Ephemerides

From d54fe7c1f704a63824c5bfa0ece65245572e9b27 Mon Sep 17 00:00:00 2001 From: Joseph Hunkeler Date: Wed, 4 Mar 2015 21:21:30 -0500 Subject: Initial commit --- src/slalib/sun67.htx/node224.html | 617 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 617 insertions(+) create mode 100644 src/slalib/sun67.htx/node224.html (limited to 'src/slalib/sun67.htx/node224.html') diff --git a/src/slalib/sun67.htx/node224.html b/src/slalib/sun67.htx/node224.html new file mode 100644 index 0000000..4cb8678 --- /dev/null +++ b/src/slalib/sun67.htx/node224.html @@ -0,0 +1,617 @@ + + + + +Ephemerides + + + + + + + + + + + + +

+ +

+
+ Next: Radial Velocity and Light-Time Corrections +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Geocentric Coordinates +

+Ephemerides +

+SLALIB includes routines for generating positions and +velocities of Solar-System bodies. The accuracy objectives are +modest, and the SLALIB facilities do not attempt +to compete with precomputed ephemerides such as +those provided by JPL, or with models containing +thousands of terms. It is also worth noting +that SLALIB's very accurate star coordinate conversion +routines are not strictly applicable to solar-system cases, +though they are adequate for most practical purposes. +

+Earth/Sun ephemerides can be generated using the routine +sla_EVP, +which predicts Earth position and velocity with respect to both the +solar-system barycentre and the +Sun. Maximum velocity error is 0.42 metres per second; maximum +heliocentric position error is 1600 km (about $2\hspace{-0.05em}^{'\hspace{-0.1em}'}$ ), with +barycentric position errors about 4 times worse. +(The Sun's position as +seen from the Earth can, of course, be obtained simply by +reversing the signs of the Cartesian components of the +Earth:Sun vector.) +

+Geocentric Moon ephemerides are available from +sla_DMOON, +which predicts the Moon's position and velocity with respect to +the Earth's centre. Direction accuracy is usually better than +10 km ( $5\hspace{-0.05em}^{'\hspace{-0.1em}'}$ ) and distance accuracy a little worse. +

+Lower-precision but faster predictions for the Sun and Moon +can be made by calling +sla_EARTH +and +sla_MOON. +Both are single precision and accept dates in the form of +year, day-in-year and fraction of day +(starting from a calendar date you need to call +sla_CLYD +or +sla_CALYD +to get the required year and day). +The +sla_EARTH +routine returns the heliocentric position and velocity +of the Earth's centre for the mean equator and +equinox of date. The accuracy is better than 20,000 km in position +and 10 metres per second in speed. +The +position and velocity of the Moon with respect to the +Earth's centre for the mean equator and ecliptic of date +can be obtained by calling +sla_MOON. +The positional accuracy is better than $30\hspace{-0.05em}^{'\hspace{-0.1em}'}$ in direction +and 1000 km in distance. +

+Approximate ephemerides for all the major planets +can be generated by calling +sla_PLANET +or +sla_RDPLAN. These routines offer arcminute accuracy (much +better for the inner planets and for Pluto) over a span of several +millennia (but only $\pm100$ years for Pluto). +The routine +sla_PLANET produces heliocentric position and +velocity in the form of equatorial $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ for the +mean equator and equinox of J2000. The vectors +produced by +sla_PLANET +can be used in a variety of ways according to the +requirements of the application concerned. The routine +sla_RDPLAN +uses +sla_PLANET +and +sla_DMOON +to deal with the common case of predicting +a planet's apparent $[\,\alpha,\delta\,]$ and angular size as seen by a +terrestrial observer. +

+Note that in predicting the position in the sky of a solar-system body +it is necessary to allow for geocentric parallax. This correction +is essential in the case of the Moon, where the observer's +position on the Earth can affect the Moon's $[\,\alpha,\delta\,]$ by up to + $1^\circ$ . The calculation can most conveniently be done by calling +sla_PVOBS and subtracting the resulting 6-vector from the +one produced by +sla_DMOON, as is demonstrated by the following example: +

