DATA MESSAGES CCSDS 502 0 B 2 prsps VERS 7 6 COMMEMT CHES STELA VERSIDH 2 4 0 d SHAPSHDT CREATION DATE 2612 12 16716 46 Mi iti OREGEMATOR CHES START OBJECT WAHE EXAMPLE space objeri EJECT 10 a EXAMPLE tpace object CENTER MAE EARTH HER HU TIHE UTE STAET m PERS Beds ESTIS Ah ee died TOF 2BLB 10 RTE 28 10 457 TF CDHMEMT Matura Aen CDHMEMT CDMMEHI Formar xl x3 Et x35 EB Unita km Heg OTO example Statistical simalatlon eBLS EwG D5TZ3 085 00 050 4116 STL 5471 0 1323562 10205
15. and complementary results about each criterion STELA example GTO sim xami File Tools a 929 919 kd aros Run statistics ES gt Extrapolation Computation mfarmatian Complementary statistical results Parameters Number of executions 160 Final observed probability f 0 95 Final confidence interval pl p3 0 9005 0 9766 Maimun value af pl 0 9005 for n 160 Mean computation time 1 48 Minimum value of p2 0 9669 for n 121 Min required number of executions for orterion status 45 General Advanced Computation duratian amin 495 Ebatmins Results Summary Statistical values computed from 95 confidence intervals For 0 9 probability level Computed lifetimes shorter than LT2 19 57 years Plat type SC 1 Lifetimes wrt execution numbers LT canfidence interval 16 29 22 16 years Statistical results plot Plat Not available Final observed probability f 1 Final confidence interval p1 p2 0 9708 1 Maximum value of pl 0 8708 far n 160 SC3 Minimum value of pz 1 form 160 Min required number of axecutians for onterion status 45 Final observed probability f 1 Final confidence interval p1 n2 0 3708 1 Maximum value af pl 0 9708 for n 160 C4 Minimum value of p2 1 for n 160 Min required number of executions for onterion status 45 d Ep H CIT fl J 17 12 2012 15 29 17 End of extrapolation number 164 l7 l2 2012 15 20 20 End stat
16. with the extension _stm txt when this computation is enabled by the user This is an ephemeris file containing the orbital elements and the state transition matrix See Appendix A 7 3 10 2 Single extrapolation mode output view The Output view is intended once the simulation is properly done to allow the user to plot some orbit parameters or to save an ephemeris file STELA example GTO E Pul File Tools 3 3 5 kd GTO S Run extrapolatio e Extrapolation Parameters General Advanced Results Plot type Perigee amp Apogee E Summary j de Plot Extrapolation results plot Save ephemeris file Format COSDS OEM Mature Mean parameters Cartesian Save ephemeris file Date uL Message tev TUSTZUT Wl T ZIP zt inu 24 05 201 Start extrapolating 24 09 201 Extrapolation ends after 2 seconds 3 10 2 1 Plots The user has the possibility to choose between eleven plots of results the values of Perigee and Apogee altitude km vs the simulation duration duration is relative to the start time 10 and expressed in years he values of Perigee altitude km vs the simulation duration duration is relative to the start time tO and expressed in years he values of Apogee altitude km vs the simulation duration duration 1s relative to the start time 10 and expressed in years he values of Semi major axis
17. 16 59 9356 397 541521206 35618 8407004 30 6059902226 94 3474130883 50 1505228 65017A 1993 12 18T12 50 26 535 386 010424967 407 743497495 51 6391042997 12 3332999276 6 59 72419 J Copy into STELA session One must pay attention to the fact that converted state s date 15 defined in the UTC Time System Indeed STELA default Time System is UTI therefore while copying the selected state into current STELA session a Time System conversion UTC to UTI 1s performed to meet the STELA standards using the TT minus UTI value of the Advanced Parameters panel Two options are provided for the conversion from TLE data Conversion from TLE to osculating orbit parameters This conversion is done using SGPA SDPA theory as described in Ref 10 This conversion is not valid for high eccentricities due to limitations in the SGP4 SDP4 short period model It is recommended for quasi circular orbits when importing into STELA session Conversion to SGP SDP mean parameters Brouwer convention This conversion is valid for all eccentricities since no short periods are added to the orbital elements It is recommended for high eccentricity orbits when importing into STELA session It includes a conversion of the Kosai mean motion of TLE orbital products to the Brouwer mean motion see TLE conversion 5 13 When the impossibility to carry out a controlled reentry is duly proven the conform
18. 6 Me nstan State Sitio Appendix B 1 Using STELA as a library 1 STELA purpose The Semi analytic Tool for End of Life Analysis software STELA has been designed by CNES The French Space Agency to support the French Space Act When the impossibility to carry out a controlled reentry is duly proven an uncontrolled reentry or a stable disposal orbit can be chosen given that the orbit respects the different criteria established in the French Space Operations Act STELA reflects the standard concerning the protection of LEO and GEO regions lifetime and protected regions crossing of disposal orbits and provides the user with tools to assess compliance with the requirements The software allows efficient long term propagation of LEO GEO and GTO types orbits based on semi analytical models statistical analysis and assessment of protected regions criteria STELA produces a report file that summarizes the computation spacecraft characteristics initial final orbits computation parameters criteria status and optionally an ephemeris file For GTO orbits due to resonances phenomena a statistical analysis 1s performed using Monte Carlo method STELA software includes an iterative computation mode adjusting the initial orbit to achieve a given atmospheric reentry duration or to avoid GEO region crossing for a given duration a tool that computes the cross sectional mean area of a spacecraft a tool that converts Two Li
19. Af I1 f 1 Me i pa pac tnu ian F274 Fd D 2 22 dr uu With 1 2 for a confidence interval of 95 cumulative normal distribution function observed probability of SCi being compliant on the available distribution based on n single extrapolations number of OK runs divided by n n number of single extrapolations In order to conclude on a criterion status n has to be greater than a minimum value nmin depending on the confidence rate see SRef 9 1 2 pSCi tao qq TA 2 pSCi u mn A l pSCi The following graph displays the result of the analysis for SCi criterion SCi criterion needs to be verified with a pSCi probability hu aaa nS UN 9575 confidence interval nl nl na Akenbar af extrapolations The 95 confidence interval gives the interval which has a 0 95 probability to contain the converged probability of SCi being compliant As soon as the lower limit of the confidence interval p1 is above the Statistical Criterion probability pSCi for instance 0 9 for SC1 SCi becomes Compliant Conversely if the upper limit p2 1s below the pSCi threshold the Statistical Criterion SCi is Not Compliant When neither pl nor p2 has crossed pSCi the status 1s not computable and needs more extrapolations to be able to conclude NB In the very unlikely case where the limits pl and p2 are both crossing pSCi the criter
20. Be careful parameters are automatically rounded to 12 digits and angles are restricted to interval 0 360 when entered by user The output ephemeris step defined as a number of integration steps that will be used for plots and output ephemeris file saving 27 Note that in GTO case when the transition matrix computation 1s activated this 1s also the step of the transition matrix ephemeris file For Terrestrial Frozen at Epoch frame two additional fields are displayed Frame Terrestrial Frozen at Epoch Freeze epoch 2008 07 23T04 07 03 011 Cal Reference longitude B2 deg Fields Freeze epoch and Reference longitude are two parameters of Terrestrial Frozen at Epoch frame see SFrames 3 8 3 Advanced Parameters The advanced default parameters contain recommended values Fie Tac 7 GT kd GTO is Run statistics ba TLE ches 737 ka Extrapolation Algar amp hrns Parameters Integrator General 255 __1 z h Statistics Atrmespheric drag 7 Besuks abl eer Summary lt Ena sadalle reg Outputs Quadrature points 3 z Recompute every 4 1 steps Soler radiation pressure Enable SAP D Quadrature poirits 6 11 Third bady Sun perturbations HB Mean perturbations Earth perturbation Zonal order g 7 Enable tesseral perturbation 10 Tesseral order 11 7 Minimum perad 12 5 steps Reentry Reentry alttude
21. Sd No negative area dispersion m G it 110 5d nom 3 No negative area dispersion m Constant coefficient Cd Uniform l No negative dispersion 96 DUM coefficient Gaussian No negative dispersion E eg coefficient Variable coefficient or Cook coefficient Cd Gaussian l No negative dispersion po dU d coefficient Solar activity Variable Flux F10 7 0 100 3 Gaussian ao Gaussian dispersion 96 0 100 3 No negative Ap Constant Flux F10 7 No negative flux Uniform dispersion sfu DOLEO Gaussian 0 F10 7 nom dispersion sfu 3 NOME ve Uniform dispersion 0 Ap nom No negative Ap unitless Gaussian dispersion unitless cs 0 400000 Average memory limit executions Max number of Number of Optimum use of processors physical cores resources Warning limits for LEO model library mode only Params Interval Explanation o LEO model parameters Dv 1 not adapted to equatorial orbits 0 nom 3 Inclination Eccentricity 050 125 LEO modelisation coherence and validation domain Integration step Recommended unto i 0 10 12h integration step Integration step inclination above 10 12h oe integration step 120 Warning limits for GEO model library mode only P
22. Type2PosVel Frame CELESTIAL_MEAN_OF_DATE Nature MEAN a Semi major axis 8562 5 km e Eccentricity 0 0 I Inclination 98 59 deg RAAN Right Ascension of Ascending Node 277 51331 deg w Argument of perigee 0 0 deg M Mean anomaly 0 0 deg Final Bulletin Date 2109 07 29T00 00 00 000 Type Type2Pos Vel Frame CELESTIAL MEAN OF DATE Nature MEAN a Semi major axis 8561 84930142 km e Eccentricity 3 6114658E 4 I Inclination 98 5731535225 deg RAAN Right Ascension of Ascending Node 178 161920203 deg w Argument of perigee 157 348667255 deg M Mean anomaly 37 1931945988 deg Results Effective simulation duration 100 01 years Criteria 1 NotApplicable Lifetime under 25 years Criteria 2 Compliant No LEO crossing within 100 years Min distance to the LEO protected region 166 93 km Criteria 3 NotApplicable No GEO crossing between 1 and 100 years Criteria 4 NotApplicable No GEO crossing within 100 years Appendix A 5 Statistical report file An example of statistical report file 1s presented hereunder This file contains all simulations input output generated with STELA statistical mode One line corresponds to one orbit propagation The number of columns depends on the number and type of dispersed parameters Note that Nb is the extrapolation number The first MJD sec corresponds to the beginning date of the orbit propagation The second MJD s
23. added to text field as STELA will not be able to save load it STELA File Tools 7 97977 bed coe gt HU Extrapolation Simulation inte statistical mode Parameters m Author Default Author Mame 1 1 Enable statistical mode 15 Advanced statistics is is a default comment Maximum number of executions 1000 16 Results B i Summary initial state P Comments 2 Mature Mean parameters 17 Type Perigee Apogee 18 Simulation Frame Celestial Mean of Date 19 100 years duration Object Characteristics Name Sat 4 Mess ball ort perernctare Reflecting Area Reflectivity coefficient ta Drag Coefficient Constant Variable fle C Cook 9 za 22 0 km cd 10 2 2 23 o deg a 24 O deg Atmospheric Drag Atmospheric model wuwsseo 11 7 25 0 de Solar activity Constant user defined 12 E EDEN OUP x 14 15 Number of integration steps 27 for each ephemeris step 1 steps The user may fill in The simulation information the author name 7 comments 2 he simulation duration in years 5 The spacecraft main characteristics its name 4 its total mass kg 5 its mean cross sectional reflecting area m 6 its reflectivity coefficient 7 its mean cross sectional drag area m 8 its drag coefficient Cd w
24. by the French Space Act Plot of stela drag coefficient values Sphere or Tumbling Flat Plane Mean Drag Coefficient 400 BOO al 1000 1200 1400 200 Altitude km Appendix A 2 Solar activity file The solar activity file stela solar activity can be provided into different formats the solar activity file provided by default by STELA he solar activity file generated by Debris Assessment Software 1 Stela solar activity file An example of stela solar activity file 1s presented hereunder It contains the following values Date JD1950 and seconds daily solar flux F10 7 sfu eight 3 hr AP index for current day version 1 kc oc oc c oc opc oc oc oc oc oc oc oc oc opc oc opc opc oc oc oc xc oc opc ac oc oc oc oc oc oc oc opc ac oc oe oe oc oc oc c ac ac oc oc oec oc oc oc oc ac ac oc oe STELA SOLAR ACTIVITY FILE xk kc occ pep oe ok ake kk ake ae oe oe cocco pc bcc oe oe je cec pcc a a a ak ak ka ak aa a a ak ak a a a a DATE JJ 1950 SEC DAILY FLUX 8x 3H AP 2556 61200 258 63 6439 123 4 4 2557 61200 269 17 23 3 22 15 7 6 3 2558 61200 279 7 9 6 9 48 12 9 56 48 2559 61200 278 7 22 12 9 15 95 5 6 2560 61200 287 8 J 3 43 4 4 446 3 9 5 dk dk dk dk dk SE 2561 61200 290 2552 61200 295 1469 75 6 7 2553 61200 268 71212 7 5 2 2964 61200 252 12 18 7 22 18 12 12 15 2555 61200 236 7 7 7 6 6 18 22 15 22 4 2566 61200 219 5 18 32 48 27 27 27 32 39 2557 61200 2
25. compatible with STELA Conversion can be performed in osculating parameters or in mean parameters according to SGP SDP theory Once converted the user can select an output state and retrieve it in the initial TLE list The selected state can also be copied in current STELA session assuming that a simulation has previously been created If so the bulletin is copied in the orbital parameters frame the International Designator in the space object s name text area and the ballistic coefficient in the commentary text area STELA TLE Convertor Tool Input state FORMAT Two Line Elements 1 255441 98067 10035 38351289 00015217 10103 3 6 5145 225544 51 5448 192 5852 0010686 260 9766 159 7494 15 756495936427556 1 298447LU 10 12116 26180481 00006156 00000 0 18119 10 3142 2 29447 030 0074 094 3643 7215 80 209 8197 006 2702 02 2 892435 29580 1 16605U B6017A 23 3352 535022334 00007889 00000 0 10529 30 34 216609 51 6190 13 3340 0005770 102 5660 257 5950 15 59114070 44786 Convert to asculating parameters Convert fo mean parameters Output state MATURE Osculating TYPE Perigee Apogee FRAME TIME SYSTEM UTC FORMAT ID Date yyyy MM dd T HH mm 5s 555 Zp km Zal km 1l deg 2 deg w deg M deg 58067A 2010 O02 04TO9 12 15 514 332 8675224975 342 745049525 51 6254682208 187 406553658 88 9513700 B6010F 2012 04 25706
26. for STELA resources Directory that are not meant to be modified even by advanced users installationInformation Fil Needed for the uninstaller tool Uninstaller Directory Contains the uninstaller tool configuration Directory 3 Using STELA 3 1 Run STELA software Please note that several instances of STELA can run concurrently at the same time even from the same installation directory Each instance is fully independent and uses its own system resources PID memory However STELA simulation or tool files are not protected from damage if one is accessed by several STELA instances at the same time 3 1 1 GUI mode Be careful In GUI mode input parameters of simulation are rounded before extrapolating in order to respect the number of digits displayed This rounding can produce differences between GUI mode and Library or Batch mode 3 1 1 1 Run STELA on Windows Run the command file stela bat located in the bin subdirectory of STELA installation path or double click the STELA shortcut of your desktop 3 1 1 2 Run STELA on Linux Run the shell stela sh located in the bin subdirectory of STELA installation path 3 1 1 3 Run STELA on Sun Solaris Run the shell stela sh located in the bin subdirectory of STELA installation path 3 1 2 Batch mode 3 1 2 1 Run STELA on Windows Run the shell stela batch bat located in the bin subdirectory of STELA ins
27. hundredth included extrapolation year 35 786 200 h km lt altitude lt 35 786 200 h km e 15 deg lt latitude lt 15 deg h is a margin to be considered due to the fact that the modelization is a simplified modelization wrt precise reference numerical propagators taking into account a full dynamical model Its values are given in Physical and key parameters Method of use The method is the same as for the C4 criteria See next paragraph 4 2 4 C4 criterion No GEO crossing within 100 years Title The C4 criterion is violated if the following conditions are fulfilled during the first hundred extrapolation years 35 786 200 h km lt altitude lt 35 786 200 h km e 15 deg lt latitude lt 15 deg h is a margin to be considered due to the fact that the modelization 1s a simplified modelization wrt precise reference numerical propagators taking into account a full dynamical model Its values are given in Physical and key parameters Method of use The mean parameters are first propagated till the periapsis and the apoapsis mean anomaly set to zero and pi The geocentric periapsis and apoapsis altitude are zp a_mean 1 e mean 6 378 km za a mean 1 e mean 6 378 km If za lt 35786 200 h C4 margin or zp gt 35786 200 h C4 margin C4 margin is a value larger than the effect of the short period terms on the orbit radius Then the criterion 1s not viol
28. initial orbit with a user defined constant solar flux sfu and geomagnetic index Ap 14 and 15 The initial state the nature of the initial orbital parameters mean or osculating see Orbital elements 76 the type of the initial orbital parameters see Orbital elements 7 the frame in which the initial orbit is expressed see 18 he orbit parameters the calendar date of the initial orbit see S Time scales 79 he six parameters describing the orbit 20 to 25 Be careful parameters are automatically rounded to 12 digits and angles are restricted to interval 0 360 when entered by user The output ephemeris step defined as a number of integration steps that will be used for plots and output ephemeris file saving 26 For Terrestrial Frozen at Epoch frame two additional fields are displayed Frame Terrestrial Frozen at Epoch Freeze epoch 2009 07 29704 07 03 011 Cal Reference longitude b2 deg Fields Freeze epoch and Reference longitude are two parameters of Terrestrial Frozen at Epoch frame see SFrames When the software runs in iterative mode 1 the following parameters shall be defined The type of iteration mode eccentric orbit tunes the periapsis altitude or frozen orbit tunes the semi major axis and the frozen eccentricity value see SIterative mode for LEO and GEO orbits 2 The expected lifetime of the searched orbit 5 STELA
