MCWP 3-16.7 Chapter 8: Astronomy for Marine Artillery
Contents
1. c Remarks Entries The remarks page includes both required entries and some optional information that may be needed by the computer or for future reference See Figure 8 33 1 Required Entries The remarks section will include the following information Easting and Northing of the Occupied Station UTM Grid Zone Horizontal Datum Ellipsoid Source of the position information Center leading or trailing edge if using the sun Time Zone Letter If using local time an entry must be made indicating Daylight Savings or Standard Times Sketch as close to scale as possible 2 Optional Entries Optional entries can include but are not restricted to the following Location of occupied and rear stations Route to these locations from a known point Changes to data in trig list concerning the stations Weather phenomena not covered in header information RCDR IO COP initial blocks Approx azimuth to AZMk LCPL SMUCKATELLY LCPL GUNGHO LCPL_GRUNT CHIEF OF PARTY INSTR OPR WEATHER CLEAR WARM RCDR INST _T2E 123456 2 REMARKS OS is a wqoden hub 1 ey eres eee dirt trail south of GP 2 The EGL is 102 m ters west offthe OS Jsme saos WGS 84 frontne aese eeg l Figure 8 33 Remarks For Arty Astro d Recording Field Data 1 Field data will be recorded in the columns and rows corresponding to the pointing In other words the ini2. 12 hours GMT 0 Long Figure 8 18 Concepts of Solar Time 8 7 Sidereal Time a General 1 Sidereal time is based on the Earth s rotation with respect to the stars A sidereal day is the amount of time necessary for two successive passes of the vernal equinox over a meridian of longitude The sidereal day begins when the vernal equinox crosses the observer s meridian at the upper transit sidereal Noon Celestial North Pole Vernal a Equinox Celestial Equator Figure 8 19 Concepts of Sidereal Time 2 Sidereal time for any point is the amount of time that has elapsed since the vernal equinox last passed the meridian at that point Hence Local Sidereal Time LST is the amount of time that has elapsed since the vernal equinox last passed the observer s meridian Greenwich Sidereal Time GST is the amount of time that has elapsed since the vernal equinox last passed the Greenwich meridian See Figure 8 19 b Sidereal Year The annual apparent motion of the Sun along the ecliptic is opposite in direction to its daily path Consequently the relationship between solar time and sidereal time is variable For example on 21 September at the instant the vernal equinox crosses the observer s meridian the mean sun is crossing the lower transit of the observer s meridian At this instant the sidereal clock of the observer will read Oh Om Os and a solar civil clock will read Oh Om Os Twenty four sidereal hours lat
3. See Figure 8 3 Observer s Observer s Position i Celestial Equator Figure 8 3 Zenith Position e Prime Vertical The prime vertical for the position of an observer is a great circle on the celestial sphere that is perpendicular to the observer s meridian at the zenith and intersects the observer s horizon at points due east and west of the observer f Star Position The position of a star on the celestial sphere is defined in terms of Right Ascension and Declination DRAFT 1 Right Ascension RA a As the Sun moves across the celestial sphere it traces a path referred to as the ecliptic The ecliptic is tilted approximately 23 30 417 78 mils from the celestial equator due to the tilt of the celestial sphere on its axis It crosses the celestial equator at two points along its path The point where the ecliptic crosses the celestial equator from the southern hemisphere to the northern hemisphere is the Vernal Equinox the first day of spring usually around March 21 See Figure 8 4 b Right Ascension RA is the arc distance eastward along the celestial equator measured from the vernal equinox to the hour circle of a celestial body In most cases RA is expressed in terms of arc time i e hours h minutes m and seconds s It can vary from Oh to 24h east of the vernal equinox See Figure 8 5 Celestial Sphere Vernal Equinox Ecliptic Figure 8 4 Ecliptic and Vernal Equinox Vernal Equin
4. as such are measured with angular values The three sides of the triangle are the Polar Distance the Coaltitude and the Colatitude 1 Polar Distance Polar distance is a segment of the hour circle of the celestial body It is the arc length of the side of the PZS triangle from the celestial North Pole to the celestial body the PS side It is determined by applying the celestial body s declination to 90 In other words if the declination is north the polar distance equals 90 minus the declination if the declination is south the polar distance equals 90 plus the declination See Figure 8 7 DRAFT Celestial P a North Pole Distance Polar Celestial Hour Circle of Celestial Body Celestial Sphere Figure 8 7 Polar Distance 2 Coaltitude Coaltitude is the arc length of the side of the PZS triangle from the celestial body to the observer s zenith Coaltitude Observer s a r Zenith F i Celestial Observer s Meridian a Hour Circle of s rae Celestial Body Ce gt elestan N i Mato ee eae eee ene 1 1 i Celestial Sphere Figure 8 8 Coaltitude a Observer s Horizon The observer s horizon is a plane that is tangent to the surface of the Earth at the observer s position it is also perpendicular to the observer s zenith See Figure 8 9 b Determining Coaltitude Coaltitude is determined by subtracting the vertical angle altitude of the celestial body
5. clockwise start at the bottom of the template and are readable for south latitudes The 0 180 line represents the observer s meridian the other numbers represent the azimuth from the celestial pole north or south to the line identified by those numbers The templates display the observer s horizon as the outer ellipse The center of the ellipses is the observer s zenith The series of concentric ellipses represent the altitude in degrees above the horizon of the celestial body 8 21 Orienting the Star Finder and Identifier The star finder and identifier is oriented by placing the arrow at the 0 180 line of the template over the local sidereal time LST on the outer edge of the base Local sidereal time can be determined in several ways each requiring the same information Observation Date Observation Time Longitude of the Observer a DA Form 6 21 This manual computation form allows the user to determine the LST by means of simple mathematical computations and the extraction of several data from charts displayed on the back of the form b Survey Computer Systems Survey computer systems HCS will allow the user to compute the LST by means of input of the above data For instructions on the operations of these systems consult the user s manual for that equipment c Haught Method This is an easy field expedient method of determining LST accurate to 1 and can be used for any time and location The fin
6. point Changes to data in trig list concerning the stations Weather phenomena not covered in header information RCDR IO COP initial blocks Approx azimuth to AZMk d Recording Field Data 1 The first set in this method is recorded the same as the procedures listed for 5th order except that the solution is not circled it is placed in parenthesis See Figure 8 36 2 The T telescope column will be filled out as shown in Figure 8 36 There will be three spaces between the last direct reading in the first set and the initial circle setting R reverse reading in the second set 3 The second set is recorded as follows a The rear station AzMk name will be recorded in the reverse R mode row in the second set Skip one line to record the occupied station name Skip one line to record the forward station celestial body name to the left of the first reverse pointing on the body If the celestial body is a star the star name must be recorded b When the fieldwork was completed for the first set the instrument operator had a pointing on the rear station in the reverse mode This was the closing angle for the first set The recorder will enter that closing angle as the initial circle setting for the second set The instrument operator needs only to observe the celestial body in the reverse mode and close the angle in the direct mode to complete the second set See Figure 9 37 b When recording times