+      *  Demonstrate the size of the geocentric parallax correction
+      *  in the case of the Moon.  The test example is for the AAT,
+      *  before midnight, in summer, near first quarter.
+
+            IMPLICIT NONE
+            CHARACTER NAME*40,SH,SD
+            INTEGER J,I,IHMSF(4),IDMSF(4)
+            DOUBLE PRECISION SLONGW,SLAT,H,DJUTC,FDUTC,DJUT1,DJTT,STL,
+           :                 RMATN(3,3),PMM(6),PMT(6),RM,DM,PVO(6),TL
+            DOUBLE PRECISION sla_DTT,sla_GMST,sla_EQEQX,sla_DRANRM
+
+      *  Get AAT longitude and latitude in radians and height in metres
+            CALL sla_OBS(0,'AAT',NAME,SLONGW,SLAT,H)
+
+      *  UTC (1992 January 13, 11 13 59) to MJD
+            CALL sla_CLDJ(1992,1,13,DJUTC,J)
+            CALL sla_DTF2D(11,13,59.0D0,FDUTC,J)
+            DJUTC=DJUTC+FDUTC
+
+      *  UT1 (UT1-UTC value of -0.152 sec is from IERS Bulletin B)
+            DJUT1=DJUTC+(-0.152D0)/86400D0
+
+      *  TT
+            DJTT=DJUTC+sla_DTT(DJUTC)/86400D0
+
+      *  Local apparent sidereal time
+            STL=sla_GMST(DJUT1)-SLONGW+sla_EQEQX(DJTT)
+
+      *  Geocentric position/velocity of Moon (mean of date)
+            CALL sla_DMOON(DJTT,PMM)
+
+      *  Nutation to true equinox of date
+            CALL sla_NUT(DJTT,RMATN)
+            CALL sla_DMXV(RMATN,PMM,PMT)
+            CALL sla_DMXV(RMATN,PMM(4),PMT(4))
+
+      *  Report geocentric HA,Dec
+            CALL sla_DCC2S(PMT,RM,DM)
+            CALL sla_DR2TF(2,sla_DRANRM(STL-RM),SH,IHMSF)
+            CALL sla_DR2AF(1,DM,SD,IDMSF)
+            WRITE (*,'(1X,'' geocentric:'',2X,A,I2.2,2I3.2,''.'',I2.2,'//
+           :                              '1X,A,I2.2,2I3.2,''.'',I1)')
+           :                                                SH,IHMSF,SD,IDMSF
+
+      *  Geocentric position of observer (true equator and equinox of date)
+            CALL sla_PVOBS(SLAT,H,STL,PVO)
+
+      *  Place origin at observer
+            DO I=1,6
+               PMT(I)=PMT(I)-PVO(I)
+            END DO
+
+      *  Allow for planetary aberration
+            TL=499.004782D0*SQRT(PMT(1)**2+PMT(2)**2+PMT(3)**2)
+            DO I=1,3
+               PMT(I)=PMT(I)-TL*PMT(I+3)
+            END DO
+
+      *  Report topocentric HA,Dec
+            CALL sla_DCC2S(PMT,RM,DM)
+            CALL sla_DR2TF(2,sla_DRANRM(STL-RM),SH,IHMSF)
+            CALL sla_DR2AF(1,DM,SD,IDMSF)
+            WRITE (*,'(1X,''topocentric:'',2X,A,I2.2,2I3.2,''.'',I2.2,'//
+           :                              '1X,A,I2.2,2I3.2,''.'',I1)')
+           :                                                SH,IHMSF,SD,IDMSF
+            END
+

+The output produced is as follows: +

+       geocentric:  +03 06 55.59 +15 03 39.0
+      topocentric:  +03 09 23.79 +15 40 51.5
+

(An easier but +less instructive method of estimating the topocentric apparent place of the +Moon is to call the routine +sla_RDPLAN.) +