29. km vs the simulation duration duration is relative to the start time tO and expressed in years he values of Eccentricity vs the simulation duration duration is relative to the start time t0 and expressed in years the eccentricity vector ey vs ex for quasi circular orbit with ex e cos W and eyze sin u that makes perfect sense for LEO orbit the eccentricity vector ey vs ex for quasi circular and quasi equatorial orbits with 0 and 51 0 that makes perfect sense for GEO orbit he values of Inclination deg vs the simulation duration duration 1s relative to the start time t0 and expressed in years he inclination vector 1y vs for quasi equatorial orbits with 1x sin 1 2 cos 3 and 1y sin i 2 sin that makes perfect sense for GEO orbits the values of Argument of Perigee deg vs the simulation duration duration is relative to the start time 0 and expressed in years he values of Right ascension of the ascending node deg vs the simulation duration duration 1s relative to the start time tO and expressed in years the values of the sum M deg vs the simulation duration duration is relative to the start time tO and expressed in years The solar flux F10 7 used in the extrapolation for atmospheric density computation The geomagnetic index Ap used in the extrapolation for atmospheric density computation Please note that the plotted orbit parameters are mean
30. of the initial orbit might already be It is not necessary to iterate to reduce the below the expected lifetime please extrapolate lifetime as it 1s already below the 25 years the initial state threshold Error saving file filename The file could not be saved Error loading file filename The file 1s corrupted Unable to connect to the JMX client on port Port 15 not available Log from simulation number Remote Error from process running simulation n Execution error simulations generated for the statistical Out of memory error Please reduce maximum mode are stored in memory Requiring too number of simulations many simulations may lead to a memory overload Statistical analysis failed The statistical analysis has failed one of the propagation has failed RTT It should never happen unless some internal parameters files have been modified 5 13 TLE conversion The conversion of Two Lines Elements to STELA inputs uses the SGP SDP4 model in the TEME frame SRef 10 The osculating orbital elements are computed from the TLE using SGP SDP4 theory This conversion is not valid for high eccentricities due to limitations in the SGP4 SDP4 short period model It is then recommended for quasi circular orbits when importing into STELA session For higher eccentricity Orbits it is recommended to use mean orbital elements when importing into STELA session The mean elements usable by STELA are directly thos
31. progress 1 Estimated remaining duration 1h 4min Extrapolation finished 41 1000 3 3 Open a LEO simulation example The user can learn how to use STELA software with the help of a simulation example A configurated file 1s available in the directory installation directory examples In order to select the example the user must use the STELA menu File gt Open a new simulation and then select the example file example LEO sim xml ETSI 5 example GEO sim ximl 5 example GTO sim xml 3 example LEO sim xml File Name lexample LEO sim xml Files of Type STELA Simulation files sim xmD 7 Only files with the extension sim xml can be opened by STELA The rest of the current chapter will consider this simulation example in order to describe the different GUI views 3 4 Parameters of a LEO simulation 3 4 1 Navigation The left part of the STELA window allows the user to navigate and to select the STELA window File Tools oe Extrapolation Simulation info Parameters il General Author Defa ult Advanced his is a v Results Summary Ephernaris Comments 3 4 2 General Parameters The following image displays a view of the General Parameters window These parameters are listed below Note that tooltips are available for the simulation parameters They appear as soon as the mouse is pointing the name of a parameter Warning special characters
32. required by the quadrature theory Reentry altitude 0 inf Physics coherence Earth zonal 10 15 Not implemented potential order beyond J15 0 value in the physical constant file 0 inf Physics coherence period Blocking limits for LEO simulations Params Interval Explanation Expected lifetime only in iterative 10 inf Physics coherence mode Bounded by the physical constant file Earth tesseral potential order Max duration expected duration Me 0 inf Coherence only in iterative mode Algorithm convergence 10 Expected threshold only in lifetime Coherence iterative mode Blocking limits for GEO simulations Params Interval Explanation Exclusion duration only in iterative 10 inf mode Physics coherence Min perigee altitude minus GEO altitude ony 10 ntl Coherence in iterative mode Algorithm convergence MT threshold only in 10 221 Coherence iterative mode Blocking limits for Statistical Analysis Params Interval Explanation Mass Physics coherence Uniform dispersion kg Gaussian dispersion ke O inf Physics coherence SRP Area Unif dude d O inf Physics coherence G 0 inf Physics coherence Coefficient Cr Uniform 0 inf Physics coherence dispersion Gaussia
33. see 4 1 Termination Criteria for more information the initial seed It can be regenerated using the button Generate on the left the date dispersion panel the hour dispersion panel the mass dispersion panel the solar activity dispersion panel the orbit dispersion panel the orbital parameters dispersion matrix correlation covariance or no dispersion In the case of correlation a vector of standard deviation delta has to be provided as well the orbital parameters dispersion type the nature of the orbital parameters dispersion the type of the orbital parameters dispersion Initial bulletin will be converted into it before dispersion the frame in which the initial bulletin 1s expressed in This is simply a reminder and cannot be changed 13 the covariance correlation matrix 14 the multiprocessing mode activate deactivate parallel computing 15 the number of processes that will be launched For an optimal execution number of processes should be equal to the number of computer cores Be careful in some cases your processor can be run in hyperthreading mode In this case divide the number by two See also your processor documentation 16 the reflecting area dispersion panel 17 the reflectivity coefficient dispersion panel 18 the drag area dispersion panel 19 the drag coefficient dispersion panel For more information on available dispersions see 5 9 Dispersions used for statistical analysis NB Mean Nominal values
34. such as should not be added to text field as STELA will not be able to save load them STELA example LEO sim mi File Taals Tj 49 kal LEO S Run extrapalatio uc Extrapolation Simulation iteratie mode Parameters sc E Ade d Example LEG simulation file Results for STELA Initial state Summary Outputs m P ET Mature Mean parameters 16 Type Kaplerian 17 Frama Celestial binan of Data 18 Simulation 100 wears duration Y Object Characteristics Hama EXAMPLE space abject 5 Mass 1470 kg Reflecting Area 15 m Date 15 2003 07 29T00 00 00 000 Orbit parameters Reflectivity coefficient 15 20 70625 km Drag area 9 15 m Ml 3 ee zi 00159292035 Drag coefficient sj Constant Variable fle Cook 22 ga 59 deg a 23 277 51331 deg Atmospheric Drag I deg Atmospheric model MALMSISE 00 12 0 deg Solar activity Constant user defined Constant value Number of integration steps for each ephemerrs step 09 10 2012 13 52 New LEO simulation created 09 10 2012 13 53 0 simulation example LEO sxm xml loaded The user may fill in The simulation mode J the default mode performs a single extrapolation the iterative mode performs an iterative search of an init
35. the atmospheric model in the following way Mean and current solar flux values F10 7 geomagnetic index values AP 5 5 3 5 Simpson s quadrature The atmospheric drag effect on osculating parameters can be easily computed but we rather need to know the effect on mean parameters The STELA software uses the Simpson quadrature method to compute the drag perturbation effect on mean parameters First the drag perturbation is computed at Nquad osculating points as follows The mean orbital parameters are propagated from the perigee of the orbit to the Nquad 1 other points of the orbit points are equidistant in true anomaly in order to have more points near the perigee these are the quadrature points The mean parameters of quadrature points are converted to osculating parameters At each quadrature point using osculating parameters he atmospheric drag force is computed he atmospheric drag force is transformed in the T W frame OSC the derivatives of the osculating parameters dt computed using the drag force in the T N W frame and the Gauss formula Then the drag perturbation on mean parameters 1s computed using the Simpson quadrature B Nquad P dEamg dEang l ejcosE d Fang v lt dt 2 a dt 1 r Note the sum 1s done following the Simpson theory the first term using the eccentricity and the eccentric anomaly takes into account the reparti
36. the resources and the configuration folders in order to work properly Therefore your program should start with the following line Prop defineROOT C NRootDirectory The argument in defineROOT method being the folder where you installed STELA it contains bin configuration lib and resources sub folders 3 RUNNING IT Using STELA library in your Java code is very straight forward You simply need to call the function you want to use Open the file example java e g C Program Files STELA v2 0 2 examples example java In this example a new GEO simulation has been created executed and then results have been displayed in the Eclipse console Remarque The pathway of the load C Program Files STELA v2 0 2 examples example GEO sim xml 1s the pathway of the xml file we want to run If working under Windows environment it is the direct pathway inverting the slash Once the Java class saved errors may appear these are due to missing imports declarations To organise and add automatically imports with Eclipse press Ctrl Shift o In order to know the name of the methods to use and their package you have to search the Javadoc presented in the following paragraph 4 JAVADOC Go and download the Javadoc from the http logiciels cnes fr S TELA fr logiciel htm website Unzip the folder and then open all the target subfolders and unzip the JAR file that you will find To access the Javadoc of each STELA modul
37. to 0 9 The computation method is explained in paragraph 4 2 9 4 2 7 Statistical SC3 criterion No GEO crossing between 1 and 100 years with a probability of psC3 Title Ihe SC3 criterion is compliant if the C3 criterion is compliant with a probability of pSC3 Method of use pSC3 15 equal to 0 9 The computation method 1s explained in paragraph 4 2 9 4 2 8 Statistical SC4 criterion No GEO crossing within 100 years with a probability of pSC4 Title Ihe SC4 criterion is compliant if the C4 criterion is compliant with a probability of pSC4 Method of use pSC4 is equal to 0 9 The computation method is explained in paragraph 4 2 9 4 2 9 Method used to compute statistical criteria statistical criteria are computed following the same method Let s consider the computation of SCi criterion During the Statistical Analysis a number n of single extrapolations has been runned Status of Ci criterion for each single run 1s either OK if Compliant or NOK otherwise The probability of SCi being compliant 1s based on the the number of OK runs over the total number of runs n This probability is then surrounded by the Wilson Confidence Interval with continuity correction of the Binomial law The bounds of this interval are used to check the compliance For more information about this topic please see Ref 9 The upper and lower limits of this interval are given by the following formula Paf usa 1 2 1lina
38. to obtain a local time of perigee dispersion because it is a key parameter in the propagation sensitivity to initial conditions he can give the initial orbit parameters in the Terrestrial Frozen at Epoch frame and disperse the initial date When using the Terrestrial Frozen at Epoch frame and dispersing the initial date the difference frozen epoch initial date is kept constant 5 9 2 Mass Areas drag and reflectivity coefficients Dispersions These parameters can be dispersed in a uniform or Gaussian way The mean or central value is the one filled in by the user in the General tab The standard deviation for a Gaussian dispersion is in percent or in the unit of the dispersed parameter The Delta for a Uniform dispersion is in percent or in the unit of the dispersed parameter Note that when a variable file 1s given as a nominal value the uniform or Gaussian dispersion generates a multiplicative coefficient that 1s applied to the whole file Correcting the dispersed values When dispersing values non physical values may appear These values are corrected following this method Mass If the generated mass 1s smaller than 0 1 of the nominal value mass is corrected to 0 1 of the nominal value to avoid value too closed to zero Areas negative dispersed values are corrected to 0 Reflectivity Coefficient negative dispersed values are corrected to 0 and values greater than 2 are corrected to 2 Drag Coefficie
39. value 14 140 sfu AP 15 15 Number of integration steps 26 for each ephemeris step 1 steps The user may fill in e The simulation mode J the default mode performs a single extrapolation the iterative mode performs an iterative search of an initial orbit that will stay above a minimal altitude during a given exclusion time see Iterative mode for LEO and GEO orbits The simulation information the author name 2 comments 3 he simulation duration in years 4 The spacecraft main characteristics its name 5 its total mass kg 6 its mean cross sectional reflecting area m 7 its reflectivity coefficient 8 its mean cross sectional drag area m 9 its drag coefficient Cd which may be defined 10 by an input file stela drag coefficient see Appendix A 1 as a constant value given in field 77 from Cook formula The atmospheric drag settings he theoretical atmospheric model NRLMSISE 00 12 the solar activity it is an entry for the atmospheric model The solar activity can be defined 13 with a solar activity file stela solar activity report to Appendix A 2 that contains daily information made of the daily solar flux sfu the mean solar flux sfu and the geomagnetic 3 Hour index Ap eight values defined for 24 hours with a solar activity file from DAS solarflux table txt report to Appendix A 2 that contains daily inform
40. 0 UL Inclination 80 110 U See below 130 180 Mean area mass reflecting and 0 0 1 drag areas Simulation LEO validation MN 7 100 years Lo TAi kan LEO validation P domain Expected lifetime LEO validation domain Max duration only in iterative O 100 years LEO validation mode domain 0 expected duration 100 Expected LEO validation only in iterative n domain lifetime mode 199 l A frozen eccentricity Inclination only in iterative mode frozen orbit computation near the critical inclination values may not be relevant 68 4 111 5 Warning limits for inclination has the following source the dynamical properties of LEO inclined between 40 80 and 110 130 At these inclinations resonance effects due to various perturbation sources solar radiation pressure third body perturbation and drag in particular have been shown to have significant effects on LEO lifetime in some particular cases As a result criteria status may be very sensitive to initial parameters For more information on the resonance effects please refer to Ref 11 Warning limits for GEO simulations Params Interval Explanation Perigee altitude 34 786 km GEO validation Type 0 36 786 km domain Apogee altitude Zp 36 786 GEO validation Type 0 km domain Initial Bocentricity 0 0 009 EDO HOD domain Initial Inclinati
41. 0 years with a probability of 0 9 Net compliant c4 Mo GEO crossing within 100 years with a probability of 0 9 gm Probabdity 0 092 for n 48 ic ETT gel el iG ee rrm her values computed from 55 canfidenze intervals Message 24 05 2012 1124 Monte Carlo automatica 24 09 2012 11 24 End statistical analysis 3 10 Output data and Plots 3 10 1 Output files When the user saves a simulation three output files are generated four when using GTO statistical mode the simulation file with the extension sim xml It 1s an xml file that contains all the simulation information and can be re loaded by STELA software he report file with the extension _sim txt It is a copy of the simulation file with round results as GUI but in a text format In particular if the simulation has already been run the report file contains the summary of the compliance with the protected LEO amp GEO region criteria The report file can not be re loaded by STELA A display of a report file 15 available in Appendix A 4 he log file with the extension log txt It is a text file that contains all the log messages that have been displayed The log file can not be re loaded by STELA GTO statistical mode only the statistical text file with the extension sim stat txt It contains a matrix of all simulations generated with the statistical mode inputs and computed outputs GTO mode only the state transition matrix file
42. 1 F35491E32738534HT 0 2115244 57252 JOGOO L5265 863p2 34 T5 T7656 4704H7 8E327985 IDA THES 7554 551759E08D373 4d 3371734429111485 7 502358507183J7216 3721428245 58 31568655 5253 EBSB 22 12 241953b 1 12721 1428 7458 SE GESE SS IAEE 21 193 385B727043 1 1231515221 E 24D B ALINE 12325357 Appendix 4 Report file An example of report file is presented hereunder This file contains output data from STELA CNES STELA VERSION 2 0 0 LEO Simulation Report General Author U N Owen Comment Example LEO simulation file for STELA Simulation duration 100 0 years Ephemeris step 864000 0 s Difference between terrestrial and universal time 66 184 s Integration Step 864000 0 s Drag quadrature Points 33 Solar radiation pressure quadrature Points 11 Atmospheric Drag Recompute step 2 steps Solar radiation pressure switch true Sun Moon Switch true Reentry Altitude 120 0 km Space Object Mass 1470 0 kg Drag Area 15 0 m 2 Reflecting Area 15 0 m 2 Orbit Type LEO Reflectivity Coefficient 1 5 Drag Coeficent Type VARIABLE Name EXAMPLE space object Atmospheric Model Atmospheric model NRLMSISE 00 Solar Activity Solar Activity Type MEAN_CONSTANT AP Constant Equivalent Solar Activity 15 F10 7 Constant Equivalent Solar Activity 134 83734638 Initial Bulletin Date 2009 07 29T00 00 00 000 Type