7. when Polaris is in elongation See Figure 8 27 Upper Culmination Celestial Western North Pole 6 hrs Eastern 1S hirs Elongation Elongation Lower Culmination Figure 9 27 Orbit of Polaris b Identification of Polaris 1 Polaris is the brightest star in the constellation Ursa Minor Little Dipper which is near the constellations Ursa Major Big Dipper and Cassiopeia Lazy W Polaris is the anchor end star of the handle of the Little Dipper DRAFT 2 Polaris can be identified by its relative position to Ursa Major The two stars forming the side of the bowl farthest from the handle of the Big Dipper are called the pointer stars An imaginary line extended through the pointer stars towards Cassiopeia nearly passes through the celestial North Pole Polaris is approximately five times the distance between the pointer stars along the imaginary line from the Big Dipper See Figure 8 28 3 Polaris can also be identified by its relative position to Cassiopeia Since Cassiopeia is on the same side of the celestial North Pole as Polaris its position relative to the pole is approximately the same as Polaris Therefore Cassiopeia can be used to determine whether Polaris is in elongation or culmination A line drawn from the star Ruchbah bisecting the shallow side of Cassiopeia will pass closely by Polaris See Figure 8 28 4 The vertical angle to the celestial North Pole is equal to the observer s latit
8. 30 4 7 5 52 5 LST for 2230 on 23 July is 256 5 selection of a star by its star rate can be performed by plotting the position of selected stars on the star rate charts listed in Appendix E b Determine the Position of a Star Once the stars have been selected the observer can either plot the azimuth and altitude to the celestial body from the template of the star finder and identifier or he can enter the star number or name dependent on the system of the celestial body into a survey computer system Either method is adequate for locating the star in the telescope of a T 2E Theodolite C Identification of stars other than Polaris is aided by the Star Cards and the World Star Chart included in Appendix E The star cards display the stars in their constellations and the star list provides the star number and magnitude Section IV RECORDING ASTRONOMIC OBSERVATIONS 8 23 Recording Arty Astro Method Field Notes 5th order a General The procedures listed below for recording Arty Astro Method astronomic observations will be used for 5th order accuracy b Heading and Column Titles As with all field notes the first page of the recorder s notebook is the index The heading and column titles will be filled out as described below See Figure 8 32 1 The designation block should be filled in with ARTY ASTRO Sun or Star as the method of survey being conducted 2 The date block must be filled in with the date the fi
9. DRAFT CHAPTER 8 ASTRONOMY FOR MARINE ARTILLERY Marine artillery surveyors are required to provide an azimuth to the supported unit or to determine a starting azimuth for conventional survey If an azimuth is not provided in a Trig list or cannot be computed the surveyor can establish an azimuth by performing observations of celestial bodies Section I BASIC ASTRONOMY 8 1 The Tilted Polar Axis and Movement of the Earth a The Earth s Tilted Axis The Earth can best be visualized as an ellipsoid The line connecting the flattened ends or the shorter axis is the Earth s rotating axis The points on the Earth where this axis intersects the surface are the north and south poles therefore the rotating axis is also referred to as the polar axis If the Earth s polar axis were perpendicular to its orbit around the Sun there would be no change in seasons the Sun s rays would always be directed at the equator Because the Earth s axis is tilted at an angle of approximately 23 30 417 78 mils the Sun s rays are directed at different portions of the Earth as it orbits the Sun See Figure 8 1 Figure 8 1 Earth s Rotational Axis b Movement of the Earth The Earth and its motions are of primary interest to the artillery surveyor These motions form a complex pattern all of which affect the Earth s relationship to the stars and other planets 1 Precession The Earth s axis has a cone shaped motion or precession making on
10. E is split between the columns in the top half of the blocks Hours h are listed in the lower left corner of column 3 minutes m centered between the columns and seconds s in the lower right corner of column 4 d Column 5 HORZ to record horizontal readings to the azimuth mark and to the celestial body DRAFT Figure 8 35 Heading and Column Titles 4 Order Arty Astro e Column 6 MEAN to record the solutions for the direct and reverse sets and to record the mean solution of the sets f Columns 7 12 REMARKS this side of the page will be used to record information pertinent to these observations Entries are discussed in the following paragraph c Remarks Entries The remarks page includes both required entries and some optional information that may be needed by the computer or for future reference See Figure 8 33 1 Required Entries The remarks section will include the following information Easting and Northing of the Occupied Station UTM Grid Zone Horizontal Datum Ellipsoid Source of the position information Center leading trailing edge if using the Sun Time Zone Letter If using local time an entry must be made indicating Daylight Savings or Standard Times Sketch as close to scale as possible 2 Optional Entries Optional entries can include but are not restricted to the following Location of occupied and rear stations Route to these locations from a known
11. Figure 8 23 Time Zone Letter Designations and Corrections Local to Greenwich Mean Time DRAFT Figure 9 24 World Time Zone Chart Local to Greenwich Greenwich standard time Zulu time also known as Greenwich Mean Time GMT or Universal Time is defined as the length of time since the mean sun last crossed the 180th meridian lower transit of the Greenwich Meridian or solar midnight This time can be expressed as the reading of the standard 24 hour clock at the Greenwich observatory at the moment an observation is made on a celestial body hence it is the same time throughout the world Therefore since the observer s clock is usually set to standard local time that time LMT must be converted to GMT See Figure 8 18 8 9 Daylight Savings Time Daylight savings time is clock time advanced by 1 hour from standard time Effective 1987 federal law required that daylight saving time be observed from the first Sunday in April until the last Sunday in October however individual states may exempt DRAFT themselves During World War II a double daylight saving time 2 hour advance was observed nationwide and was called wartime 8 10 Greenwich Mean Time GMT a Converting LMT to GMT Local Mean Time can easily be converted to Greenwich Mean Time by applying a time zone correction See Figure 8 23 1 Western Hemisphere If the observer is located in the western hemisphere divide the value of the standard meridian of