+As an example of using +sla_PLANET, +the following program estimates the geocentric separation +between Venus and Jupiter during a close conjunction +in 2BC, which is a star-of-Bethlehem candidate: +

+      *  Compute time and minimum geocentric apparent separation
+      *  between Venus and Jupiter during the close conjunction of 2 BC.
+
+            IMPLICIT NONE
+
+            DOUBLE PRECISION SEPMIN,DJD0,FD,DJD,DJDM,DF,PV(6),RMATP(3,3),
+           :                 PVM(6),PVE(6),TL,RV,DV,RJ,DJ,SEP
+            INTEGER IHOUR,IMIN,J,I,IHMIN,IMMIN
+            DOUBLE PRECISION sla_EPJ,sla_DSEP
+
+
+      *  Search for closest approach on the given day
+            DJD0=1720859.5D0
+            SEPMIN=1D10
+            DO IHOUR=20,22
+               DO IMIN=0,59
+                  CALL sla_DTF2D(IHOUR,IMIN,0D0,FD,J)
+
+      *        Julian date and MJD
+                  DJD=DJD0+FD
+                  DJDM=DJD-2400000.5D0
+
+      *        Earth to Moon (mean of date)
+                  CALL sla_DMOON(DJDM,PV)
+
+      *        Precess Moon position to J2000
+                  CALL sla_PRECL(sla_EPJ(DJDM),2000D0,RMATP)
+                  CALL sla_DMXV(RMATP,PV,PVM)
+
+      *        Sun to Earth-Moon Barycentre (mean J2000)
+                  CALL sla_PLANET(DJDM,3,PVE,J)
+
+      *        Correct from EMB to Earth
+                  DO I=1,3
+                     PV(I)=PVE(I)-0.012150581D0*PVM(I)
+                  END DO
+
+      *        Sun to Venus
+                  CALL sla_PLANET(DJDM,2,PV,J)
+
+      *        Earth to Venus
+                  DO I=1,6
+                     PV(I)=PV(I)-PVE(I)
+                  END DO
+
+      *        Light time to Venus (sec)
+                  TL=499.004782D0*SQRT((PV(1)-PVE(1))**2+
+           :                           (PV(2)-PVE(2))**2+
+           :                           (PV(3)-PVE(3))**2)
+
+      *        Extrapolate backwards in time by that much
+                  DO I=1,3
+                     PV(I)=PV(I)-TL*PV(I+3)
+                  END DO
+
+      *       To RA,Dec
+                  CALL sla_DCC2S(PV,RV,DV)
+
+      *        Same for Jupiter
+                  CALL sla_PLANET(DJDM,5,PV,J)
+                  DO I=1,6
+                     PV(I)=PV(I)-PVE(I)
+                  END DO
+                  TL=499.004782D0*SQRT((PV(1)-PVE(1))**2+
+           :                           (PV(2)-PVE(2))**2+
+           :                           (PV(3)-PVE(3))**2)
+                  DO I=1,3
+                     PV(I)=PV(I)-TL*PV(I+3)
+                  END DO
+                  CALL sla_DCC2S(PV,RJ,DJ)
+
+      *        Separation (arcsec)
+                  SEP=sla_DSEP(RV,DV,RJ,DJ)
+
+      *        Keep if smallest so far
+                  IF (SEP.LT.SEPMIN) THEN
+                     IHMIN=IHOUR
+                     IMMIN=IMIN
+                     SEPMIN=SEP
+                  END IF
+               END DO
+            END DO
+
+      *  Report
+            WRITE (*,'(1X,I2.2,'':'',I2.2,F6.1)') IHMIN,IMMIN,
+           :                                      206264.8062D0*SEPMIN
+
+            END
+

+The output produced (the Ephemeris Time on the day in question, and +the closest approach in arcseconds) is as follows: +

+      21:19  33.7
+

+For comparison, accurate predictions based on the JPL DE102 ephemeris +give a separation about $8\hspace{-0.05em}^{'\hspace{-0.1em}'}$ less than +the above estimate, occurring about half an hour earlier +(see Sky and Telescope, April 1987, p357). +