43. 1 e 6 378 km Za 1s the apogee geocentric altitude Za a 1 e 6 378 km 1 18 the inclination Q 1s the right ascension of the ascending node is the argument of periapsis Wh is the mean anomaly Type Cartesian parameters position and velocity x y z X 2 Type 2 Keplerian parameters a 1 Q M Type 3 Near circular elements a ex 1 M w where ex e cos u is the first component of the eccentricity vector e sin uJ is the second component of the eccentricity vector 6 parameters for non singular eccentricity Ju M esin a al Type 7 Poincar parameters for non singular eccentricity and inclination G4 V2Psin p Yi2V2Pcos p Xz2V2Qsin Y 2Qcos q L V Aeq C eM with V e2 p m 42 q 6l P L G 2L Lm Q GG H Lm Lmcost Type 8 Equinoctial and near circular elements ex ey 1x 1y 9 w M where ex e cos 1s the first component of the eccentricity vector ey e sin W 0 15 the second component of the eccentricity vector ix sin i 2 cos Q is the first component of the inclination vector iy sin i 2 sin Q is the second component of the inclination vector e y QO4M The use of orbit parameters types is summarized in the following table LEO GEO GTO model model model Differential equation type 6 type 7 type 8 Transformations m
44. 18 4 27 6 27 22 22 4 6 7 2568 61200 220 5 927 75202025 2569 61200 209 3 7 35 656 44 335 25 0 61200 200 2 22666432 25 1 61200 193 7 54561299 7 25 2 61200 186 6 9 7 7 7 15 5 5 5 25 3 61200 195 7 7 5 5 7 7 6 65 Warning since STELA v2 5 the mean solar flux parameter is automatically computed by STELA using the daily values in line with what is expected by the atmospheric model Hence the corresponding column has been removed Older files including this parameter are readable by the software but the mean flux is not used Moreover for the date parameter a new column containing the number of seconds from the beginning of the Julian day has been added Older files not including this parameter are readable by the software Then a value of 0 sec is considered The user may use its own solar activity file by keeping the same format heading and column replacing the file s name in the stela_elib properties file configuration folder The values given in stela solar activity file are past measurements from 1956 and future mean prediction given by Noaa and Nasa File goes up to year 2318 STELA Solar activity file PK Daily and mean Solar Flux F1 0 7 metro ccc cae eee eae ee ee 0 10000 20000 30000 40000 590000 50000 70000 JD 1850 2 DAS solar activity file An example of DAS solar activity file is presented hereunder It contains the following value daily solar flux F10 7 sfu JD
45. 3184 0141113303 1310 55051 2085 327999573201 0 0274445879281025 1 0 56093387 1 1 1 1 1 0 56093387 1 0 0 0 43906613 8 55041 0 0 150 35892 1666666 2 92 238 48 178 0 505 50 2 344595436327977 2237 3303144241 13 1 0 55049 59819 5039997343 0 023798371992802006 1 0 5977033 1 1 1 1 1 0 5977033 1 0 0 0 4022967 9 55041 0 0 150 35892 1666666 2 92 238 48 178 0 505 50 2 3762255490847677 71 3231012040 1310 55051 24525 0979995355 0 02815566133038792 1 0 62880974 1 1 1 1 1 0 62880974 1 0 0 0 37119026 10 55041 0 0 150 35892 1666666 2 92 238 48 178 0 505 50 2 1845094431168657 2655 3242031101 1310 55051 9075 144999939948 0 02766608 1863004156 1 0 65546278 1 1 1 1 1 0 65546278 1 0 0 0 34453722 Appendix Mean Constant Flux for LEO orbits The mean constant solar activity is a constant value vs time depending on the ballistic coefficient of the spacecraft and on the initial apoapis altitude of the orbit It has been tuned through a statistical approach to achieve a 25 years re entry duration as a mean value A disposal orbit that re enters the atmosphere in 25 years with this Mean Constant Solar Activity will have a lifetime that is not modified whether the end of mission date shifts whereas using a variable solar activity leads to a variability of the computed lifetime Orbit Lifetime sensitivity to start date 29 Variable Solar Activity Mean Constant Solar Activity Pono 5 27 26
46. 4 67184 s The Advanced Parameters view contains the integration step aflag used to enable disable the atmospheric drag force 3 the number of points for the Simpson quadrature used for the modeling of the atmospheric drag force see Algorithm features 4 the number of integration steps where the atmospheric drag force 1s considered to be constant therefore the drag force recomputation occurs every N integration steps a flag used to enable disable the Solar Radiation Pressure SRP perturbation the number of points for the Simpson quadrature used for the modeling of SRP see Algorithm features a flag used to enable disable the Sun perturbations a flag used to enable disable the Moon perturbations the zonal harmonics order of Earth gravity model a flag used to enable disable the Earth potential tesseral perturbation 11 the tesseral harmonics order of Earth gravity model 12 the minimum period used in the tesseral effect computation The tesseral effect 1s taken into account if its effect has a period greater than the given value expressed as a multiple of the integration step 13 the reentry altitude The spacecraft enters the atmosphere when the perigee altitude of its orbit goes bellow this value Ne ov EN pU de ey 14 the delay TT UT1 used in frame transformations see Time scales and when importing TLE The right part of the view appears only if the softw
47. 5 4 3 Partial derivatives The transition matrix ephemeris is saved with the same frequency as the bulletin ephemeris To compute the partial derivatives make sure that the flag transitionMatrix is set to true in the STELA advanced parameters file stela advanced parameters properties in configuration folder The state transition matrix file contains the ephemeris file in a STELA_OEM format see A 3 Ephemeris file plus additional columns that are the partial derivatives Here is the State transition matrix file header STELA OEM COMMENT CNES STELA VERSION 2 4 0 4 CREATION DATE 2012 12 07T17 09 12 054 ORIGINATOR Default Author Name META START OBJECT NAME Default Object Name OBJECT ID Default Object Name CENTER NAME EARTH REF FRAME MOD TIME SYSTEM UT1 START TIME 1998 01 01T00 00 00 000 STOP_TIME 1999 01 01T00 00 00 000 META STOP COMMENT Nature Mean COMMENT Type Equinoctial COMMENT Type ksi w RAAN M COMMENT Format MJD sec a ex ey ix iy ksi da da0 dex da0 dey da0 dix da0 diy da0 dksi da0 da dexO COMMENT dex dex0 dey dex0 0 diy dex0 dksi dex0 da deyO dex deyO dey deyO dix deyO COMMENT 0 dksi deyO da dix0 dex dix0 dey dix0 dix dix0 diy dix0 dksi dix0 da diyO COMMENT 0 dey diyO dix diyO diy diyO dksi diyO da dksi0O dex dksi0 dey dksi0 dix dksi0 t COMMENT diy dksiO dksi dksi0 da dK1
48. EO orbits and 80 km for GTO orbits The termination criterion TC2 triggers when the periapsis altitude becomes lower than the reentry altitude The periapsis altitude is computed by the software at every integration step as follows The mean parameters are propagated till the periapsis mean anomaly set to zero Mean parameters at the periapsis are converted to Osculating parameters The geocentric periapsis altitude is hp a osc 1 e osc 6 378 km 4 1 3 Statistical Termination criterion STC1 Statistical mode Title statistical Termination criterion STC1 the maximum number of single extrapolations given by the user has been reached Method of use The statistical analysis stops when the maximum number of single extrapolations is reached The maximum number of single extrapolations 1s an input parameter defined in the GUI 4 1 4 Statistical Termination criterion STC2 Statistical mode Title statistical Termination criterion STC2 Automatic stop Method of use When the automatic stop mode is chosen in the GUI the Statistical Analysis stops when the number of single extrapolations 1s great enough so that all the Statistical Criteria are defined status different from not computable if the extrapolation duration is lower than 100 years only SC1 needs to be defined to trigger STC2 Otherwise all four statistical criteria need to have a defined status 4 1 5 Statistical Termination criterion STC3 Statistical m
49. Orbit lifetime Ko 24 2020 2022 2024 2026 2028 2030 2032 Effective start date Considering a 25 years lifetime orbit computed with this value the real lifetime computed statistically with several past solar cycles and several initial dates in the first cycle would have a mean value of 25 years with a cumulative distribution function as follows Orbit Lifetime distribution Cumulative distribution function 10 15 20 25 30 35 40 45 Orbit Lifetime This constant equivalent solar activity is computed for LEO orbits at the extrapolation beginning using the formulas AP 15 F10 7 201 3 25 Li Ca 3 7 log Z The following figure plots the F10 7 value computed with this formula for various altitude of apogee ballistic coefficients NB if Cd has been chosen to be variable a constant Cd 2 2 value is used in STELA to compute the solar flux Constant Flux value S m 0 005 S m 0 01 s m 0 015 Sim 0 02 sim 0 025 S m 0 03 F10 7 sfu 400 500 600 TOO 800 900 1000 1100 1200 1300 Apoapsis altitude km These solar activity coefficients are used in the atmospheric model in the following way Mean and current solar flux values F10 7 geomagnetic index values AP Appendix A 7 State transition matrix file State transition matrix file stm txt is automatically saved when saving a GTO simulation in which the partial derivatives have been computed see
50. Python The script is divided in two sections Methods and Main Only the section Main should be modified by the user This script simply performs several extrapolations As an example the semi major axis is reduced by 1km at every iteration 3 1 4 Parallel computing In order to decrease the computation time for GTO statistical mode STELA will run the extrapolations in multiprocessing mode enabled by default This mode can be disabled in the GUI by unchecking the corresponding checkbox in the Statistics parameters section For further customization the number of processes launched may be changed Parallel computing is used only for GTO statistical mode When running STELA on a cluster one must specify in the batch mode shell the maximum size of used random access memory Edit the stela batch file and add option of java program Xmx512m Note in order to obtain the same statistical result with or without parallel computing the extrapolation results are taken into account in the ascending order in the statistical analysis It means that if the the result of extrapolation number k 1 is available before the result of extrapolation number k the process will wait for the result of extrapolation number k to compute the statistical results at step k As a result it may lead to unsorted log messages TS Run extrapolatio Date Message bevel Functionalities provided by this window are listed be
51. STELA 1s to be installed di IzPack Installation of STELA Select the installation path C Program Files STELA Made with IzPack http Irzpack org If the chosen directory does not exist a pop up will ask the user to confirm or cancel the creation of the target directory Message The target directory will be created C Program Files STELA Click OK to continue If the directory exists a pop up will ask the user to erase the existing version of software see Install anew version of STELA Warning Click Yes to continue 5 Packs Selection a new window appears in order to allow the user to choose the packages he wants to install example below is for version 1 2 0 IzPack Installation of STELA Select the packs you want En install Mote Grayed packs are required Description STELA application Total space Required Available space hada with IzPack http izpack arg Clicking on next will proceed to the software installation 6 Before exiting the installation program the user can set STELA shortcuts by clicking on Next The delivery contains an icon bin stela ico that will be used for the shortcut d IzPack Installation of STELA 185 Pack installation progress Finished 185 Overall installation progress with lzPack http izpack org Previous 7 The user can add the STELA program in the Windows start menu by
52. age appears in the logbook to indicate the necessary correction General blocking limits Params Interval Explanation 557 10 inf Physics coherence ME Zp inf Sa Physics coherence 0 1 1 ee coherence Mas 0 0 Physics coherence coherence Mean 0 inf Physics coherence Physics coherence Reflectivity 0 means that the 0 inf coefficient SRP is not taken into account Eu 0 inf Physics coherence i duration Integration step step 10 inf 0 sinf Physics coherence coherence Date of the initial Al existing Physics coherence Orbit dates Reference date of the Terrestrial existing Frozen at Epoch dates Frame Physics coherence Number of Natural number not integration steps Ne null for each ephemeris coherence with the step used integrator Constant solar activity Flux et 0 inf Physics coherence Drag Mean area 0 inf Physics coherence If null value Drag coefficient 0 inf simulation is executed with no drag force Number must be Number of points of Simpson drag ME c uadrature this 1s required by the Period of drag D Expressed as a number i 1 inf reevaluation of integration step Number must be uneven Number of points of Simpson solar radiation pressure this 1s
53. ame TEME is the frame in which TLE are displayed It is a CIRF like frame with the X axis pointing toward the vernal direction defined by Greenwich Mean Sideral Time 1982 It can be deduced from the PEF Pseudo Earth Fixed frame at a reference date by a Z axis rotation of GMST angle see SRef 10 PEF can be deduced from TIRF by a Z axis rotation of angle s 0 00005 This frame is used in STELA software to import TLE data 5 2 Orbital Elements The term nature 1s related to mean osculating and the word type 1s used to describe the orbit parameters form cartesian keplerian 5 2 1 Orbit parameters nature The Osculating orbit corresponds to the real spacecraft state vector position and velocity at a given date The Mean orbit corresponds to the osculating orbit minus the short period variations short period orbit period In STELA the mean orbit parameters are those computed by the semi analytical model at each integration time step as the osculating parameters at a given date are the mean parameters plus the added short period effects computed in the MOD frame The perturbations taken into account in the short period computation depends on the kind of dynamical model LEO GEO GTO See Osculating orbit 5 4 2 5 2 2 Orbit parameters type Different types of orbit parameters are used in STELA 0 parameters Zp Za 1 Q M where e Zp is the perigee geocentric altitude Zp a
54. arams Interval Explanation GEO model parameters Inclination 0 179 5 not adapted to inverse equatorial orbits Eccentricity 050 125 ee Warning limits for GTO model Params Interval Explanation GTO model parameters Inclination O 179 5 not adapted to inverse equatorial orbits Integration step inclination above 120 Recommended Tom integration step 5 12 Logbook error list The following table lists the errors that can appear in the logbook when an exception is thrown Logbook errors and warnings Signification Listed parameters are out of their expected Error in validity control of parameters list bounds blocking limit and STELA model is not valid outside of Listed parameters are out of their expected bounds warning limit and STELA model may not be fully valid outside of Solar activity file or solar cycles files have not been found Error reading solar activity file filename The solar activity file 1s corrupted Warning parameters are out of advocated bounds list Error initializing variable drag coefficients file Variable drag coefficient file has not been found REMIT QUE Napa The variable drag coefficient file 1s corrupted filename The NRLMSISE 00 atmospheric model returns The atmospheric density computation has a non physical value of density possibly due to failed possibly due to a wrong solar a
55. are runs in iterative mode Then the right part contains 15 the definition of the algorithm convergence threshold 3 7 Open a GTO simulation example The user can learn how to use STELA software with the help of a simulation example A configurated file 1s available in the directory installation directory examples In order to select the example the user must use the STELA menu File gt Open a new simulation and then select the example file example sim xml Look I JE 5 example GEO sim xml example GTO sim xml 5 example LEO sim xml File Name example sim xml Files of Type STELA Simulation files sim xmD 7 Only files with the extension sim xml can be opened by STELA The rest of the current chapter will consider this simulation example in order to describe the different GUI views 3 8 Parameters of a GTO simulation 3 8 1 Navigation The left part of the STELA window allows the user to navigate and to select the STELA window File Tools 7 LEG SEG y b PEE v Extrapolation General Advanced Statistics Results surrnarny Outputs 3 8 2 General Parameters The following image displays a view of the General Parameters window These parameters are listed below Note that tooltips are available for the simulation parameters They appear as soon as the mouse 1s pointing the name of a parameter Warning special characters such as should not be
56. are those from the General Panel 3 9 Results of a simulation 3 9 1 Summary for single extrapolation mode When a simulation ends STELA software automatically switch to the Results Summary view that 1s divided in two topics The left part describes the final orbit state as followed he nature type and frame are reminded to the user he final orbit parameters date position and velocity The right part reports the compliance with criteria through the plot of the effective simulation duration and the status of the four criteria see Assessing Compliance with LEO GEO amp GTO Protected Region criteria If a criterion is violated the first violation date or the estimated lifetime is indicated The user shall keep in mind that the Criteria are evaluated through the osculating parameters expressed at evaluation points along the orbit see Assessing Compliance with LEO amp GEO Protected Region criteria whereas the orbital parameters given in the left part of the view come from the last point computed by the integrator which is not necessary at the perigee or the apogee and may be given through mean parameters It explains that the crossing of a protected region or the reentry of the spacecraft may not be blindingly obvious by looking at the final orbit parameters If Criteria 2 is compliant the minimum distance to LEO protected region is displayed If Criteria 3 is compliant the minimum distance to GEO altitude and the cor