12. al result from these computations is the LST for 1900 hours on the date of observation The time arc relationship is then used to determine the LST for the actual observation time The Haught Method is performed as follows 1 Count the number of months this year prior to the current month Multiply that number by 30 2 Add the calendar day of the current month If the Julian Date of the observation is known use the Julian Date instead of steps 1 and 2 3 Add a constant of 24 4 Determine the difference between the observer s longitude and the longitude of the time zone central meridian CM Add the difference if the observer is east longitude subtract if the difference is west longitude 5 If using daylight savings time DST subtract 15 In the US DST is from the first Sunday in April to the last Sunday in October The result is the LST for 1900 hours 6 Determine the difference between 1900 and the time of observation Add 15 for each hour after 1900 and 1 for each 4 minutes after the whole hour If the observation time is prior to 1900 subtract the correction DRAFT 7 Sample An astronomic observation will be made at 2230 on July 23 The observer s longitude is 98 Step 1 of full months x 30 180 Step 2 Observation Date 23 Step 3 Add 24 24 227 Step 4 Offset from CM _ 8 219 Step 5 Correction for DST 15 LST for 1900 hours 204 Step 6 Observation time difference is 3h 30m 3x 15 45
13. and Templates The star finder and identifier consist of a base ten templates and a case 1 Base The base is a two sided star chart One side displays stars of the northern hemisphere the other side the southern hemisphere The center of each side represents the celestial pole north or south dependent on the side of the base The edge of the base is a circle graduated in half degrees and numbered counter clockwise every five degrees These graduations represent the local hour angle of the vernal equinox or the local sidereal time LST 2 Templates The star finder and identifier include ten templates One which is used to plot the Sun and planets not used by artillery surveyors and nine to identify stars and determine their position once the template is properly oriented The nine templates are clear plastic that allow the user to view the stars displayed on the base Each template is constructed for a specific latitude starting at 5 and increase in 10 degree increments to 85 The templates are two sided one side for north latitudes and the other side for south latitudes The user selects a template that corresponds closest to his latitude On each template is a series of concentric ellipses Around the outer edge of these ellipses are two sets of numbers from 0 to 360 The inner set of numbers numbered clockwise start at the top of the template and are readable for north latitudes The outer set of numbers also numbered
14. atural unit of time for ordinary purposes The solar day begins at solar midnight or the point when the Sun crosses the observer s lower transit Solar noon is when the Sun crosses the observer s upper transit b Apparent Solar Time 1 Time indicated by the position of the actual Sun is called Apparent Solar Time 2 Apparent solar time for any point is the amount of time that has elapsed since the apparent Sun last crossed the meridian at that point Greenwich Apparent Time GAT is the amount of time that has elapsed since the apparent sun last crossed the lower transit of the Greenwich Meridian 180 long Local Apparent Time LAT is the amount of time that has elapsed since the apparent Sun last crossed the lower transit of the observer s meridian solar midnight Since the calendar day begins at solar midnight the apparent solar time at any instant is equal to the hour angle of the Sun plus or minus 12 hours See Figure 8 18 3 Apparent Solar Time is not usually considered accurate enough for most modern applications For several reasons the length of an apparent solar day varies from season to season First the movement of the Sun is along the ecliptic and not the celestial sphere also because the rate of this movement is not uniform and lastly because the Earth s orbit is elliptical and not circular Thus 25 December is 50 seconds longer than 13 September and days in January average 15 seconds longer than days in J
15. ch hour angle is the time elapsed since the celestial body last crossed the Greenwich meridian The GHA is obtained by subtracting the right ascension from the Greenwich sidereal time Local Hour Angle LHA The local hour angle LHA of a celestial body is the time that has elapsed since that celestial body last crossed the observer s meridian The formula used to determine the local hour angle depends on the hemisphere east or west of the observer In the western hemisphere both the longitude and the Greenwich hour angle are measured west from the Greenwich meridian therefore the LHA equals the GHA minus Longitude LHA GHA Long In the eastern hemisphere longitude is measured to the east the GHA is still measured to the west therefore the LHA in the eastern hemisphere is equal to the sum of the GHA and the longitude minus 360 LHA GHA Long 360 e Computations Survey computer systems i e HCS contain the Arty Astro program that easily computes an azimuth from the astronomic observations performed The required ephemeris data and time calculations are completed within the program and do not require any manual computation 8 15 Azimuth Specifications a The arty astro method can be used to determine either fourth or fifth order azimuth For Marine artillery surveyors a T2 E theodolite is used in each echelon of survey b At least three sets of observations must be made on the celestial body For
16. e When that plane is set perpendicular to the celestial equator it is referred to as an hour circle and includes both poles of the celestial sphere c Observer s Meridian The observer s meridian is an hour circle that includes the plane of the observer s longitude The upper transit of the observer s meridian is that part which includes the observer s longitude and the observer s zenith the observer s plumb line extended upward to the celestial sphere The lower transit of the observer s meridian is 180 from the upper transit and includes the observer s nadir the observer s plumb line extended downward to the celestial sphere d Zenith Position The position of the observer on the surface of the Earth is located by latitude and longitude When the observer s plumb line is extended upward to the celestial sphere a point referred to as the observer s zenith or the zenith position is established The zenith position is also located by latitude and longitude and provides a fixed position of the observer s instrument on the celestial sphere The zenith latitude is the arc distance from the celestial equator to the observer s zenith The zenith longitude is the arc distance along the celestial equator from the plane of the Prime Meridian Greenwich Meridian to the plane of the observer s meridian extended to intersect the celestial sphere Zenith longitude is also the angle between those two planes as measured at the celestial poles