+The following program demonstrates +sla_RDPLAN. +

+      *  For a given date, time and geographical location, output
+      *  a table of planetary positions and diameters.
+
+            IMPLICIT NONE
+            CHARACTER PNAMES(0:9)*7,B*80,S
+            INTEGER I,NP,IY,J,IM,ID,IHMSF(4),IDMSF(4)
+            DOUBLE PRECISION R2AS,FD,DJM,ELONG,PHI,RA,DEC,DIAM
+            PARAMETER (R2AS=206264.80625D0)
+            DATA PNAMES / 'Sun','Mercury','Venus','Moon','Mars','Jupiter',
+           :              'Saturn','Uranus','Neptune', 'Pluto' /
+
+
+      *  Loop until 'end' typed
+            B=' '
+            DO WHILE (B.NE.'END'.AND.B.NE.'end')
+
+      *     Get date, time and observer's location
+               PRINT *,'Date? (Y,M,D, Gregorian)'
+               READ (*,'(A)') B
+               IF (B.NE.'END'.AND.B.NE.'end') THEN
+                  I=1
+                  CALL sla_INTIN(B,I,IY,J)
+                  CALL sla_INTIN(B,I,IM,J)
+                  CALL sla_INTIN(B,I,ID,J)
+                  PRINT *,'Time? (H,M,S, dynamical)'
+                  READ (*,'(A)') B
+                  I=1
+                  CALL sla_DAFIN(B,I,FD,J)
+                  FD=FD*2.3873241463784300365D0
+                  CALL sla_CLDJ(IY,IM,ID,DJM,J)
+                  DJM=DJM+FD
+                  PRINT *,'Longitude? (D,M,S, east +ve)'
+                  READ (*,'(A)') B
+                  I=1
+                  CALL sla_DAFIN(B,I,ELONG,J)
+                  PRINT *,'Latitude? (D,M,S, (geodetic)'
+                  READ (*,'(A)') B
+                  I=1
+                  CALL sla_DAFIN(B,I,PHI,J)
+
+      *        Loop planet by planet
+                  DO NP=0,8
+
+      *           Get RA,Dec and diameter
+                     CALL sla_RDPLAN(DJM,NP,ELONG,PHI,RA,DEC,DIAM)
+
+      *           One line of report
+                     CALL sla_DR2TF(2,RA,S,IHMSF)
+                     CALL sla_DR2AF(1,DEC,S,IDMSF)
+                     WRITE (*,
+           : '(1X,A,2X,3I3.2,''.'',I2.2,2X,A,I2.2,2I3.2,''.'',I1,F8.1)')
+           :                          PNAMES(NP),IHMSF,S,IDMSF,R2AS*DIAM
+
+      *           Next planet
+                  END DO
+                  PRINT *,' '
+               END IF
+
+      *     Next case
+            END DO
+
+            END
+

+Entering the following data (for 1927 June 29 at $5^{\rm h}\,25^{\rm m}$ ET +and the position of Preston, UK.): +

+      1927 6 29
+      5 25
+      -2 42
+      53 46
+

+produces the following report: +

+      Sun       06 28 14.03  +23 17 17.5  1887.8
+      Mercury   08 08 58.62  +19 20 57.3     9.3
+      Venus     09 38 53.64  +15 35 32.9    22.8
+      Moon      06 28 18.30  +23 18 37.3  1903.9
+      Mars      09 06 49.34  +17 52 26.7     4.0
+      Jupiter   00 11 12.06  -00 10 57.5    41.1
+      Saturn    16 01 43.34  -18 36 55.9    18.2
+      Uranus    00 13 33.53  +00 39 36.0     3.5
+      Neptune   09 49 35.75  +13 38 40.8     2.2
+      Pluto     07 05 29.50  +21 25 04.2      .1
+

+Inspection of the Sun and Moon data reveals that +a total solar eclipse is in progress. +