57. ated Else the spacecraft could possibly violate the C4 criterion therefore Mean parameters of periapsis and apoapsis are converted to Osculating parameters The geocentric periapsis and apoapsis altitude are zp a osc 1 e osc 6 378 km za 1 e osc 6 378 km If za lt 35786 200 h or zp gt 357864 200 h Then the criterion 1s not violated Else if the mean inclination is below 15 deg or above 165 deg Then the criteria is violated Else the 4 mean anomalies corresponding to the 15 latitude points are computed to compare the corresponding osculating altitude to 35786 200 h and 35786 200 h Depending on these 4 osculating altitudes the criteria may be violated or not The geocentric altitudes and latitudes of these osculating points are saved 4 2 5 Statistical SC1 criterion Lifetime lt 25 years with a probability of pSC1 Title Ihe SC1 criterion is compliant if the criterion is compliant with a probability of pSC1 Method of use is applicable when nominal non dispersed orbit crosses Region A 5 1 15 equal to 0 9 The computation method 1s explained in paragraph 4 2 9 4 2 6 Statistical SC2 criterion No LEO crossing within 100 years with a probability of pSC2 Title Ihe SC2 criterion is compliant if the C2 criterion is compliant with a probability of pSC2 Method of use SC2 1s applicable when nominal non dispersed orbit does not cross Region A 5 2 is equal
58. ation made of the daily solar flux sfu The AP coefficients are not defined in this file and then are set by default to 15 with a user defined constant solar flux sfu and geomagnetic index Ap 14 and 15 The initial state the nature of the initial orbital parameters mean or osculating see Orbital elements 6 Be careful when SRP is active nature conversion relies on S M ratio and reflectivity coefficient and when Sun or Moon perturbation 1s active it relies on the initial date he type of the initial orbital parameters see SOrbital elements 17 he frame in which the initial orbit is expressed see 18 he orbit parameters the calendar date of the initial orbit see S Time scales 79 he six parameters describing the orbit 20 to 25 Be careful parameters are automatically rounded to 12 digits and angles are restricted to interval 0 360 when entered by user The output ephemeris step defined as a number of integration steps that will be used for plots and output ephemeris file saving 26 When the software runs in iterative mode 1 the following parameters shall be defined The GEO region exclusion duration 2 The targetted eccentricity ex and ey see SIterative mode for LEO and GEO orbits 3 and 4 The minimal perigee altitude above the GEO altitude that must not be reached during the exclusion duration 5 example GEO dn File Tools 7
59. ce coherence __ Wc Element 1 1 1 1 Physics coherence coherence Standard sae caer O inf Physics coherence es Delta 0 XO 0 Physicscoherence coherence Mat numer oi Physics coherence executions Number of TU MAX number of Physics coherence processors executions If value isn t in the recommended interval the degraded extrapolating starts a message appears in the logbook to describe the warning General warning limits Params Interval Explanation Maximum computed points 0 146 200 by extrapolation Computer Coherence The reflectivity Bay coefficient should range from to 2 Reflectivity coefficient 0 58 4 U 2 68 4 111 5 Inclination 10 121 5 See below 179 5 50 km inf Model not validated for lower altitudes Model not validated Integration step 10 24h for larger integration steps Warning limits for inclination has the following source a computation near the critical inclination value may require to increase the development of the Earth potential for a better accuracy Warning limits for LEO simulations Params Interval Explanation Perigee altitude LEO validation Type 0 domain JP 2 200 km Apogee altitude Zp 2 200 km LEO validation Type 0 domain Initial Eccentici 0 0 125 omain 0 4
60. cessings The default value is TT MINUS UTI TT UTI TT TAD TAI UTC UTC 32 184 35 0 67 184 seconds Values at 01 09 2012 TT MINUS UT is used to compute the date in TT used in Lieske and al theory of precession to compute frame conversion EME2000 Mean Of Date to compute the frame conversion ICRF TIRF and also to compute the Sun and Moon positions using the simplified Meeus amp Brown theory TT MINUS UTI default value can be modified by the user through the Advanced Parameters panel The date of orbital parameters are expressed in the Universal Time UTI NB a 0 UTC UTI value can be generally considered The real value is significant especially in precise frame conversions from or to TIRF or when importing TLE 5 3 7 CNES Julian day Opposite to classical Julian days JD witch are counted from January Ist of 4713 BC at midday CNES 1950 Julian days JD1950 start is January Ist of 1950 AC at midnight JD1950 JD 2 433282 5 5 3 8 Modified Julian Day MJD The Modified Julian Day 1s defined as MJD JD 2400000 5 The MJD 1s a downward rounded JD Julian Date that would start on 00 00 November 17 1858 In STELA MJD are given as fractional days MJD MJDN SEC Where MJDN is the integer part of the Modified Julian Day and SEC its decimal part in seconds between 0 midnight and 86400 next day 5 4 Propagation model 5 4 1 Mean orbit Aimed at long term simulations STELA
61. ctivity bad solar activity inputs file or non physical orbital parameters The conversion of type bulletin nature or The expected conversion has failed bulletin frame has failed due to some incoherent input parameters Nature bulletin conversion has failed due to Osculating to Mean bulletin conversion non convergence of the algorithm algorithm has not converged Unfortunately there 1s nothing that can be done to overcome it Impossible to plot graph you don t have enough Plotting data requires memory you don t have memory Please decrease the simulation duration The ephemeris file could not be written Ephemeris file writing failed possibly due to hardware malfunction or limited disk capacity Memory is full and ephemeris cannot be stored Out of memory error Please reduce the any more When transition matrix flag 1s extrapolation duration or increase the time step activated for very long simulations the required memory can be over 500MB The propagation has failed possibly due to Extrapolation failed wrong internal parameters 1f changed or variable solar activity out of file bounds The iterative mode has failed due to the failure Iteration failed of one propagation Inclination very close to critical inclination the computation keeps the eccentricity vector defined by the user in the initial state When inclination is very close to critical inclination eccentricity vector 15 not adjusted Lifetime
62. d GTO model have been developed and tuned for an efficient propagation of LEO GEO and GTO orbit types However since STELA V2 5 2013 only the so called dynamical model is used through the GUI Then whatever simulation you choose LEO GEO GTO the GTO dynamical model will be used to propagate the orbit since it is the most generic complete and precise one It is indeed more generic because it is able to deal with eccentric orbits LEO and GEO models are written for quasi circular orbits As a counterpart the computations are more time consuming It can be used with different settings for the dynamics depending on the orbit type for example a 4x4 earth gravity model for GEO propagation or a 7x0 earth gravity model for most of the LEO propagations and a 7x7 earth gravity model for the GTO propagations STELA default settings for these orbit types Note that the dedicated LEO and GEO dynamical models remain in the STELA software and can be used through the library mode 5 1 Frames 5 1 1 Schematic frames transformation STELA Frame Conventions Date Date of orbital parameters EME 2000 IERS 2070 Constant Frame Blas IERS 20 Lieske Precession Garr Mutation Celestial MOD TEME Mean Sraenwhich Wean Sidera Time Sideral Time PEF rotating TIRF rotating Terrestrial Frozen at Epoch Reference longitude Jon ref Orbital Frames Frames used d
63. d by the user in the initial state 0 1 sin ira 5 5 8 2 Iterative research of a specific GEO Orbit STELA software is able to work in a GEO Iterative mode This computation mode allows the user to search an initial orbit that will stay above a minimal altitude during a given exclusion time both defined by the user in the GUI The degree of freedom is the initial semi major axis The initial other parameters ex ey 1x 1y longitude remain as defined by the user in the GUI STELA software compute the osculating geocentric perigee altitude at each integration step to evaluate whether it remains above the minimal altitude or not Note that The default targeted minimal altitude for iterative mode is 200 h km above the GEO altitude 35 786 km h is a margin to be considered due to the fact that the modelisation is a simplified modelisation vs reference numerical propagators Its value 1s given in Physical parameters The default exclusion time for iterative mode is 100 years which is compliant with the GEO region protected criterion At the end of an iteration STELA software displays the current altitude relative to GEO it is the minimal altitude above the GEO altitude 35 786km that have been reached by the current orbit The precision on the expected minimal altitude can be given by the user in the GUI through the Algorithm convergence threshold field in the advanced parameters view Default value is 1 km
64. dimensions blue segments set to 1 To customize each shape the user may ranslate the shape by repositionning the reference point position vector field rotate the shape by changing no need to keep the vector unitary the coordinates of the shape bound orientation vector orientation vector field the rotation which transforms the default orientation vector 2 into the user defined t is applied to the whole shape the position of the orientation vector remains unchanged with respect to the shape The characteristics of this rotation are e AX S orontis GEZA 0 arbitrary axis 1s chosen and if t applied e angle arcos Z v rotate the shape on the orientation vector by a given angle angle field resize the shape by filling in the dimensions fields with its actual dimensions The current shape is outlined in red in a 2 D view showing the three orthogonal view Y X Y Z X Z The computation of the Mean area can be done considering several orientation model Random tumbling the spacecraft attitude 1s variable and has no particular direction e Spin the spacecraft has a spin movement along one particular axis case of gravity gradient for example The user can define the rotation axis vector the direction of observation Fixed orientation the user simply defines the direction of observation the mean area will be the cross sectional area perpendicular
65. e GEO crossing X between 1 and 100 years applicsnle 4 GEO crossing X within LPO years 1 i i 1 d zs o z2234 ei E a EEL k For LEO orbits with specific inclination the following message may appear Due to resonance phenomena extrapolation results may be very sensitive to initial parameters See User Manual See paragraph Control of validity domain for more details 3 9 2 Limitations of the GTO single extrapolation mode For GTO orbits the extrapolation results may be very sensitive to the initial conditions or to the parameters of models tiny modification of the initial conditions or the computation parameters S m ratio drag and SRP coefficients solar activity might end up with significant different results The following plot shows an example of the evolution of the semi major axis of a GTO orbit and the difference in reentry dates for the same initial orbit only slightly changing the S m ratio SMA evolution sensitivity to slight S m variation 26000 24000 22000 20000 18000 16000 SMA km 14000 12000 10000 2000 6000 1 20 30 40 50 90 time years It is clear that a modification of less than one percent of one parameter of the initial configuration can change the reentry date by more than 10 years This sensitive behaviour is due to the sun moon perturbation and to resonance phenomena In order to get a reliable statu
66. e open the index html filed stemming from the unzipped JAR STELA Javadoc contains the information about STELA code hence names and exact function of the methods and classes you wish to re use in your project For more information about Javadoc please visit http docs oracle com javase 1 3 docs tooldocs win32 javadoc html Here is a brief description of STELA different modules stela batch Contains the code of the batch mode commands inputs and help sections stela commons Basics classes interfaces abstract classes for example only stela commons would be necessary to create a new atmospheric model errors messages and dates management Contains the generated code as well Earth potential stela eapp Classes dealing with the GUI view and controller stela elib Classes of STELA physical model atmospheric model differential equations various forces LOS criteria It is STELA main component It also contains Monte Carlo simulations and probabilities computation stela etoo Entry point of all simulations stela processing Basic routines but non abstract hence implemented unlike stela commons type nature and frame conversions Gauss equations operations on vectors etc stela slib Only contains classes about the mean area tool stela tle Only contains classes about the Two Line Element tool stela validation Validation component
67. e Coordinated Universal Time UTC and TAI have the same rate But some adjustments are regularly made so that the UTI deviates from UTC no more than 0 9 seconds IUTC UTII 0 9 seconds UTC TAI number of leap seconds 5 3 4 TT The Terrestrial Dynamic Time TT or TDT is a theoretical time which is tied to TAI by a constant offset of 32 184 seconds Initially the TT was used to replace the old Ephemeris Time model at the beginning of 1984 Thus the Terrestrial Dynamic Time runs parallel to UTC TT TAI 32 184 seconds UTC number of leap seconds 32 184 seconds 5 3 5 The Barycentric Dynamic Time TDB is the same as the Terrestrial Dynamic Time TT except that the TDB takes into account the relativistic corrections due to the Earth s motion in the gravitational potential of the solar system These corrections amount to as much as about 1 6 milliseconds and are periodic with an average of zero The dominant terms in these corrections have annual and semi annual periods Planetary motions are now computed using Barycentric Dynamic Time TDB which is more uniform than TT 5 3 6 Assumptions for STELA Since STELA runs long term extrapolations in the future and because future leaps on UTC can not be predicted the STELA software generates propagations assuming that The Barycentric Dynamic Time and the Terrestrial Dynamic Time are approximately equal TT TDB The difference TT UTI remains constant in STELA pro
68. e delay TT UT1 used in frame transformations see Time scales and when importing TLE 3 8 4 Statistics Parameters The statistics view contains all parameters related to the statistical mode STELA example CGTO sim xm Fila Took 7 Ey i i bal ETO 5 Run statistics lew a t C cn Extrapolation Parameters Cere 1 7 Automatic Stop 14 E Ensbie multipracessing z proczesses on 4 processors Advances rat stical Mode Hultipracessing Saad 2 1494779018253900150 Generara Pefecting Ares Rasuks 16 Cispersion Mo disparsian Sumerary Date 7 Ca puts 3 Diparsion dispersion Caefficiant 17 Digperske Liiber m Mean value 15 Figur 4 Dispersion LinPorrm Datta 20 valua 7300 0000 Drag Area DiepemEm Be dsperson kin z1 00 00 00 18 a binis 000 Mass 5 Dispersion Hn dispersicn Drag caoslficieani 19 Dispersion Livform value Ur 34 a0 l20 Solar Cisparsian Randem Orbit Parameters 7 Cisparsion Matric Correlation B Disparsicn Gaussian 9 Nature Mean pararecers E eed area 11 Frame Terrestrial Frozen at Epacl 2 a L 0 99 0 0 1 0 08 1 0 1 a CE i L 8 o 0 1 0 1 0 0 L a 1 u o 0 1 al The Statistics view contains ee ui 10 11 12 the stop mode automatic manual
69. e entry and exit E of the eclipse Earths shadow 15 out considered as a cylinder Determination of M quadrature points evenly spaced in eccentric anomaly between and E n lighted up part of the orbit Computation of the solar radiation pressure perturbation in the inertial frame Expression of this perturbation at each quadrature point in the TNW orbital frame Derivatives computation with Gauss equations e Simpson quadrature alike the one for the atmospheric drag 5 5 6 Zero inclination singularity The type of orbital parameters used in STELA LEO semi analytic theory leads to a singularity when 120 and 1 180 Then the mean inclination value 1s forced to 0 5 when 1 0 5 and to 179 5 when 1 gt 179 5 5 6 Algorithm features for GEO model 5 6 1 Earth potential The derivatives of mean parameters due to Earth potential perturbation are analytically expressed through Poison series using a complete four by four model zonal and tesserals for the Earth potential development 5 6 2 Lunisolar potential The lunisolar potential is modeled as for LEO orbits 5 6 3 The atmospheric drag force The atmospheric drag force is supposed to be negligible for GEO orbits propagation 5 6 4 Solar radiation pressure The solar radiation pressure force is defined as follows p c d E i Where Cris the reflectivity coefficient PO 15 the solar constant at 1 UA see P