17. e time that has elapsed since that celestial body last crossed the observer s meridian The formula used to determine the local hour angle depends on the hemisphere east or west of the observer In the western hemisphere both the longitude and the Greenwich hour angle are measured west from the Greenwich meridian therefore the LHA equals the GHA minus Longitude LHA GHA Long In the eastern hemisphere longitude is measured to the east the GHA is still measured to the west therefore the LHA in the eastern hemisphere is equal to the sum of the GHA and the longitude minus 360 LHA GHA Long 360 4 Several formulas can be derived for the solution of the spherical triangle when two sides and an included angle are known The following formula was selected for use in artillery survey because of its simplicity cos 2 Lat Dec cot 1 2 t sin 2 Lat Dec tan 1 2 A q sin 1 2 Lat Dec cot 1 2 t cos 1 2 Lat Dec tan 1 2 A q Where A is the astronomic azimuth true of the Sun measured east or west of the meridian q is the parallactic angle cancels out in computations Lat is the latitude of the station Dec is the apparent declination of the sun t is the local hour angle less than 12h of the sun e Computations Survey computer systems i e HCS contain the Arty Astro program that easily computes an azimuth from the astronomic observations performed The req
18. e turn in 25 800 solar years or one platonic year great year This is caused by torque imposed on the Earth mostly by the Moon and Sun It can be visualized as a spinning top as the spinning slows the top begins to wobble creating a cone shaped motion in its rotating axis 2 Rotation The Earth makes one 360 rotation on its axis every 23h 56m 04 091s The rotation is from west to east therefore because of revolution the Earth must rotate more than 360 for the same point to face directly at the sun on subsequent days See Figure 8 1 3 Revolution The Earth revolves around the Sun once every 365 days approx over a 600 million mile orbit at a rate of 18 5 miles per second The counter clockwise orbit is elliptical with an average distance to the Sun of about 93 million miles 4 Other types of motion affect the Earth For instance the north and south poles are not stationary they vary through rough circles approximately 40 feet in diameter Also there is solar motion of 12 miles per second while the Earth s portion of the galaxy is moving through space at approximately 170 miles per second 8 2 Celestial Sphere a General For purposes of practical astronomy we assume that the Earth is at the center of the Universe and that everything else i e Sun stars planets etc falls on the surface of a sphere of infinite radius referred to as the Celestial Sphere We also assume that the Earth is stationary and that t
19. ed and related to the Greenwich meridian the time is referred to as Greenwich apparent time GAT By simply adding 12 hours to or subtracting it from the GAT the result cannot exceed 24 hours the surveyor determines the value of the Greenwich hour angle GHA The Greenwich hour angle is the amount of time that has elapsed since the Sun last crossed the Greenwich upper meridian upper transit 2 To determine the Local Hour Angle in mils of arc the GHA and the observer s longitude must be converted to mils of arc If the observer is located in the western hemisphere the LHA is determined by subtracting the observer s longitude mils of arc from the GHA in mils If the observer is located in the eastern hemisphere the LHA is determined by adding the observer s longitude mils of arc to the GHA in mils b Determining Angle t Angle t is the angle in the PZS triangle at the polar vertex It is determined as discussed below 1 If the local hour angle is greater than 3200 mils angle t equals 6400 mils minus the LHA 2 If the local hour angle is less than 3200 mils angle t equals the LHA Section II ASTRONOMIC MET 8 12 Methods of Determining Azimuth a General The primary astronomic method Marine artillery surveyors will use is the Arty Astro Method Arty Astro is based on the Hour Angle Method and can be used with the Sun or stars With the advent of the PLGR and SINCGARS accurate time is now readily availab
20. eldwork was performed This will be the date used in the computations WM As I ee a a a De a ee TV E Figure 8 32 Heading and Column Titles 5 Order Arty Astro a General A star should be selected for its star rate or the rate of its apparent motion There are however other considerations depending on the method of astronomic observation used Once the star finder and identifier is properly oriented include the weather description T 2E serial number Party Chief COP name Instrument Operator I0 name and Recorder RCDR name DRAFT 4 The column titles under the heading will be labeled from left to right as follows a Column 1 STA to identify the occupied rear and forward stations The forward station star name will be listed b Column 2 T to identify the telescope mode direct D or reverse R c Column 3 and 4 TIME h m s to designate the exact time the instrument operator announced TIP during the observations TIME is split between the columns in the top half of the blocks Hours h are listed in the lower left corner of column 3 minutes m centered between the columns and seconds s in the lower right corner of column 4 d Column 5 HORZ to record horizontal readings to the azimuth mark and to the celestial body e Columns 7 12 REMARKS this side of the page will be used to record information pertinent to these observations Entries are discussed in the following paragraph
21. er the vernal equinox will again cross the observer s meridian but the mean sun will not yet have crossed the lower transit of the meridian From this we observe the solar clock reads 23h 56m 04 091s which shows the sidereal clock gains on the solar clock about 4m per sidereal day This interval is accumulated throughout the tropical year so that while a solar year contains 365 2422 mean solar days a sidereal year contains 366 2422 days 8 8 Time Zones a The mean sun revolves around the Earth once every 24 mean solar hours one mean solar day and each hour the mean sun travels along an arc that is 15 wide Each of these 15 arcs is referred to as a time zone Each of the 24 time zones is designated by a letter A Z J omitted See Figure 8 23 b The Prime Meridian is used as a basis of reference for time zones Time at a point lying 15 west of the Prime Meridian is 1 hour earlier than at the Prime Meridian because the Sun has not yet crossed 15 W longitude The opposite is true for a point lying 15 east of the Prime Meridian where time is hour later since the sun has already crossed 15 E longitude Therefore the difference in local time between two places equals the difference in longitude between the two places See Figures 8 20 and 8 23 c Each 15 meridian east and west of the Prime Meridian is referred to as a standard meridian Each zone extends 7 5 east and west of the standard meridian Therefore the
22. es of the PZS triangle are the parallactic angle the hour angle time angle and the zenith angle 1 Parallactic Angle The interior angle at the celestial body formed by the intersection of the polar distance side PS side and the Coaltitude side ZS side is the parallactic angle It is used in determining astronomic azimuths but is canceled out during the computations See Figure 8 13 Celestial Observer s Celestial Body Celestial Sphere Figure 8 13 Parallactic Angle 2 Hour Angle Time Angle The interior angle at the celestial North Pole formed by the intersection of the polar distance side PS side and the Colatitude side PZ side is the hour angle It is sometimes referred to as the time angle The letter t designates the hour angle The local hour angle represents the elapsed time since the celestial body crossed the observer s meridian See Figure 9 14 J Celestial Equator Figure 9 14 Hour Angle Time Angle or Angle t 3 Azimuth Angle The interior angle at the zenith formed by the intersection of the Coaltitude side ZS side and the Colatitude side PZ side is the azimuth angle or zenith angle This angle is the product of computations and is the angle used to compute the DRAFT true azimuth from the observer to the celestial body When the celestial body is east of the observer s meridian the true azimuth is equal to the azimuth angle When the celestial body is west of the observer