+SLALIB also provides for the case where orbital elements (with respect +to the J2000 equinox and ecliptic) +are available. This allows predictions to be made for minor-planets and +(if you ignore non-gravitational effects) +comets. Furthermore, if major-planet elements for an epoch close to the date +in question are available, more accurate predictions can be made than +are offered by +sla_RDPLAN and +sla_PLANET. +

+The SLALIB planetary-prediction +routines that work with orbital elements are +sla_PLANTE (the orbital-elements equivalent of +sla_RDPLAN), which predicts the topocentric $[\,\alpha,\delta\,]$ , and +sla_PLANEL (the orbital-elements equivalent of +sla_PLANET), which predicts the heliocentric $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ with respect to the +J2000 equinox and equator. In addition, the routine +sla_PV2EL does the inverse of +sla_PLANEL, transforming $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ into osculating elements. +

+Osculating elements describe the unperturbed 2-body orbit. This is +a good approximation to the actual orbit for a few weeks either +side of the specified epoch, outside which perturbations due to +the other bodies of the Solar System lead to +increasing errors. Given a minor planet's osculating elements for +a particular date, predictions for a date even just +100 days earlier or later +are likely to be in error by several arcseconds. +These errors can +be reduced if new elements are generated which take account of +the perturbations of the major planets, and this is what the routine +sla_PERTEL does. Once +sla_PERTEL has been called, to provide osculating elements +close to the required date, the elements can be passed to +sla_PLANEL or +sla_PLANTE in the normal way. Predictions of arcsecond accuracy +over a span of a decade or more are available using this +technique. +

+Three different combinations of orbital elements are +provided for, matching the usual conventions +for major planets, minor planets and +comets respectively. The choice is made through the +argument JFORM: +
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
JFORM=1 JFORM=2 JFORM=3
t₀ t₀ T
i i i
$\Omega$ $\Omega$ $\Omega$
$\varpi$ $\omega$ $\omega$
a a q
e e e
L M
n
+
+
+
+
+
+
+The symbols have the following meanings: +


+		 t₀ epoch at which the elements were correct
+		 T epoch of perihelion passage
+		 i inclination of the orbit
+		  longitude of the ascending node
+		  longitude of perihelion ()		  argument of perihelion
+		 a semi-major axis of the orbital ellipse
+		 q perihelion distance
+		 e orbital eccentricity
+		 L mean longitude ()		 M mean anomaly
+		 n mean motion 
+

+The mean motion, n, tells sla_PLANEL the mass of the planet. +If it is not available, it should be claculated +from n² a³ = k² (1+m), where k = 0.01720209895 and +m is the mass of the planet ( $M_\odot = 1$ ); a is in AU. +

+Conventional elements are not the only way of specifying an orbit. +The $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ state vector is an equally valid specification, +and the so-called method of universal variables allows +orbital calculations to be made directly, bypassing angular +quantities and avoiding Kepler's Equation. The universal-variables +approach has various advantages, including better handling of +near-parabolic cases and greater efficiency. +SLALIB uses universal variables for its internal +calculations and also offers a number of routines which +applications can call. +

+The universal elements are the $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ and its epoch, plus the mass +of the body. The SLALIB routines supplement these elements with +certain redundant values in order to +avoid unnecessary recomputation when the elements are next used. +

+The routines +sla_EL2UE and +sla_UE2EL transform conventional elements into the +universal form and vice versa. +The routine +sla_PV2UE takes an $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ and forms the set of universal +elements; +sla_UE2PV takes a set of universal elements and predicts the $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ for a specified epoch. +The routine +sla_PERTUE provides updated universal elements, +taking into account perturbations from the major planets. +

+ +

+
+ Next: Radial Velocity and Light-Time Corrections +
+Up: EXPLANATION AND EXAMPLES +
+ Previous: Geocentric Coordinates +

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +

+ + -- cgit

`JFORM=1`	`JFORM=2`	`JFORM=3`
t₀	t₀	T
i	i	i
$\Omega$	$\Omega$	$\Omega$
$\varpi$	$\omega$	$\omega$
a	a	q
e	e	e
L	M
n