70. e of the TLE except for the semi major axis a that has to be deduced from the mean motion The following equations are used to convert the Kozai based mean motion n standard for TLE orbital products to a Brouwer based mean motion n see Annex B in Ref 13 a 243 7 5 3 J Rg 35cos i 1 4 2 The applicable constants are those of WGS 72 Ref 10 398600 8 km s2 Earth radius Rg 6378 135 km The proposed ballistic coefficient m A Cd is deduced from D Vallado Fundamentals of Astrodynamics and Applications 2 4 p114 et 115 pos 5t 2 With 2 461 10 kg m7 Ey Then PH 1 KE 12741621 B 6 Glossary CCSDS Consultative Committee for Space Data System CIRF Celestial Intermediate Reference Frame EME2000 Earth Mean Equator and Equinox at epoch J2000 GEO Geostationary Earth Orbit GTO Geostationary Transfer Orbit GUI Graphical User Interface ICRF International Celestial Reference Frame IERS International Earth Rotation Service LEO Low Earth Orbit MOD Mean Equator and Equinox of Date MTCO Monte Carlo SRP Solar Radiation Pressure TAI International Atomic Time TBC To Be Confirmed TBD To Be Defined TEME True Equator Mean Equinox frame TFE Terrestrial Frozen at Epoch frame TIRF Terrestrial Intermediate Reference Frame TT Terrestrial Time UTI Universal Time UTC Coordinated Universal Time
71. e right part describes the final state computed from the adjusted initial orbit state he nature type and frame are reminded to the user he orbit parameters date position and velocity A button 1s provided to copy the adjusted initial state to general parameters view in order to perform a single extrapolation to check the compliance with protected region criteria Iteration report summary Final min perigee altkude 205 57487055 km Number ofiterations Adjusted initial state Mabching final state Nature Fean parameters Nature Mean parameters Equinoctial Type Equinactial Frame Mean celestial of date Frame Mean celestial of date Orb parameters Orbit parameters pae 1998 01 01TOD 00 00 000Z cal Due 20988 01 01100 00 00 0002 a _ 4290530905238 o 42405 05291885 km ex o ex 0000025186 ey fo e amp ARAi sesz v wf 06039332 wom 8144 deg wim 255 86434327 deg Copy adjusted initial state to general parameters view 3 9 5 Summary for GTO statistics mode When a Statistics simulation starts STELA software automatically switches to the Results Summary view that is divided in two topics The left part display the four graphs The 95 confidence interval and observed probability vs execution number for SC1 or SC2 criterion depending on applicable criterion The lifetime cumulative distribution function for SCI criter
72. ean lt gt ie bored osculating JP YP YP Atmospheric drag force type 1 type 1 type 0 type 0 type 0 type 1 type 1 type 1 Input output orbit parameters type 2 type 2 type 2 type 8 type 8 type 8 Note that the type 6 parameters have a singularity for null inclination so has the LEO dynamic model Similarly the type 8 parameters have a singularity for an inclination of 180 so has the GTO dynamic model Note since STELA V2 5 2013 only the GTO dynamical model is used through the GUI Whatever simulation you choose LEO GEO GTO the GTO dynamical model will be used to propagate the orbit since it is the most generic complete and precise one The LEO and GEO dynamical models remain in the STELA software and can be used through the library mode 5 3 Time scales 5 3 1 TAI The International Atomic Time is a time coordinate based on the readings of approximately 150 atomic clocks around the world each corrected for known environmental and relativistic effects A few clocks such as the cesium clock ensemble at the U S Naval Observatory carry considerable weight in the TAI 5 3 2 UTI The Universal Time UTI is a measure of the actual rotation of the Earth It is the observed rotation of the Earth with respect to the mean sun corrected for the observer s longitude with respect to the Greenwich Meridian and for the observer s small shift in longitude due to polar motion 5 3 3 UTC By definition th
73. ec corresponds to the last date of the orbit propagation Ar is the reflectivity area and Cr is the reflectivity coefficient Ad is the drag area Cd is the drag coefficient or the multiplying factor of the variable Cd file F10 7 and Ap are the solar activity coefficients or the multiplying factors of the variable solar activity file 5 1 15 the observed probability of SCi criterion for Nb extrapolations number of OK Nb 1 if the criterion is not applicable pl SCi and p2 SCi are the Wilson confidence interval bounds for Nb extrapolations 1 if the criterion is not applicable If random cycles IstDay is the day number in the first solar cycle and SeqCycles is an integer that gives the statistical solar cycles sequence ijkImn corresponds to cycle 1 then cycle then cycle k then cycle m then cycle n 1 J k m n from 1 to 9 and for 10 e Cl C2 C3 C4 give the status of C1 C2 and C4 criteria not OK 1 2 not computable 3 2 not applicable STELA STAT COMMENT Generated by STELA 2 3 1 CREATION DATE 2009 07 29T00 00 00 000 ORIGINATOR U N Owen META START OBJECT NAME EXAMPLE space object OBJECT ID EXAMPLE space object CENTER NAME EARTH REF FRAME CELESTIAL MEAN OF DATE TIME SYSTEM UTI META STOP COMMENT Nature MEAN COMMENT Type Perigee Apogee COMMENT Format Nb MJD sec Zp Za i raan w M Mass Ad Cd IstDay SeqCycle
74. ed The integrator is numerical and is based by default on a sixth order Runge Kutta method the classical fourth order Runge Kutta method can be chosen instead in the advanced parameters file located in the configuration folder The combination of those two methods explains why the propagator is said to be semi analytic The type of perturbations taken into account in the propagation depends on the kind of model LEO GEO GTO See the corresponding paragraphs for more informations Perturbation LEO model GEO model GTO model J2 J22 J3 J4 and zonals Complete o 9 Complete 4x4 Model 15 15 Model 8 including J22 eccentricity and RAAN Solar and Yes Yes Yes Lunar Yes Yes Oblate Earth Oblate Earth Atmospheric Rotating No Rotating drag Atmosphere Atmosphere Simpson Simpson Quadrature Quadrature Solar Yes Yes Simpson Yes Simpson SRP Quadrature Quadrature Yes The Earths shadow Earth s Yes The is a cylinder and the Yes The shadow for Earths shadow space objects orbitis Earths shadow SRP is a cylinder supposed to be is a cylinder quasi circular Numerical Sixth order Sixth order Integrator Runge Kutta A Kutt Runge Kutta Note since STELA V2 5 2013 only the GTO dynamical model is used through the GUI Whatever simulation you choose LEO GEO GTO the GTO dynamical model will be used to propagate the orbit since it i
75. eration report summary Effective 2473672575 years Number of kerations 8 Adjusted initial state Matching Final state Nature Mean parameters Nature Mean parameters Type Keplerian Type Keplerian Frame Mean celestial of date Frame Mean celestial of date Orbi parameters Orbit parameters Date 2009 07 29T00 00 00 000F cal Date 2034 04 24 Te OS 16 4912 cal 4 7056 44487348 km 5477 22724513 km e entes e DODDOS i 59 deg i f 98 52529383 o m5 deg 22048577 deg a f e OTSR deg M 0 deg 10289243298 deg Copy adjusted initial stare to general parameters view 3 9 4 Summary for iterative mode in GEO When a simulation in iterative mode ends STELA software automatically switches to the Results Summary view that 1s divided in three topics The top part displays the minimal altitude minus the GEO radius see Protected Region criteria for computation method of C4 criterion reached by the propagated adjusted initial orbit This altitude 1s equal or bigger with respect to the algorithm convergence threshold than the minimal altitude given by the user The number of iterations needed to adjust the initial state 1s also indicated The left part describes the adjusted initial orbit state as followed he nature type and frame are reminded to the user he orbit parameters date position and velocity Th
76. erefore the atmospheric drag force can be easily expressed in the Celestial Mean Of Date Frame at any date as F tpt yy om where Cd is the drag coefficient e S is the cross sectional area representing the spacecraft is the atmosphere density e is the satellite velocity with regard to the rotating Earth m is the satellite total mass 5 5 3 1 Drag Coefficient The drag coefficient can be defined as constant with a value chosen by the user variable vs altitude being read in the file stela_drag_coefficient see Appendix A 1 computed by the Cook formula The file of n Cd values is used in the following way h being the geodesic spacecraft altitude and 1 being a line numbering the file 1 lt 1 lt if h i lt h lt h i 1 then Cd h Cd h i e if h gt h n then Cd h Cd h n e if h lt h 1 then Cd h h 1 Cook formulae The C is computed in line with the mean cross sectional area hypothesis It is based on the value of the drag coefficient of a plate in tumbling mode SRef 3 amp 5 CQ eub dao au i 252 1 i e xp 62 al T 1 25 1 exp 52 Cr ll 411 a st 1 2 s 1 erf sz i 24 s ic Af 2 Wik Hu cu MO 2 with v and T v Af 2 erf x qlee ae 0 Cy absorption coefficient C re emission coefficient V plate velocity vs atmosphere T temperature
77. erence longitude The user can choose this frame in order to define the initial orbit parameters Note that when using this frame in the statistics mode and dispersing the initial date the difference frozen epoch initial date 1s kept 5 1 7 EME2000 The Earth Mean Equator and Equinox at epoch J2000 frame is very close to ICRF the difference is about 0 02 arc seconds Indeed the transformation is the following A ICRF BX FMF 2000 MN ICRF BV EME2000 With B A YR e SUL y 529z5 gaal Aliula 2 0 041775 94301 406 1 sin in 0 Rye 0 R t 1 0 cos nd 0 sin9 cos ini 0 coag 9 Su E i The user can choose this frame in order to define the initial orbit parameters 5 1 8 Transformations from ICRF to MOD The transformation from ICRF to the Celestial Mean of Date Frame is a two step transformation 1 From ICRF to EME2000 using a constant frame bias see above 2 From EME2000 to MOD using Lieske precession theory 5 1 9 Local orbital frame T N W The local orbital frame O T N W is defined with O the spacecraft center of mass T the axis along the track parallel to the spacecraft velocity W the axis along the orbit kinetic momentum N the axis completing the direct orthonormal trihedron This frame is used in STELA software to compute the atmospheric drag force 5 1 10 The True Equator Mean Equinox fr
78. essed with the J2 and J2 zonal contributions developed in Poisson series he J3 zonal contribution developed in Poisson series he J4 zonal contribution also developed in Poisson series some complementary terms in order to take into account the effects of the other zonal coefficients up to J15 on eccentricity and right ascension of ascending node These effects are significant for orbits close to the critical inclination about 63 and 117 and for some LEO inclined between 40 80 and 110 130 At these particular inclinations resonance effects due to various perturbation sources solar radiation pressure third body perturbation and drag in particular have been shown to have significant effects on LEO lifetime in some particular cases SRef 11 5 5 2 Lunisolar potential The lunisolar potential computation is based on the knowledge of the Sun and Moon positions that are computed using a simplified Meeus and Brown model The Meeus and Brown model used in STELA has a 6 terms development in longitude 4 terms development in latitude and 4 terms development in Earth Third body distance Then like for the Earth potential the lunisolar perturbation 1s developed in Poisson series 5 5 3 Atmospheric drag force In Stela software the atmosphere 1s supposed to rotate at the same velocity as the Earth rotating atmosphere The oblate shape of the Earth is taken into account At LEO altitudes no wind is considered Th
79. hich may be defined 9 by an input file stela drag coefficient see Appendix A 1 as a constant value given in field 70 from Cook formula The atmospheric drag settings he theoretical atmospheric model NRLMSISE 00 11 the solar activity it is an entry for the atmospheric model The solar activity can be defined 72 with a solar activity file stela solar activity report to Appendix A 2 that contains daily information made of the daily solar flux sfu the mean solar flux sfu and the geomagnetic 3 Hour index Ap eight values defined for 24 hours with a solar activity file from DAS solarflux table txt report to Appendix A 2 that contains daily information made of the daily solar flux sfu The Ap index are not defined in this file and then are set by default to 15 value tunable in the stela advanced parameters file with a user defined constant solar flux sfu and geomagnetic index Ap 13 and 14 The statistics mode switch 15 The maximum number of runs in statistics mode 16 The initial state he nature of the initial orbital parameters mean or osculating see Orbital elements 17 he type of the initial orbital parameters see SOrbital elements 76 he frame in which the initial orbit is expressed see 19 he orbit parameters the calendar date of the initial orbit see S Time scales 20 the six parameters describing the orbit 27 to 26
80. hysical parameter values e S is the cross sectional area representing the spacecraft d0 1 UA see Physical parameter values dis the sun spacecraft distance u is the sun spacecraft vector In STELA software The SRP perturbation is seen as a potential thanks to the term in 1 d so the derivatives of mean parameters due to SRP perturbation are also analytically expressed through Poisson series The albedo of the Earth is not taken into account The eclipse due to Earth s shadow is taken into account through a multiplicative coefficient lighted part of the orbit applied to the perturbation The reflectivity coefficient is a constant value given by the user at the GUI It should be greater than 1 absorbent surface and less than 2 reflecting surface e S is the cross sectional area perpendicular to the sun spacecraft direction The user can use the STELA Mean Surface Area tool see Tools to compute it The sun spacecraft vector is compute using the simplified Meus amp Brown model 5 7 Algorithm features for GTO model Note that the following describes the algorithms for a single extrapolation The results given by the single extrapolations are then used to perform the statistical analysis via Monte Carlo methods for GTO see 5 8 The GTO model is the most generic one usable for LEO GEO and GTO orbits because it is able to deal with eccentric orbits LEO and GEO models are written for quasi circular orbi
81. ial Applicable if the initial orbit does orbit does C2 criterion Ao not belong to protected not belong to protected applicable LEO region LEO region a Not C4 criterion Not applicable Applicable Applicable NB Applicable means that the criteria is checked by the software When using the statistical mode the termination criteria and Protected LEO amp GEO Regions criteria applicability depends on initial nominal orbit parameters as well The following table summarizes the conditions of use for these criteria in STELA software GTO Statistical Mode lt Statistical Mode SC3 criterion criterion Applicable SCA criterion Applicable 4 4 Protected regions criteria status At the end of the simulation the STELA software checks the compliance with the four Protected LEO amp GEO Regions criteria Five status are possible and depend on initial parameters and simulation results Not applicable this status is written in the output results when the current Protected Region criterion 1s not applicable report to 4 3 Not computable this status is written in the output results when the current Protected Region criterion is fulfilled during the simulation duration but when the simulation duration is too short to allow any conclusion or when the number of simulations is too short for a statistical analysis or when the statistical analysis was not conclusive report to 4 2 9
82. ial orbit with a given orbit lifetime see SIterative mode for LEO and GEO orbits The simulation information the author name 2 comments 3 he simulation duration in years 4 The spacecraft main characteristics its name 5 its total mass kg 6 its mean cross sectional reflecting area m 7 its reflectivity coefficient S its mean cross sectional drag area m 9 its drag coefficient Cd which may be defined 70 by an input file stela drag coefficient see Appendix as a constant value given in field 77 from Cook formula The atmospheric drag settings he theoretical atmospheric model NRLMSISE 00 12 the solar activity it is an entry for the atmospheric model The solar activity can be defined 13 with a solar activity file stela solar activity report to Appendix A 2 that contains daily information made of the daily solar flux sfu the mean solar flux sfu and the geomagnetic 3 Hour index Ap eight values defined for 24 hours with a solar activity file from DAS solarflux table txt report to Appendix A 2 that contains daily information made of the daily solar flux sfu The Ap index are not defined in this file and then are set by default to 15 value tunable in the stela advanced parameters file with a mean constant normalized solar activity computed from the ballistic coefficient of the spacecraft and the apoapsis altitude of the
83. in order to define the initial orbit parameters 5 1 4 CIRF The CIRF Celestial Intermediate Reference Frame 1s defined by the IERS conventions It is deduced from the ICRF by taking into account the precession nutation model The user can choose this frame in order to define the initial orbit parameters 5 1 5 Rotating TIRF The TIRF Terrestrial Intermediate Reference Frame if defined by the IERS conventions as follows the Earth mass center The z axis aligned with the true Earth s spin axis at date and north oriented it is aligned with the Celestial Intermediate Pole x y true equator of date The x axis aligned with the intersection between true equator and Greenwich meridian The y axis completing the direct orthonormal trihedron The TIRF is deduced from the CIRF by a rotation of angle ERA Earth Rotation Angle depending on UTI around z axis It can also be deduced from the ITRF International Terrestrial Reference Frame by rotations describing the polar motion The user can choose this frame in order to define the initial orbit parameters 5 1 6 Terrestrial Frozen at Epoch The Terrestrial Frozen at Epoch frame TFE is a TIRF like frame but frozen at a reference date and whose X axis 15 oriented along a reference longitude It can be deduced from the CIRF at reference date by two consecutive rotations along the z axis First rotation of angle ERA e Second rotation of angle ref