23. experienced instrument operator may observe the Sun Local Hour Angle 2 Gr Q Azimuth i vi ti 3i w j Si qj mi Spena Celestial Equator Figure 8 25 Solving the Arty Astro Method above 800 mils with an elbow telescope or with the card method c Time In the Arty Astro Method Sun time is critical to the accurate determination of the local hour angle For this reason time must be accurate to 1 second Accurate time is available through radio time signals and GPS receivers i e PLGR MSGR SINCGARS d Solving the PZS Triangle The formula for solving the PZS triangle has been arranged in a manner as to require only the determination of the local hour angle The two sides are stated in the formula in terms of declination of the sun and latitude thus eliminating the need for the computations of polar distance and Colatitude 1 The computation of the polar distance is not necessary since the formula uses the Sun s declination 2 The computation of the Colatitude is not necessary since the formula uses the observer s latitude 3 Determination of Local Hour Angle LHA For the hour angle solution the element of the PZS triangle that is necessary is the local hour angle This angle is determined by using the time of the observation In general terms the local hour angle is determined by converting the local mean time watch time to Greenwich mean time to Greenwich apparent time to Greenwich hour a
24. fifth order mean the three sets and reject any set that varies from the mean by more than 0 3 mils For fourth order mean the three sets and reject any set that varies from the mean by more than 0 15 mils At least two sets must remain to determine the final azimuth both fourth and fifth order c The considered accuracy for a fifth order astronomic azimuth is 0 3 mils and 0 15 mils for a fourth order azimuth 8 16 Selection of Methods of Observation a General The Marine artillery surveyor must consider several factors when selecting a method of observation These considerations include the following 1 Day or night north or south latitude 2 Accuracy of the watch time 3 Positions of celestial bodies at specific times 4 Degree of accuracy required 5 Observer s position accuracy This consideration is more important for the computation of UTM grid convergence true azimuth to grid DRAFT azimuth than for the actual observation computations 6 The experience of the instrument operator b Procedures Specific procedures to observe celestial bodies are outlined in Chapter 7 Section I Section III STAR SELECTION AND IDENTIFICATION 8 17 General a There are important advantages to using stars rather than the sun as a source for astronomic azimuths Since stars appear as pinpoints of light in the telescope they are easier to track At least one of the 73 survey stars can be found in a position that wil
25. from 90 1600 mils This vertical angle must be corrected for refraction and parallax for sun observations and corrected for refraction for star observations The resultant angle is side ZS of the PZS triangle and can be referred to as the zenith angle of the celestial body See Figure 8 9 Figure 8 9 Determining Coaltitude c Parallax Parallax can be defined as the apparent displacement of a body on the celestial sphere caused by a change in position of the observer In other words the observed altitude or vertical angle of a celestial body must be corrected for the error introduced by the observer s location on the surface of the Earth vice the center of the Earth The nearest star is 26 x 10 miles from Earth the Sun is only 93 x 10 miles from Earth because the stars are so distant the apparent displacement of the stars is nearly immeasurable For this reason parallax corrections are used for observations on the Sun only Parallax on the Sun varies from 9 when the it is on the observer s horizon vertical angle 0 mils to 0 when it is on the observer s meridian For artillery survey a constant value of 7 0 04 mils is used See Figure 8 10 CENTER OF EARTH Figure 9 10 Parallax d Refraction Refraction can be defined as the apparent displacement of a body on the celestial sphere caused by the deflection of light rays as those rays pass through the Earth s atmosphere A ray of light passing thr
26. he celestial sphere rotates around the Earth from east to west This is because the Earth rotates west to east DRAFT counterclockwise so the apparent motion of celestial bodies is the opposite direction See Figure 8 2 Celestial North Pole Celestial Equator Celestial South Pole Figure 8 2 Celestial Sphere b Celestial Poles and Equator The celestial sphere rotates around the stationary Earth on an axis that coincides with the polar axis of the Earth The locations of the celestial poles are at the point in the sphere where the Earth s polar axis would intersect the sphere if they were extended into space If the plane of the Earth s equator was extended into space the point where that plane intersects the celestial sphere is the celestial equator See Figure 8 2 8 3 Celestial Coordinates a General Computations of astronomic observations are performed in part using the celestial coordinates of points on the celestial sphere Since these coordinates are located on the surface of a sphere they are referred to as spherical coordinates In general there are two systems of spherical coordinates the horizon system and the equator system For artillery survey methods the equator system is used b Great Circle Hour Circle Any circle on the surface of the celestial sphere whose plane passes through the center of the celestial sphere is called a great circle For example the celestial equator is a great circl
27. l allow for astronomic observation regardless of the observer s location or the time of night b Polaris should always be used when it is visible Polaris is the most desirable star to observe because it is usually easy to locate and because its slow apparent motion makes it easy to track Because of weather conditions ambient light line of sight barriers or the observer s latitude Polaris may not always be available In this case an east west star must be used East west stars must be selected based on their star rate and their position relative to the observer A Star Finder and Identifier will aid in selecting and identifying usable east west stars 8 18 Polaris a Orbit of Polaris Polaris appears to move in a small elliptical counterclockwise orbit about the celestial North Pole The size of this apparent orbit varies slightly with the observer s latitude at 35 N latitude its minor diameter is about 45 mils Because Polaris stays so close to the north celestial pole it is visible throughout the night in most of the northern hemisphere When the Polaris local hour angle is 0 or 12 hours the star is said to be in its upper or lower culmination respectively When the Polaris local hour angle is 6 or 18 hours it is said to be in its western or eastern elongation The small orbit of Polaris results in a very slow apparent motion so the star may be observed at any point in its orbit The least chance of error will occur
28. le to surveyors making Arty Astro the preferred method At the battery level the Hasty Astro Method of observation will be used and is discussed in Chapter 11 b Arty Astro Hour Angle Method In the Arty Astro Method using two sides and the included angle DRAFT solves the azimuth angle of the PZS triangle The sides are the polar distance and the Colatitude the angle is the local hour angle angle t In addition to the horizontal angle from an azimuth mark to the observed body three elements must be determined See Figure 8 25 1 Latitude of the observer to determine the side Colatitude 2 Declination of the observed body to determine the side polar distance 3 Accurate time of the observation to determine the local hour angle 8 13 Arty Astro Hour Angle Method Sun a General The Arty Astro Method may be used to determine azimuths from Sun observations The Arty Astro Method does not require the measurement of a vertical angle or temperature and the computations do not include a refraction or parallax correction This method was once referred to as the Hour Angle Method because the solution of the PZS triangle is dependent on solving the local hour angle b Position of the Sun For the Sun to be suitable for use with the Arty Astro Method it must not be within one hour of the observer s meridian It must be between 175 mils and 1300 mils preferably between 175 and 800 above the observer s meridian An
29. ngle and finally to the local hour angle More specifically this conversion can be performed as outlined below DRAFT Local mean time time zone correction Greenwich mean time equation of time for Oh daily change for portion of day Greenwich apparent time 12 hours Greenwich hour angle longitude local hour angle Greenwich Mean Time GMT The watch time of the observation is referred to as local mean time This watch time is standard time for the area of operation By applying a time zone correction the Greenwich mean time Zulu Time is obtained This step can be skipped if the watch is set to Zulu time See Figure 8 26 Greenwich Apparent Time GAT Greenwich apparent time GAT is the time that has elapsed since the last passage of the apparent sun over the lower transit of the Greenwich meridian GAT is obtained by applying the equation of time and the proportionate part of the daily change in the equation of time to the GMT Greenwich Hour Angle GHA The Greenwich hour angle GHA is the amount of time that has elapsed since the sun last crossed the Greenwich meridian therefore Greenwich apparent time is always 12 hours from the Greenwich hour angle To determine the Greenwich hour angle simply add or subtract 12 hours to or from the Greenwich apparent time remembering that the result must be between 0 and 24 hours Local Hour Angle LHA The local hour angle LHA of a celestial body is th
30. ough the Earth s atmosphere at a large angle of incidence the angle formed by the line of the light ray and a line which is perpendicular to the atmosphere will have a larger refraction correction than a ray of light passing through an area close to the observer s zenith Refraction of a body varies DRAFT according to the altitude vertical angle of the body above the horizon and the temperature For example refraction of a celestial body located on the observer s horizon 0 mils at a temperature of 70 is 10 26 mils refraction of a body located on the observer s zenith is O mils Refraction increases with an increase in barometric pressure and a decrease in temperature Refraction corrections are always negative See Figure 8 11 OBSERVED CELESTIAL BODY ATMOSPHERE ACTUAL o CELESTIAL BODY Figure 8 11 Refraction 3 Colatitude Colatitude is a segment of an hour circle known as the observer s meridian It is the arc length of the side of the PZS triangle from the celestial North Pole to the observer s zenith the PZ side It is determined by applying the observer s latitude to 90 In other words if the observer s latitude is north Figure 8 12 Colatitude the Colatitude equals 90 minus the observer s latitude if the observer s latitude is south the Colatitude equals 90 plus the observer s latitude See Figure 8 12 d Angles The three angles formed by the intersection of the three sid
31. ox RA Celestial Sphere Figure 8 5 Right Ascension and Declination 2 Declination Dec Declination is the arc distance measured from the celestial equator to the body along the hour circle of the star It can be north or south of the celestial equator and is usually expressed in terms of degrees minutes and seconds It can be expressed in terms of mils Declination can vary from 0 to 90 north or south of the celestial equator See Figure 8 5 8 4 Astronomic Triangle PZS Triangle a General The determination of an astronomic azimuth is dependent upon the solution of a spherical triangle located on the surface of the celestial sphere This triangle is referred to as the PZS triangle The method of astronomic observation determines the sides and vertices of the triangle to be solved b Vertices The PZS triangle has vertices at the celestial North Pole at the observer s Zenith and at the Star or Sun These vertices are the intersections of great circles that include the triangle s sides See Figure 8 6 Celestial P P North Pole Observer s Celestial Body Observer s Meridian Hour Circle of gt T Celestial Bod Observer s we estial Body Position __ gt Celestial Sphere Figure 8 6 Vertices of the PZS Triangle c Sides The sides of the PZS triangle are segments of great circles passing through any two of the vertices Therefore the sides are arcs and
32. rder accuracy In this method two sets of observations will be made one with the telescope in the direct mode the second in the reverse mode This method will minimize the effects of small pointing errors on the observed stations b Heading and Column Titles As with all field notes the first page of the recorder s notebook is the index The heading and column titles will be filled out as described below Note that except for the addition of column 6 MEAN everything else is the same as Sth order recording See Figure 8 35 1 The designation block should be filled in with ARTY ASTRO Sun or Star as the method of survey being conducted 2 The date block must be filled in with the date the fieldwork was performed This will be the date used in the computations 3 The heading of the right side of the page will be filled out the same as with traverse This heading will include the weather description T 2E serial number Party Chief COP name Instrument Operator IO name and Recorder RCDR name 4 The column titles under the heading will be labeled from left to right as follows a Column 1 STA to identify the occupied rear and forward stations If the forward station is a star the star name will be listed b Column 2 T to identify the telescope mode direct D or reverse R c Column 3 and 4 TIME h m s to designate the exact time the instrument operator announced TIP during the observations TIM
33. record the seconds minutes and then hours 24 hr format c When recording angles record the entire number then read the value back to the instrument operator d Record the closing angle and verify that the horizontal collimation error is within specifications 0 150 mils e If the azimuth is being computed in the field using the computer s internal clock the solution is part of the fieldwork and must therefore be included in the field recorder s book The solution is recorded in column 6 MEAN in the row listing the occupied station and is placed in parenthesis The azimuth DRAFT determined from the direct readings must equal the DESIGNATION _ ARTILLERY ASTRO SUN pare 4 DEC 49 90 azimuth from the reverse readings 0 150 mils See Figure 8 37 STATION MEAN OCS WT 4 After the second set is computed the solutions for the two sets are meaned The mean azimuth is recorded in column 6 MEAN in the center row of the three spaces between the two sets See Figure 8 37 5977 221 DESIGNATION ARTILLERY ASTRO SUN pare 4 DEC 49 90 STATION Figure 8 37 Field Data 4th Order For Arty Astro Figure 8 36 Field Data 4th Order For Arty Astro