84. ion Installation of STELA Version 1 2 0 hd ade with IzP ack http izpack org 3 n order to go through the next step the user must accept the terms of the license agreement and click on the button Next d IzPack Installation of STELA Please read the Following license agreement carefully Please read attentively the provisions of this Licence before downloading the SOFTWARE The use of the SOFTWARE by the Licensee means the latter has agreed with the provisions of this Licence The SOFTWARE as described thereof property of the CHES and named STELA has been registered at the Agence pour la Protection des Programmes 119 rue de Flandres 75019 Paris on January 2011 the Sth under the number 101101 On the SOFTWARE CNES concedes to the Licensee who can be a physical or a moral person a non exclusive free Licence LANGUAGE OF THE LICENCE AND APPLICABLE LAW The Licence is established in French and English In the case of a dispute the French version is the one that prevails This Licence is governed by French law If any dispute should arise litigation Shall be brought before the applicable courte I accept the terms of this license agreement hada with IzPack http izpack arg 4 Installation path selection a new window appears with a browser The default directory already appears in the installation path The Browse button enables the user to choose another location in which
85. ion The 95 confidence interval and observed probability vs execution number for SC3 criterion The 95 confidence interval and observed probability vs execution number for SC4 criterion The right part reports the compliance with the four statistical criteria see Assessing Compliance with LEO GEO amp GTO Protected Region criteria For each criterion the value of the lower bound 1f compliant upper bound if not compliant of Wilson confidence interval is displayed This is the probability value used to check the compliance File Tools 1 53795 bd GTO S Rum statistics STELA example _ GTO Sim aml cnes Extrapolation 7 Parameters General Advanced Statistics 7 Results outputs Report summary Graphs Er d Ceandidierere imrmrwu al X elewerved nemisaiziliiy 7 EErEE ECH mre JD mlewerved pirislzaiziliiy io zd 54 c comhidanmces interme amp nrobabiliry Compliance ortara Compliant 01 Lifetime under 25 years oF with a probability of 0 9 Prababdity gt 0 908 for ns 45 hot applicable SCA Mo LEO crossing x within 100 years with a probability of 0 9 Compliant 503 Mo GEO crossing of Probabdity gt 0 908 for nz 4B between 1 and 10
86. ion is said not computable as well but increasing the number of single extrapolations will not be useful to solve the problem as the results displayed are likely to be among the 5 of cases out of the confidence interval In this very case there is no other choice but to replay the statistical analysis changing the initial seed The results displayed by Stela can be summarized in the following table Status Condition at current n Display D Dain and an value with n pin lt n n exists Probability pln min Compliant such As pin 5 1 for n n and min p2 n gt pSCi min and Not an value with Nip lt D HN exists Probability lt p2 n compliant such as p2 n lt 5 1 for n n and max pl n n pSCi min Probability gt p1 n for n n Probability p2 n for n n None of the two above conditions 4 3 Criteria applicability The termination criteria and Protected LEO amp GEO Regions criteria applicability depends on initial orbit parameters The following table summarizes the conditions of use for these criteria in STELA software GEO Termination ERI ems Applicable Applicable Termination Applicable Applicable Applicable if the initial Applicable if the initial orbit orbit criterion belongs to protected belongs to protected LEO region LEO region Applicable if the init
87. istical analysis The user has the possibility to choose between six plots of results Lifetime vs execution number Lifetime distribution histogram Lifetime cumulative distribution function The 95 confidence interval and observed probability vs execution number for SC1 or SC2 depending on applicable criterion The 95 confidence interval and observed probability vs execution number for SC3 The 95 confidence interval and observed probability vs execution number for SC4 It is easy to change the axes or title names or to zoom in and out by making a right click on the new window 3 11 Tools 3 11 1 Compute Mean Area The user can select Tools in order to start the STELA tool Mean Area Computation The Mean Area Computation Tool allows the user to draw a simplify model of the Spacecraft and to compute the effective cross sectional area to be used in drag force or solar radiation pressure computation The cross sectional area unit is the square of the input unit area bool exemple E X 0 Crientation Parameters Adeanced parameters The spacecraft 15 modelled as a collection of shapes chosen from the following list e Sphere Rectangle Cuboid Triangle Truncated cone When created each shape is initially defined by see screenshot one reference point red cross set to 0 0 0 one shape bound orientation vector green vector set to the z vector 0 0 1 its
88. ity domain The validity domain for each kind of simulation LEO GEO GTO corresponds to the validation domain 5 11 1 STELA validation STELA results have been validated for a certain range of parameters To ensure that this range is respected parameters are tested at extrapolation start this control of validity domain is described in 5 11 2 STELA validation has consisted in a comparison with runs of CNES reference numerical propagators PSIMU and ZOOM including complete dynamical models of forces The STELA precision is about on a computed lifetime of 25 years and better than 2 km for the minimum and maximum altitudes for 100 years for LEO extrapolation The precision is better than 3 km for the minimum and maximum altitudes for 100 years GEO extrapolation For GTO extrapolations the precision is better than 10 km for the minimum and maximum altitudes for 100 years extrapolation except for orbits close to critical inclinations For lifetime computation the result of one run may not be very close to a numerical propagator result but statistical results based on several runs are This 1s due to resonance phenomena between earth gravity field and sun moon perturbation See Ref 6 and Ref 8 5 11 2 Control of validity domain Before extrapolating each parameter is controlled and compared to authorized and recommended warning limits intervals If value is out of the authorized interval the extrapolation doesn t start and a mess
89. ity with the French Space Operations Act requirements is evaluated through four Protected LEO amp GEO Regions criteria Violation of these criteria never arouses the end of simulation A simulation will stop only when one of the two termination criteria 1s reached The protected LEO amp GEO Regions are defined as follows Protected LEO region extends from the Earth surface up to the geocentric altitude of 2 000 km Protected GEO region is defined by boundaries in latitude 15 deg 15 deg and orbit radius 200 km with respect to the geocentric altitude of 35 786 km 445 S ZcEo AH min R gion B Region A il cnes DLE ILES AE 4 1 Termination criteria Two termination criteria can trigger the end of simulation for a single extrapolation Three termination criteria are specific to the statistical mode 4 1 1 Termination criterion TC1 Title Termination criterion the extrapolation duration defined by the user has been reached Method of use The simulation stops when the simulation duration 1s reached The simulation duration is an input parameter defined in the GUI 4 1 2 Termination criterion TC2 Title Termination criterion TC2 the space object has begun its atmospheric reentry Method of use The simulation stops as soon as the spacecraft enters the reentry atmosphere The reentry altitude 1s defined by the user with the help of GUI default value 1s 120 km for L
90. k Report 3 Rev2 2006 6753 Rev2 http www celestrack com publications AIA 2006 6753 Lamy et al Resonance Effects on lifetime of Low Earth Orbit Satellites 23rd ISSFD 2012 for high eccentricity orbits AAS AIAA 2013 Felix R Hoots History of analytical orbit modeling in the U S Space Surveillance System Journal of Guidance and Dynamics Vol 27 No 2 March April 2004 Appendix 1 Drag coefficient file The drag coefficient file allows to use a drag coefficient variable vs altitude An example of drag coefficient file 1s presented hereunder It contains the following values geodetic altitude km corresponding drag coefficient The file of n Cd values 15 used in the following way h being the geodesic spacecraft altitude and 1 being a line numbering the file 1 lt i lt n if h i lt h lt h i 1 then Cd h Cd h i e if h gt h n then Cd h Cd h n e if h lt h 1 then Cd h h 1 The user may use its own drag coefficient file by keeping the same format heading and column replacing the file s name in the stela_elib properties file configuration folder The drag coefficient values written in the stela drag coefficient default file are based on formula described in ref 5 based on ref 1 2 and 3 see References Atmospheric density and molecular composition computed by the empirical model NNLMSISE 00 The stela drag coefficient default file 1s the recommended one
91. low 3 2 1 Create a new simulation In order to create a new simulation the user can click on the specific button New LEO simulation New GEO simulation or New GTO simulation or select New in the File menu File Tools rises QU HS Go Or Exit Ctrl4Q 3 2 2 Save current simulation In order to save the current simulation the user can either click on the specific button Save simulation or save simulation as The user can also select options Save simulation or Save simulation as by the File menu File Tools Or New Open simulation STELA will save the following files see Output data and plots sim xml file that contains the simulation context sim txt file that contains the simulation context and synthesis file that contains the log outputs sim stat txt file that contains the statistical data and results 3 2 3 Open an existing simulation An existing simulation can be loaded by clicking on the specific button Open simulation or by selecting Open simulation by the File menu File Tools Or Open simulation Gave simulation Save simulation as Exit Ctrl Q 3 2 4 Run extrapolation The user can run an extrapolation by clicking on the button Run extrapolation File Tools a9 29 i y bal 4 Run extrapolation If no simulation has been opened or created the buttons Save simula
92. mplemented by Stela uses double precision and has a more precise Pi value than the reference one 5 5 3 4 Solar Activity The solar activity 1s defined by the geomagnetic activity Ap and the solar flux F10 7 The solar activity can be constant and tuned by the user variable vs time being read in the file stela solar activity see Appendix A 2 constant and computed by STELA as a normalized mean constant solar activity The mean constant solar activity is a constant value vs time depending on the ballistic coefficient of the spacecraft and on the initial apoapsis altitude of the orbit It has been tuned through a statistical approach to achieve a 25 years reentry duration as a mean value Considering a 25 years lifetime orbit computed with this value the real lifetime computed statistically with several past solar cycles and several initial dates in the first cycle would have a mean value of 25 years see SRef 5 and Appendix A 6 This constant equivalent solar activity is computed at the extrapolation beginning using the following formulas AP 15 F10 7 22014325 5 7 log Z m geomagnetic index e F10 7 solar flux in sfu S Cd m ballistic coefficient in m kg 7a geocentric mean apogee altitude of the initial orbit in km log neperian log NB if Cd has been chosen to be variable a constant Cd 2 2 value is used to compute the solar flux These solar activity coefficients are used in
93. mplified modelization wrt precise reference numerical propagators taking into account a full dynamical model Its values are given in Physical and key parameters Method of use The C2 criterion is checked at every integration step as follows The mean parameters are propagated till the periapsis mean anomaly set to zero Mean parameters at the periapsis are converted to Osculating parameters The geocentric periapsis altitude is hp a osc 1 e osc 6 378 km If the geocentric altitude is higher than 2 000 h km C2 margin C2 margin is a value larger than the effect of the short period terms on the orbit radius the spacecraft 15 considered as far enough from the LEO protected region There 15 nothing else to do the C2 criterion 1s not violated If the geocentric altitude is lower than 2 000 h km C2 margin the spacecraft is close to the LEO protected region and could possibly violate the C2 criterion therefore N C2 points are defined along the orbit evenly spaced in eccentric anomaly For each point the corresponding osculating point is computed The geocentric altitudes of these osculating points are compared to the protected area altitude If one of these geocentric altitudes is lower than 2 000 h km the C2 criterion is violated 4 2 3 C3 criterion No GEO crossing between 1 and 100 years Title Ihe C3 criterion is violated if the following conditions are fulfilled between the first and the
94. mulation until date 1 and with uniform or Gaussian dispersion from date 1 to date 2 After date 2 until the end of simulation a random set of solar cycles using the measured past solar cycles 15 generated The same approach 1s applicable to the geomagnetic indices by keeping consistency with the measured solar flux Date 1 can be for example the last date of measured data and Date 2 an expected end date of the current solar cycle The next figure 1s an example of a dispersed solar flux with this method F10 7 sfu E Correcting the dispersed values When dispersing values non physical values may appear These values are corrected following this method Flux F10 7 negative dispersed values are corrected to Ap negative dispersed values are corrected to Note that these corrections change the distribution form that cannot be considered as purely uniform or Gaussian The user may change the law parameters entered Standard deviation or Delta to end up with a real uniform or Gaussian law 5 9 4 Orbit Parameters Dispersion Orbit parameters can be dispersed either from a covariance matrix or a correlation matrix in a uniform or gaussian Way 5 9 4 1 Correlation and Covariance Matrices Considering y as X standard deviation and yy as X and Y covariance Covariance Matrix is given by Tye Oy lg Ug For clarity reasons a 3 by 3 matrix will be considered here instead of the 6 by 6
95. n f the initial orbit has a lifetime smaller than the expected one the iterative mode stops after the first extrapolation The precision on the expected lifetime can be given by the user in the GUI through the Algorithm convergence threshold field in the advanced parameters view Default value is 10 days A maximum simulation duration can be specified by the user in the GUI through the Max duration expected duration field in the advanced parameters view If the initial orbit is too high simulation will stop before the spacecraft has reached the low limit altitude it could save computation time Default value is 75 25 years so for an expected lifetime of 24 75 years STELA will propagate no longer than 100 years This value can be adjusted for instance for parametric studies STELA uses zero search function using Brent s method This function takes either the semi major axis or the perigee altitude as parameter depending on the chosen iterative mode and returns the difference between the actual and the expected lifetime f a resonance phenomenon between the J2 and the Solar Radiation Pressure occurs the function could be non monotonic As a consequence the algorithm could become non convergent n the vicinity of the critical inclination 1 the orbit is naturally frozen the frozen eccentricity e B cannot be computed and becomes irrelevant The eccentricity and the argument of Periapsis used are the one define
96. n WE rco O inf Physics coherence Drag Area Unif Pisae O inf Physics coherence G 0 inf Physics coherence Constant coefficient Cd one 0 inf Physics coherence dispersion Gaussian dispersion 95 0 inf Physics coherence Variable coefficient or Cook coefficient Cd Min Uniform 5 dispis 100 inf Physics coherence Max Uniform dispersion 0 100 inf Physics coherence Gaussian dispersion 96 Solar activity Variable Flux F10 7 Min Uniform EP disneision 9 100 inf Physics coherence O inf Physics coherence Uniform 100 inf Physics coherence dispersion Gaussian E dispersion 95 0 inf Physics coherence d 1 Min Uniform e d e 100 inf Physics coherence Max Uniform m 100 inf Physics coherence Gaussian a depen on 0 inf Physics coherence Constant Flux F10 7 Uniform NU Hot cni 0 inf Physics coherence Gaussian me dispersion shi 0 inf Physics coherence Ap Uniform dispersion 0 inf Physics coherence unitless Gaussian dispersion 0 inf Physics coherence unitless Dates Physics coherence dates Covariance matrix O inf Physics coherence inf inf inf inf Physics coheren
97. nes Elements into STELA orbital elements STELA can also be used in batch mode and as a java library STELA contact stela cnes fr 2 Getting Started 2 1 System Configuration The Oracle Sun Java Runtime Environment release 1 6 must be available in the system configuration in order to install and run STELA software STELA has been tested on x86 platforms with the following operating systems Windows XP 32 bits Linux 32 bits and Linux 64 bits SOLARIS 10 32 bits STELA has been less intensively tested with the following operating systems Windows 2000 32 bits Windows 7 64 bits The STELA software can run with JRE 32 bits or JRE 64 bits In all cases the platform and the Java Runtime Environment release should be consistent We recommend the use of Linux 64 bits for execution time On the same machine the computation time 1s about 5 lower with JRE 64 bits than with JRE 32 bits STELA performance can be affected by additional factors notably by the fact the JRE optimizes itself differently according to the platform it runs on The JRE automatically runs a client class JRE on these environments Windows 32 bits Linux and Solaris 32 bits with less than 2GB ram The JRE automatically runs a server class JRE on these environments Windows 64 bits Linux and Solaris 32 bits with more than 2GB ram Linux and Solaris 64 bits The server class JRE takes more time to start but 1s faster overall STELA 15 better suited for the