34. s meridian the true azimuth is equal to 360 6400 mils minus the azimuth angle See Figure 8 15 Observer s Celestial Celestia Equator Celestial Sphere Figure 8 15 Azimuth Angle e If any three elements of the PZS triangle are known the other three elements of the PZS triangle can be determined by spherical trigonometry In the end the element that must be solved is the azimuth angle This angle is necessary to establish a true azimuth on the ground Figure 8 16 depicts the complete PZS triangle Figure 8 16 PZS Triangle 8 5 Time a General Since the celestial bodies are in constant motion with the apparent rotation of the celestial sphere the PZS triangle for each body is constantly changing In order to compute an astronomic azimuth the precise moment of each observation must be fixed in time as to fix the position of the observer with respect to the position of the vertices of the PZS triangle Because the rotation of the Earth is extremely constant it is an excellent timekeeper In the field of practical astronomy two classes of time are used solar time and sidereal time b Time References Both classes of time are based on one rotation of the Earth with respect to a reference point The reference point is the difference between the two time classes 1 Solar time is referenced to the Sun and a solar day is the amount of time necessary for two successive passes of the sun over a meridian of longit
35. st west stars Accurate time is available through radio time signals and GPS receivers i e PLGR MSGR SINCGARS d Solving the PZS Triangle The formula for solving the PZS triangle with star observations is the same as for the Sun The only difference in the computations is that sidereal time is used to determine the local hour angle In general terms the local hour angle is determined by converting the local mean time watch time to Greenwich mean time to Greenwich sidereal time to Greenwich hour angle and finally to the local hour angle as outlined below Local mean time time zone correction Greenwich mean time sidereal time for Oh GMT correction for GMT Greenwich sidereal time right ascension of the star Greenwich hour angle longitude local hour angle Greenwich Mean Time GMT The watch time of the observation is referred to as local mean time This watch time is standard time for the area of operation By applying a time zone correction see Figure 9 20 the Greenwich mean time Zulu Time is obtained This step can be skipped if the watch is set to Zulu time Greenwich Sidereal Time GST Greenwich sidereal time is the time elapsed since the vernal equinox last crossed the Greenwich meridian GST is obtained by applying the sidereal time at Oh GMT Army Ephemeris Table 2 and the correction for GMT Army Ephemeris Table 4 to the Greenwich mean time Greenwich Hour Angle GHA The Greenwi
36. the local time zone by 15 The result is the time zone correction in hours Add this correction to the LMT to determine GMT of the observation If this result is greater than 24 hours subtract 24 hours and add 1 day to obtain the Greenwich time and date 2 Eastern Hemisphere If the observer is located in the eastern hemisphere divide the value of the standard meridian of the local time zone by 15 The result is the time zone correction in hours Subtract this correction from the LMT to determine the GMT of the observation b Converting Greenwich Apparent Time GAT to GMT When the Marine artillery surveyor makes observations on the Sun he actually observes the apparent sun on the celestial sphere and not the mean sun on which his clock is based Consequently the surveyor must convert his Greenwich Apparent Time GAT to GMT This correction is contained within the Arty Astro program and need not be determined manually The correction is provided in Table 2 of the Army Ephemeris using the observation date as an entry argument The resultant equation of time see paragraph 8 6 d for zero hours GMT Oh and the daily change are used to determine a correction for the date and proportionate part of the day to be applied to the GMT of the observation 8 11 Determining the Local Hour Angle LHA and Angle t a Determining Local Hour Angle LHA 1 When the position of the apparent sun at the time of observation has been determin
37. tial circle setting is recorded in the horizontal angle column in the rear station direct reading row See Figure 8 34 2 The T telescope column will be filled out as shown in Figure 8 36 The rear station AzMk name will be recorded in the direct D mode row directly below the STA column title Skip one line to record the occupied station name Skip one line to record the forward station celestial body name to the left of the first direct pointing on the body If the celestial body is a star the star name must be recorded DRAFT pesavon _ARTILLERY ASTRO SUN owe 4 DEC 19 90 Figure 8 34 Field Data 5th Order For Arty Astro 3 When recording times record the seconds minutes and then hours 24 hr format 4 When recording angles record the entire number then read the value back to the instrument operator 5 Record the closing angle and verify that the horizontal collimation error is within specifications 0 150 mils 6 If the azimuth is being computed in the field using the computer s internal clock the solution is part of the fieldwork and must therefore be included in the field recorder s book The solution is recorded in column 6 in the row listing the occupied station and is circled See Figure 8 34 8 24 Recording Arty Astro Method Field Notes 4th order a General The procedures listed below for recording Arty Astro Method astronomic observations will be used for 4th o
38. time zone including the Prime Meridian extends from 7 5 E longitude to 7 5 W longitude and the time zone with a standard meridian at 90 W longitude extends from 97 5 W to 82 5 W Four of these meridians 75 90 105 and 120 cross the US See Figure 9 21 DRAFT Figure 9 20 Time and Apparent Motion of the Sun d Standard time zone boundaries are often irregular especially over land areas Time zones generally follow the 7 5 boundary rule except when those boundaries are shifted to conform to geographical or political boundaries For example Ft Sill OK lies closer to the 105 W standard meridian but for political boundary purposes all of Oklahoma is located in the time zone using the 90 W standard meridian Artillery surveyors use the term local mean time LMT in referring to standard time or local time in a referenced locale In other words the time used by the local inhabitants is local mean time unless a non standard time is in use 97 30 W 90 W 82 30 W Standard Meridian 7 30 W 7 30 E T wan O 91 Min Tann Danm dantan Pacific Mountain Central Eastern Time Time Time Time Figure 8 22 Political Time Zones in the US e To preclude the problem of compiling and publishing time data for each of the 24 time zones data was computed pertaining to one standard time zone Standard time zone Z which uses the Greenwich Meridian as a Standard Meridian was chosen
39. to the Celestial North Pole 5 When a pointing is made on Polaris the observer will see two other stars nearby which are not visible to the naked eye However when the reticle pattern in the telescope is illuminated Polaris will be the only visible star 8 19 Star Rate If Polaris is not visible an east west star may be observed East west stars should be selected according to their star rate Resulting Azimuth Error Apparent Path of Star Vertical Measurement Error Figure 9 30 High Star Rate a The apparent motion of a celestial body has two measurable components a horizontal motion change in azimuth and a vertical motion change in altitude The star rate of the body is equal to the ratio between the two components In other words when a mil error in the vertical angle causes an azimuth error of 3 mils the star rate is 3 When observing a star that moves at a small angle relative to the horizon a small error in vertical angle will result in a large error in azimuth When observing a star that moves at a large angle relative to the horizon an error in vertical angle will result in a smaller error in azimuth See figures 8 30 and 8 31 Resulting Azimuth Error 4 Apparent Path of Star Vertical Measurement Error Figure 8 31 Low Star Rate b The star rate of a celestial body is largely dependent on the observer s latitude Because vertical angles are not meas
40. ude 2 Sidereal time is referenced to the stars and a sidereal day is the amount of time necessary for two successive passes of the vernal equinox over a meridian of longitude 3 Figure 8 17 shows the relationship between solar time and sidereal time Since there are approximately 365 days in a year it can be said that the Earth moves nearly 1 of its 360 orbit around the sun in one day Note that the Earth must rotate nearly a full degree more for a successive pass of a meridian in a solar day than it has to in a sidereal day This creates an apparent motion of the Sun among the stars of nearly 1 In practical astronomy with the Earth fixed and the celestial sphere rotating about the Earth intervals between transits of the Sun over the observer s meridian are nearly 4 minutes longer than transits of the vernal equinox over the observer s meridian In other words one 24 hour sidereal day is equal to 23h 56m 04 09 1s of a solar day c One apparent rotation of the celestial sphere is completed in a sidereal day therefore a star rises at nearly the same sidereal time throughout the year On solar time it rises about 4 minutes earlier from night to night or two hours earlier each month Thus at the same hour day by day the star moves slowly westward across the sky as the year lengthens DRAFT Figure 8 17 Relationship between Solar Time and Sidereal Time 8 6 Solar Time a General The solar day is considered the most n
41. ude therefore the vertical Figure 8 28 Identification of Polaris angle to Polaris is approximately equal to observer s latitude a Because the celestial sphere and therefore the celestial North Pole is an infinite distance from the Earth the line to the celestial North Pole from the observer can be considered the same as the line of the rotational axis of the Earth and celestial sphere Angle A represents the observer s latitude angle B the vertical angle to the celestial North Pole The laws of geometry prove that since the observer s zenith is perpendicular to the observer s horizon and since the line to the celestial north pole is perpendicular to the plane of the celestial equator angles A and B must be equal See Figure 8 29 b When the observer s latitude in mils is subtracted from 1600 mils the result is the vertical reading to the celestial north pole angle C in Figure 8 29 When that vertical reading is set on the vertical scale of the theodolite in the direct mode Polaris will appear in the field of view If the star is at elongation its vertical angle is equal to the observer s latitude When Polaris is moving from eastern to western elongation its vertical angle is greater than the observer s latitude when Polaris is moving from western to eastern elongation its vertical angle is less than the observer s latitude DRAFT Figure 8 29 Relationship Between the Observer s Latitude and the Vertical Angle
42. uired ephemeris data and time calculations are completed within the program and do not require any manual computation 8 14 Arty Astro Hour Angle Method Star a General The Arty Astro Method may be used to determine azimuths from observations on any of the 73 survey stars Observations of the stars are generally considered to be preferred over those or the Sun due to more accurate sighting The preferred star for this method in the Northern Hemisphere is Polaris as it displays the least apparent motion being a circumpolar star In the Southern hemisphere the preferred star is Alpha Acrux The Arty Astro Method does not require the measurements of a vertical angle or a temperature and the computations do not include a refraction or parallax correction This method was once referred to as the Hour Angle Method because the solution of the PZS triangle is dependent on solving the local hour angle b Position of the Stars Polaris may be observed any time it is visible but best results are obtained when it is 175 mils or higher above the observer s horizon East west stars can be selected by using the star finder and star rate template The 175 mil restriction minimizes the effects of refraction c Time In the Arty Astro Method star time is critical to the accurate determination of the local hour angle For this reason time must be accurate to 10 DRAFT seconds for observations on Polaris and 1 second for observations on ea
43. uly c Mean Solar Time 1 Because a more consistent measure of time is needed a fictitious sun moving at a uniform rate along the celestial equator was computed from the average apparent solar time Time measured by the position of the mean sun is referred to as Mean Solar Time Mean solar time is numbered from 0 24 uniform hours with each hour consisting of 15 of arc or longitude 360 x 24h 15 h Solar noon occurs when the mean sun crosses the observer s meridian 2 Mean solar time for any point is the amount of time that has elapsed since the mean sun last crossed the meridian at that point Greenwich Mean Time GMT is the amount of time that has elapsed since the mean sun last crossed the lower transit of the Greenwich Meridian 180 long Local Mean Time LMT is the amount of time that has elapsed since the mean sun last crossed the lower transit of the observer s meridian solar midnight See Figure 8 18 d Equation of Time The difference between apparent solar time and mean solar time is called the Equation of Time This value can vary from plus 16 minutes mean sun slow to minus 14 minutes mean sun fast depending on the season e Solar Year A year can be defined as one complete revolution of the Earth around the Sun A solar year is defined by 365 2422 mean solar days and can be referred to as a tropical year DRAFT 180 Long 0 hour GMT Celestial 90 W 0 hour 90 E Long LMT Long
44. ured in the Arty Astro method any east west star can be observed However bodies with a low star rate also have a smaller apparent horizontal motion therefore those stars with a low star rate are preferred because they are easier to track Even though Polaris has a high star rate in its culmination its apparent motion is slow so it can be observed any time it is visible with the Arty Astro method Stars below 175 mils in vertical angle even those with a low star rate must not be observed because of the increased effects of refraction c Appendix E includes star rate charts that can be used to select stars based on their star rate The chart used should be the one closest to the latitude of the user and will be the same latitude as the template of the star finder and identifier The areas marked on the charts are as follows 1 Block A Star rates from 0 0 5 The dotted line represents a rate of zero These are the most desirable stars 2 Block B Star rates from 0 5 1 0 These are the second most desirable 3 Block C Star rates from 1 0 3 0 4 Block D Star rates over 3 0 These stars can be used for Arty Astro in extreme cases 5 Star rates above 60 altitude are not listed and stars located in that area should not be used DRAFT 8 20 Star Finder and Identifier a General The star finder and identifier is a device used to determine the approximate 2 azimuth and altitude of selected stars b Base
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