98. nt negative dispersed values are corrected to 0 Note that these corrections change the distribution form that cannot be considered as purely uniform or Gaussian anymore The user may change the law parameters entered Standard deviation or Delta to end up with a real strictly uniform or Gaussian law 5 9 3 Solar Activity Dispersion 5 9 3 1 Random Cycles Random cycles dispersion uses measured values from past solar cycles F10 7 and Ap to create a pseudo real random solar activity Measured values from 1954 are divided into 5 solar cycles these 5 cycles can be found in the configuration Solar activity cycles directory Each solar cycle has its own length duration A uniform law then generates numbers between 1 and 5 to create a solar cycle sequence long enough to match the extrapolation duration A uniform law generates a departure point in the first cycle Note that the user can add its own solar cycles files in the folder configuration Solar Activity Cycles Stela will recognize them given that the format is respected Number of files and length of these files are automatically detected by Stela 5 9 3 2 Uniform Gaussian dispersion Uniform and Gaussian dispersion of the Flux F10 7 and Ap follow the method described in 5 7 2 5 9 3 3 Mixed 3 date ranges When Mixed solar activity is selected the solar activity file is used to generate solar activity data with no dispersion from the beginning date of si
99. ode Title Statistical Termination criterion STC3 Statistical Analysis stopped by the user Method of use When clicking the Stop button in the progression Window Statistical Analysis will stop as soon as all the extrapolations still being computed are finished 4 2 Protected Region criteria 4 2 1 C1 criterion Lifetime 25 years Title Ihe C1 criterion is violated if the spacecraft lifetime end of simulation date beginning date exceeds 25 years Method of use It means that the Cl criterion is violated if the spacecraft object begins its reentry more than 25 years after the initial date The C1 criterion is computable only at the end of simulation and is combined with the termination criterion TC2 reentry in the atmosphere if TC2 has been reached and the effective simulation duration is less than 25 years C1 is fulfilled if TC2 has been reached and the effective simulation duration is more than 25 years Cl is violated if TC2 has not been reached and the simulation duration is more than 25 years Cl is violated if TC2 has not been reached and the simulation duration is less than 25 years 15 not computable 4 2 2 C2 criterion No LEO crossing within 100 years Title Ihe C2 criterion is violated if the geocentric periapsis altitude reaches an altitude lower than 2 000 h km during the first 100 extrapolation years h is a margin to be considered due to the fact that the modelization 1s a si
100. of the gas atmosphere D wal temperatum of the plate Wc perfect gas constante 8 314 472 Jmol t K M mean molar mass af ihe gas MO molar mass of oxygenatom 16 107 g A accomodation constant from 2 4 recommanded value from 3 610 4 V T and M are computed by STELA and k are tunable in the stela advanced parameters file not very sensitive the higher this value the higher the default value 300 K k sensitive the higher this constant the lower the default value 4 5 5 3 2 Mean area The mean area is the area S to be used for drag computation that 1s to say the cross sectional area perpendicular to the velocity direction The user can use the STELA Mean Surface Area tool see Tools to compute it This area 1s constant during the simulation 5 5 3 3 Atmospheric density The atmospheric density model uses in STELA is the empirical model NRLMSISE 00 NRL for US Naval Research Laboratory MSIS for Mass Spectrometer and Incoherent Scatter radar E for the model that extends from Earth ground through exosphere and 00 for the year of release The calculation of density need the knowledge of the date the satellite position the Sun position and data on solar and geomagnetic activities The NRLMSISE 00 model implemented in STELA 1s adapted from the C implementation available on the following Internet site http www brodo de english pub nrlmsise index html Note that the model i
101. on 0 20 GEO domain Reflecting area l GEO validation 0 0 1 mass domain Simulation 0 150 years GEO validation duration domain p 10 150 GEO validation y domain mode Min perigee altitude minus GEO validation GEO altitude only domain in iterative mode Algorithm convergence 1 NS im GEO validation threshold only in domain target altitude iterative mode Warning limits for GTO simulations Params Interval Explanation Mean area mass reflecting and 1050 1 drag areas 10 100 years validation domain uration Earth radius T Semi major axis 40 900km GTO validation domain Warning limits for Statistical Analysis GTO validation domain The nom parameters are the nominal values entered in the general tab Params Interval Explanation Mass Uniform dispersion kg L Gaussian 0 Masse nom No negative mass dispersion kg 3 Uniform l 0 Sr nom No negative area dispersion m Gauss it L0 5r nom 3 No negative area dispersion m Coefficient Cr 0 min l Uniform Cr nom Coefficient between 1 dispersion 2 Cr nom 1 x and 2 100 0 min l Gaussian Cr nom Coefficient between 1 dispersion 2 Cr nom 1 x and 2 100 3 Dag Area Uniform l 2 0
102. on Info Parameters General Author Default Ay dvanced This is a Results Summary Ephernaris Comments 3 6 2 General Parameters The following image displays a view of the General Parameters window These parameters are listed below Note that tooltips are available for the simulation parameters They appear as soon as the mouse is pointing the name of a parameter Warning special characters such as should not be added to text field as STELA will not be able to save load it n STELA example GEO sim xml m File Tools 9 Y 319 i lal GEO S Run extrapolatio gt X ae Ces bilis damos Simulation Info erative made Author NES 2 1 Enable iterative mode l ed GEO example simulation Initial state Outputs Mature Mean parameters 16 i ee equinoctial 17 Frarne Celestial Mean of Date 18 x 4 100 years Object Characteristics Name EXAMPLE Space Object 5 Orbit parameters Mass 6 2000 kg Reflecting Area z0 ma Date 19 1998 01 01T00 00 00 000 cal 7 Reflectivity coefficient 8 15 a 20 42404 km 9 Drag ares 20 e 21 0 00001 rDrag Coefficient Constant Vanable file Cook 10 ey 22 0 00001 cd 11 23 x 23 Atmosphenc Drag iy 24 n Atmospheric model NRLMSISE 00 12 u M 25 8144 deg Solar activity Constant user defined 13 Output Constant
103. parameters he plotted orbit parameters are given in the STELA integration frame that 1s the Celestial Mean of Date Frame see SFrames the plotted perigee and apogee altitude are computed for each ephemeris point as followed e ha 1 6 378 km hp a 1 e 6 378 km Keeping in mind that the Criteria are evaluated through the osculating parameters it explains that the crossing of a protected region or the reentry of the spacecraft may not be blindingly obvious by looking at the plots It is easy to change the axes or title names or to zoom in and out by making a right click on the new window 3 10 2 2 Ephemeris file The user can save the computed ephemeris points in a text file with the extension _eph txt The ephemeris file cannot be re loaded by STELA The ephemeris can be saved in two different formats a CCSDS compliant format called CCDDS OEM see ORBIT DATA MESSAGES CCSDS 502 0 B 2 a STELA format called STELA OEM which uses Modified Julian Days see 5 3 8 The ephemerides are expressed in the integration frame that 1s to say in the Celestial Mean of Date Frame but the user can choose The nature of the parameters Mean or Osculating The type of the parameters Cartesian Keplerian or Equinoctial A display of both ephemeris files is available in Appendix A 3 3 10 3 Statistical mode output view 3 10 3 1 Plots and complementary results This section displays general results about the simulation
104. parameters At each quadrature point using osculating parameters he atmospheric drag force is computed he atmospheric drag force 1s transformed in the T N W frame OE ane the derivatives of the osculating parameters dt computed using the drag force in the T N W frame and the Gauss formula Then the drag perturbation on mean parameters 1s computed using the Simpson quadrature Nquad MEC Vs 057 2 sc dB og _ 1 252 _ I ecosE d Bing at gm dt Je di Note the sum 1s done following the Simpson theory the first term using the eccentricity and the eccentric anomaly takes into account the repartition in true anomaly of the quadrature points 5 7 4 Solar radiation pressure The solar radiation pressure force is defined as follows For low Earth positions the solar radiation pressure may have a significant influence on the long term orbit evolution for particular orbits that lead to a phasing between the J2 drift effect and the SRP effect resonance d i Sa C P 54 T R d Where The albedo of the Earth is not taken into account Cris the reflectivity coefficient PO 15 the solar constant at 1 UA see Physical parameter values e S is the reflecting area representing the spacecraft d0 1 UA see Physical parameter values dis the sun spacecraft distance u is the sun spacecraft vector The reflectivity coefficient is a constant value given by the u
105. rbit STELA software is able to work in a LEO Iterative mode This computation mode allows the user to determine an initial orbit that will have an expected lifetime given by the user in the GUI Two iteration modes can be chosen The eccentric orbit computation the STELA software will look for an initial orbit with the same apoapsis altitude than the one defined by the user in the GUI The degree of freedom is the periapsis altitude Zp The other initial parameters Za 1 M are not modified The frozen orbit computation the STELA software will look for an initial orbit with frozen eccentricity The degree of freedom is the initial semi major axis The eccentricity is computed as a function of semi major axis inclination and Earth potential development k 7 ie up to J15 1 a Fo 01 71 2Y E Jipa D sni gt ur E k a 120 Eg 2 _ J J 3 sin i a 4 2n 2 1 Hn l d PN mn m n 1 m Iz orm pnm The eccentricity and argument of Periapsis are defined as follows 1 C iT c i mi V t ig a ia The other parameters 1 M remain as defined by the user in the GUI Note that The default expected lifetime for iterative mode is 24 75 years as a margin to handle little lifetime sensibility to the start of simulation date due to Luni Solar perturbatio
106. responding latitude are displayed as well as the last date in the GEO protected region If not compliant the date of the first criterion violation is displayed as well as the last date in the GEO protected region if before a time limit t x a few years value is given in Physical and key parameters If Criteria 4 is compliant the minimum distance to GEO altitude and the corresponding latitude are displayed L STELA example LEO sim xml Eile r Ol au ra Tj Tj y kd is Hun extrapolation Orbit type LEO C cnes Report summas Parameters General Achanced t Go Results Ci Summary Enhemeris Final state Mature Mean parameters Type Keplerian Frame Celestial Mean of Dave Dbi prarameters Dair oon a 21211543 p 0 00134295 i 59184387 a 291 70223704 136 OOF OOS M 22 069 1742 Log Se T 2011 15 41 29 Mean consran solar actis OS POG 2001 15 41 28 Start axtrapolating ee Try ro Tinie 06 06 2011 15 41 45 ends aer 17 seconds Warning e See next paragraph for GTO orbits F107 132 29 AP 15 deg deg deg deg Compliance criteria Effecuve simulation duration 100 01 years Compliance criteria Hat applicsale i x Lifetime under 75 years Mo LEO crossing C2 LEO 668 3 Miri diet 10 668 34 km Mp LEO crossing c ddl Within LOD years ca applicsol
107. s C2 C4 MJD sec SimDuration f SC1 pl SC1 p2 SC1 f SC2 p1 SC2 p2 SC2 f SC3 pl SC3 p2 SC3 f SCA pl SC4 p2 SC4 COMMENT Units kg km deg years COMMENT Example GTO simulation file COMMENT for STELA 1 55041 0 0 150 35892 1666666 2 92 238 48 178 0 505 50 2 5718614906109325 1381 301443101013 1 0 55047 54263 44599989243 0 018146609564729018 1 0 05462076 1 1 1 1 1 0 05462076 1 0 0 0 94537924 2 55041 0 0 150 35892 1666666 2 92 238 48 178 0 505 50 2 5027017441655963 262 3301314112 13 10 55050 12649 98399973847 0 025041510888028647 1 0 19786746 1 1 1 1 1 0 19786746 1 0 0 0 80213254 3 55041 0 0 150 35892 1666666 2 92 238 48 178 0 505 50 2 177237172236382 929 1404343444 1 310 55050 76331 11900007352 0 027059444286006335 1 0 30998811 1 1 1 1 1 0 30998811 1 0 0 0 69001189 4 55041 0 0 150 35892 1666666 2 92 238 48 178 0 505 50 1 8627177223384974 1315 2142130344 131 0 55051 79383 11600012239 0 029894007022084137 1 0 39577303 1 1 1 1 1 0 39577303 1 0 0 0 60422697 5 55041 0 0 150 35892 1666666 2 92 238 48 178 0 505 50 2 2360858657837097 2438 3244334420 1310 55050 16930 844000307843 0 02517716315562633 1 0 46294398 1 1 1 1 1 0 46294398 1 0 0 0 53705602 6 55041 0 0 150 35892 1666666 2 92 238 48 178 0 505 50 2 0953965842310027 3234 1402114143 1310 55051 52648 21199986618 0 029046829036424384 1 0 51681705 1 1 1 1 1 0 51681705 1 0 0 0 48318295 7 55041 0 0 150 35892 1666666 2 92 238 48 178 0 505 50 2 2992092 133363697
108. s Tz Tyr Paria aA peqao Frama Celeitial Mian of Cata E 100 Geocentne reference dame where the orbit parameters are defined a Calestia Mean of Gate mean equator and aginik of data Object Characteristics amp Earth Moan Equator and Equinox at Epoch 2056 CAF intamatibnal Caleszial Ralerence fram ERE CRF Calastal intermediate Poalerenee Frame TAF Tarenna intarmmediabz References Frame retating frame lenqitude of X axi is OF Terraztrial Frozen at Epoch TAF frozen at 3 qieen pieh wh X axis ot a gen lengituda Name peimuk Object Hara idenvatiws with respect to time of its rotation amp null MEE 0 kg True Equater Mean Reflecting Ares n mi Reflectivity coaticient 15 Hil 1221325 Naw GEO siratin eraatad 3 2 11 Progress bar A progress bar is displayed when STELA is computing whether in single extrapolation mode or in statistics mode In statistical mode progress bar displays the estimated remaining duration This duration is estimated by multiplying remaining extrapolations number by averaged past extrapolation durations Averaged extrapolation duration is equal to the difference between current time and initial time then divided by the number of performed extrapolations Statistical made in
109. s regarding the criteria validation one does not simply extrapolate STELA once A statistical computation using the statistical mode through GUI or in batch mode is to be done in order to obtain relevant results This 1s the reason why a warning message and only an orange Not Reliable status appear when using GTO single extrapolation mode See Ref 6 and Ref 8 for more information on these resonance phenomena 3 9 3 Summary for iterative mode in LEO When a simulation in iterative mode ends STELA software automatically switches to the Results Summary view that 1s divided in three topics The top part displays the effective lifetime of the adjusted initial orbit This lifetime is equal or smaller with respect to the algorithm convergence threshold than the expected lifetime given by the user The number of iterations needed to adjust the initial state 1s also indicated The left part describes the adjusted initial orbit state as followed he nature type and frame are reminded to the user he orbit parameters date position and velocity The right part describes the final state computed from the adjusted initial orbit state he nature type and frame are reminded to the user he orbit parameters date position and velocity A button 1s provided to copy the adjusted initial state to general parameters view in order to perform a single extrapolation to check the compliance with protected region criteria It
110. s the most generic complete and precise one The LEO and GEO dynamical models remain in the STELA software and can be used through the library mode 5 4 2 Osculating orbit The osculating parameters are computed in the MOD Frame as follows for each orbit parameter n OSC _ mean E E short period The type of perturbations taken into account in the short period computation which is analytically computed depends on the kind of model LEO GEO GTO and enabled forces Perturbation LEO model GEO model GTO model Earth s gravity field J J J Solar and Lunar gravity none yes yes Solar radiation pressure SRP none yes none f Sun and Moon perturbations are disabled from the equations of the mean movement then their respective contributions in the short period computation are disabled as well 5 4 3 Partial derivatives A new STELA feature 15 the ability to compute the partial derivatives of the orbital parameters Partial derivatives can be used for covariance matrix propagation or in an orbit determination process STELA propagates the orbital elements and their partial derivatives at the same time using a semi analytical method allowing a large save of computation time without losing precision on long term mean evolution Let us introduce the vector E K with E being the initial state vector K multiplying factor of the drag GE force and K a multiplying fac
111. sed in the Celestial Mean Of Date Frame at any date as ges t p3 VV where Cd is the drag coefficient e S is the cross sectional area representing the spacecraft is the atmosphere density e V is the satellite velocity with regard to the rotating Earth m is the satellite total mass 5 7 3 1 Drag Coefficient The drag coefficient can be defined as constant with a value chosen by the user variable vs altitude being read in the file stela drag coefficient see Appendix A 1 computed by the Cook formula The file of n Cd values is used in the following way h being the geodesic spacecraft altitude and 1 being a line numbering the file 1 1 n e if h i lt h lt h it1 then Cd h Cd h i e if h gt h n then Cd h Cd h n e if h lt h 1 then h 1 Cook formulae The C is computed in line with the mean cross sectional area hypothesis It is based on the value of the drag coefficient of a plate in tumbling mode SRef 3 amp 5 Cu dE dms osdd zp 52 2 foe ef ral s A e iforo GP Dent 2 amp M cu MO 5 La with v SYET and A v M 2 erf a qrii 0 CY absorption coefficient Cre emission coefficient V plate velocity vs atmosphere Temperature of the gas atmosphere D wal temperatum of the plate Wc perfect gas constante 8 314 472 Jmol M mean molar mass af the gas MO molar mass of oxygenatom 16 107 g
112. selecting Create shortcuts in the Start Menu can set a shortcut on the desktop with Create additional shortcuts on the desktop d IzPack Installation of STELA Setup Shortcuts Create shortcuts in the Start Menu create shortcuk Far current user all users InfraRecorder Jeux al STELA Default dade with IzP ack http izpack org l 8 The installation is complete when the following window appears d IzPack Installation of STELA w Installation has completed successfully 18 An uninstaller program has been created in C Program Files STELA Uninstaller Made with IzP ack http zizpack argZ 2 2 1 2 Install on Linux In a shell run the installer java jar stela install X X X jar where X X X defines the release of STELA For next steps refer to the Installation on Windows 2 2 1 3 Install on Sun Solaris In a shell run the installer java jar stela install X X X jar where X X X defines the release of STELA For next steps refer to the Installation on Windows 2 2 2 Uninstall STELA The user can uninstall the product STELA by using the Windows menu D marrer Start Tous les programmes M m 1 STELA 1 0 0 E o STELA 1 0 0 Uninstaller Fermer la session D Arr ter l ordinateur 12 d marrer The following window will appear ee IzPack Uninstaller Em aS This will remove khe installed application
113. ser at the GUI It should be greater than 1 absorbent surface and less than 2 reflecting surface e S is the cross sectional area perpendicular to the sun spacecraft direction The user can use the Stela Mean Surface area tool see Tools The sun spacecraft vector is compute using the simplified Meus amp Brown model The solar radiation pressure 1s recomputed at every integration sub step In order to get an appropriate estimation of the perturbation that takes into account the eclipse duration and its position on the orbit a Simpson quadrature is used The process is described below Computation of eccentric anomalies at the entry and exit E of the eclipse Earths shadow 15 out considered as a cylinder Determination of M quadrature points evenly spaced in eccentric anomaly between E and E n lighted up part of the orbit Computation of the solar radiation pressure perturbation in the inertial frame Expression of this perturbation at each quadrature point in the TNW orbital frame Derivatives computation with Gauss equations e Simpson quadrature alike the one for the atmospheric drag 5 7 5 180 inclination singularity The type of orbital parameters used in STELA semi analytic theory leads to a singularity when 1 180 Then the mean inclination value is clamped to 179 5 when 1 gt 179 5 5 8 Iterative mode for LEO and GEO orbits 5 8 1 Iterative research of a specific Low Earth O
114. software is based on a semi analytic extrapolator method The short periods have been removed from the evolution of orbital elements allowing a large save of computation time without losing precision on long term several years mean evolution If n represents the mean orbital parameters state at the date t and Zi the mean orbital parameters Leal l ean iE State at the date then the state 1 is deduced from the state 2 with the use of the derivative dt t This derivative is calculated through the perturbation forces as follows ATL ali ATL ATL ATL d __ a Kepler Eth potential d lmisolar potential dF ane d radiation pressure dt dt dt dt dt dt UE ipei ad dt defines the non perturbed Kepler movement of the spacecraft around the Earth representing the gravitational force between two points d Earth potential dt represents perturbations due to the Earth potential irregularities the J2 contribution due to the Earth oblateness dE potential dt represents perturbations due to the gravitational forces of the Moon and the Sun dE ine dt represents perturbations due to the atmospheric drag a ari radiation pressure dt represents perturbations due to the solar radiation pressure The short periods have been analytically removed from the expression of the perturbations above so that only the middle and long term evolution of the orbital parameters are integrat
115. step the reentry altitude The spacecraft enters the atmosphere when the perigee altitude of its orbit goes bellow this value 14 the delay TT UT1 used in frame transformations see Time scales and when importing TLE The right part of the view appears only if the software runs in iterative mode Then the right part 1s divided into 15 the definition of the algorithm convergence threshold 16 the maximum delta between the expected lifetime entered by the user and the extrapolation duration computed by the propagator 3 5 Open a GEO simulation example The user can learn how to use STELA software with the help of a simulation example A configurated file 1s available in the directory installation directory examples In order to select the example the user must use the STELA menu File gt Open a new simulation and then select the example file example GEO sim xml ETSI 5 example GTO sim xml 5 example LEO sim xml File Name lexample sim xml Files of Type STELA Simulation files sim xmD 7 Only files with the extension sim xml can be opened by STELA The rest of the current chapter will consider this simulation example in order to describe the different GUI views 3 6 Parameters of a GEO simulation 3 6 1 Navigation The left part of the STELA window allows the user to navigate and to select the STELA window File Tools 3 73 v Extrapolation Simulati
116. tallation path 3 1 2 2 Run STELA on Linux Run the shell stela batch sh located in the bin subdirectory of STELA installation path Use option help to read documentation A shell can be created to automate process Two examples of script are provided in the example folder of STELA installation path see below 3 1 3 The script example batch ksh loads an existing simulation file and performs several extrapolations the second script example batch py provides the same computation in Python 3 1 2 3 Run STELA on Sun Solaris Run the shell stela batch sh located in the bin subdirectory of STELA installation path 3 1 3 Batch mode examples Two examples of script are provided in the example folder of STELA installation path example batch ksh example in ksh example batch py example in python Run them to launch the corresponding script 3 1 3 1 Script ksh Linux Sun Solaris The script is divided in two sections Methods and Main Only the section Main should be modified by the user This script simply performs several extrapolations As an example The semi major axis is reduced by Ikm at every iteration 3 1 3 2 Script python Windows Linux Sun Solaris Prior to loading this script Python has to be installed on the machine This can be done by downloading Python on the website http www python org Warning this script has been validated only with version 2 7 2 of
117. tion simulation as and Run extrapolation are not available 3 2 5 Tools The user can select Tools in order to start the STELA tool Mean Area Computation or the tool Convert Two Line elements Tools can also be accessed via the toolbar File Tools 3 2 6 Help The user can reach the User Manual of STELA software by selecting the Help option as follows STELA example LEO sim xml File Tools LE Help F E i EET m About STELA Ld Run extrapolation 3 2 7 About STELA In order to get information about the STELA release and licenses the user can activate the Help menu File Tools Jj ECT S TELA Rul 3 2 8 Exit STELA The user can close the STELA software by selecting Exit in the File menu 3 2 9 Logbook At the bottom of the main window a logbook contains the history of the user handlings The logbook also contains STELA warning or error message in case of bad parameters input or extrapolation error 04 11 2011 11 43 01 New LEO simulation created INFO 3 2 10 Tooltips Help tooltips appear when the mouse pointer 1s over an input parameter name Fide Tenh 7 ire sx a7 i i Bun rapiat Epo ae Ines 7 Parameters carm E Default ony ee L Enshle erative mendes This is a dafault comma m state Summary Dutpulx Habure Mean parameter
118. tion in true anomaly of the quadrature points 5 5 4 Solar radiation pressure The solar radiation pressure force is defined as follows For low Earth orbits the solar radiation pressure may have a significant influence on the long term orbit evolution for particular orbits that lead to a phasing between the J2 drift effect and the SRP effect resonance d y Fp C P 3 Q0 J Where The albedo of the Earth is not taken into account Cris the reflectivity coefficient PO 15 the solar constant at 1 UA see Physical parameter values e S 15 the reflecting area representing the spacecraft d0 1 UA see Physical parameter values dis the sun spacecraft distance u is the sun spacecraft vector The reflectivity coefficient is a constant value given by the user at the GUI It should be greater than 1 absorbent surface and less than 2 reflecting surface e S is the cross sectional area perpendicular to the sun spacecraft direction The user can use the Stela Mean Surface area tool see Tools The sun spacecraft vector is compute using the simplified Meus amp Brown model The solar radiation pressure 1s recomputed at every integration sub step In order to get an appropriate estimation of the perturbation that takes into account the eclipse duration and its position on the orbit a Simpson quadrature is used The process is described below Computation of eccentric anomalies at th
119. to this direction The computation of the Mean Area 15 done as follows A projection area perpendicular to an observation direction 1s designed so that this area contains the projection of the object whatever its orientation 1s The area is cut into np pixels np the number of pixels of projection area can be modified by the user through the Advanced Parameter tab It is recommended to use a high number of pixels 1n order to have a reliable computed mean area Then a ray is shooted perpendicularly from each pixel of the scene The pixel is switched on or off whether the ray intersects or not one of the shapes The fraction of switched on pixels multiplied by the area of the scene is the cross sectional area from the current direction of observation The direction of observation is then changed to take into account the orientation model given by the user The number of directions can be defined by the user through the Advanced Parameter tab mn m e um mom oum RAYS m mju m omm um mo moo om m e SCENE The model can be saved in a XML file with the extension _shap xml This file can be re opened by the STELA Mean Area Computation tool 3 11 2 Two Line Elements tool STELA provides users with a Two Line Elements hereafter called TLE conversion tool based on the SGP4 SDP4 theory STELA The user can convert one or several TLE at once into a format
120. tor of solar radiation pressure Then the partial derivatives are OO The type of perturbation taken into account for the propagation model of the solve for vector is derived from the GTO perturbation model It uses non singular orbital elements type 8 see 5 2 2 and is valid for high eccentricity and high inclination orbits The partial derivative computation is available only when using the GTO model Perturbation Partial derivatives Earth s gravity field J2 J22 J3 J4 J5 J6 J7 Solar and Lunar gravity Atmospheric drag Oblate Earth Rotating Atmosphere Simpson Quadrature Solar radiation pressure Yes SRP Earth s shadow for SRP Numerical Integrator Sixth order Runge Kutta To compute the partial derivatives make sure that you are using the GTO single propagation mode the flag transitionMatrix is set to true in the STELA advanced parameters file stela advanced parameters properties in configuration folder Then the partial derivatives will be computed and saved in the state transition matrix file see A 7 State transition matrix file when saving the simulation The force model or recomputation time step used in the propagation of the partial derivatives can be modified in the STELA advanced parameters file 5 5 Algorithm features for LEO model 5 5 1 Earth potential The derivatives of mean parameters due to Earth potential perturbation are analytically expr
121. ts 5 7 1 Earth potential The derivatives of mean parameters due to Earth potential zonal perturbation are analytically expressed with the J2 up to J15 contributions at first order and J2 contribution at second order J22 Tesseral terms of the Earth potential are also taken into account leading to a complete 15 by 15 Earth potential model each effect of the tesseral harmonics terms which as a period greater than a tunable value expressed as a multiple of the integrator step 1s included SRef 12 5 7 2 Lunisolar potential The lunisolar potential computation 15 based on the knowledge of the Sun and Moon positions that are computed using a simplified Meeus and Brown model The Meeus and Brown model used in STELA has a 6 terms development in longitude 4 terms development in latitude and 4 terms development in Earth Third body distance Then like for the Earth potential the lunisolar perturbation 1s developed in Poisson series These series are developed to the order 4 5 7 3 Atmospheric drag force Only a fraction of the GTO orbit is concerned by atmospheric drag the part in LEO region Therefore STELA computes the atmospheric drag only on that relevant part of the orbit In Stela software the atmosphere 1s supposed to rotate at the same velocity as the Earth rotating atmosphere The oblate shape of the Earth is taken into account At LEO altitudes no wind is considered Therefore the atmospheric drag force can be easily expres
122. turbations Earth perturbation Zonal order 9 Enable tesseral perturbation 19 Tesseral order 11 7 Minimum perad 12 5 steps Reentry Reentry alttude 13 30 km Time TT minus LIT 14 67184 pae Message 26 09 2013 15 42 10 cr ation dune nowele simulation LEG m INO The Advanced Parameters view contains m ov EN pU de ey 11 12 13 the integration step aflag used to enable disable the atmospheric drag force the number of points for the Simpson quadrature used for the modeling of the atmospheric drag force see Algorithm features the number of integration steps where the atmospheric drag force is considered to be constant therefore the drag force recomputation occurs every N integration steps a flag used to enable disable the Solar Radiation Pressure SRP perturbation the number of points for the Simpson quadrature used for the modeling of SRP see Algorithm features a flag used to enable disable the Sun perturbations a flag used to enable disable the Moon perturbations the zonal harmonics order of Earth gravity model a flag used to enable disable the Earth potential tesseral perturbation the tesseral harmonics order of Earth gravity model the minimum period used in the tesseral effect computation The tesseral effect is taken into account if its effect has a period greater than the given value expressed as a multiple of the integration
123. ty Ap and the solar flux F10 7 The solar activity can be constant and tuned by the user variable vs time being read in the file stela solar activity see Appendix A 2 5 7 3 5 Atmospheric bounds computation In order to save computation time an upper atmospheric boundary Z is used in the following way atmo If the orbit perigee is higher than Z no atmospheric drag is computed atmo f the orbit apogee 1s lower than Z the atmospheric drag is computed on the entire orbit like in the atmo LEO model f the other cases input and output anomalies Ve and Vs are computed and used in the quadrature process V 7008 qm Jj y V Z mo 15 tunable is the stela advanced parameters file configuration files directory 5 7 3 6 Simpson s quadrature The atmospheric drag effect on osculating parameters can be easily computed but we rather need to know the effect on mean parameters The STELA software uses the Simpson quadrature method to compute the drag perturbation effect on mean parameters First the drag perturbation is computed at Nquad osculating points as follows The mean orbital parameters are propagated from the Ve anomaly to the Vs anomaly of the orbit at the Nquad 2 points points are equidistant in true anomaly in order to have more points near the perigee these are the quadrature points The mean parameters of quadrature points are converted to osculating
124. uring the extrapolation Frames used before or after the extrapolation 5 1 2 Celestial Mean Of Date Frame MOD Date Freeze Epoch tfreez IERS 2010 Precession X Nutation IERS 2010 IERS 2010 ERA rothbtian ERA rotation T rotation Jon ret Freeze Epoch tfreez ba V X R X The Mean Equator and Equinox of Date Frame O X Y Z 1s defined with the Earth mass center The z axis aligned with the mean Earth s spin axis The x axis aligned with the mean equinox of date vernal direction The y axis completing the direct orthonormal trihedron This frame is used by STELA for the integration of the spacecraft motion This frame is not inertial because of the Earth precession but for STELA purpose perturbative acceleration due to the precession movement is supposed to be neglictible in the long term STELA also considers that the Mean Equator and the True Equator of Date of the Earth are merged the nutation is neglected when applying the Greenwich Mean Sideral Time The user can choose this frame in order to define the initial orbit parameters 5 1 3 ICRF The ICRF International Celestial Reference Frame is defined by the IERS conventions see SReferences 4 and realizes an ideal reference system by precise equatorial coordinates of extragalactic radio sources observed in Very Long Baseline Interferometry VLBI programmes The user can choose this frame
125. used by Stela The equivalent correlation matrix and standard deviation vector associated will be 1 Ai aL 1 Tyly epe d ig Cy c These matrices are symmetrical Note that when using a Gaussian dispersion STELA will ask for a Standard deviation vector but when using a uniform dispersion Stela will ask for a Delta vector The link between Standard deviation and Delta 1s given for a uniform dispersion by the relation 2 42 The following formula displays the conversion from one matrix to another 1 CT vy CT vr CT CT CT CT CET Plu les U dU xU z z ada 0 Cue JE Ce des d 1 O aap Ty ily CTy CI apm Ty TT 3b ae 0 aa rz 1 Tei CT CT 1 l 1 td 0 ex cq 0 CT CT CT CT CT CT 2 T x TO Tes x be ee usas I Oe 3D CT y Cy Cy a a 1 CT ser Oye Exi 1 0 EE e Ty C Note that when the standard deviation of a parameter is null covariances and correlations with this very parameter are null as well Dispersion through these matrices uses a Cholesky decomposition Correcting the dispersed values When dispersing values non physical values may appear These values are corrected following this method Eccentricity negative dispersed values are corrected to dispersed values greater than are corrected to 1

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