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| author | Joseph Hunkeler <jhunkeler@gmail.com> | 2015-03-04 21:21:30 -0500 |
|---|---|---|
| committer | Joseph Hunkeler <jhunkeler@gmail.com> | 2015-03-04 21:21:30 -0500 |
| commit | d54fe7c1f704a63824c5bfa0ece65245572e9b27 (patch) | |
| tree | afc52015ffc2c74e0266653eecef1c8ef8ba5d91 /src/slalib/sun67.htx/node224.html | |
| download | calfuse-d54fe7c1f704a63824c5bfa0ece65245572e9b27.tar.gz | |
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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 @@ +<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN"> +<!--Converted with LaTeX2HTML 97.1 (release) (July 13th, 1997) + by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds +* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan +* with significant contributions from: + Jens Lippman, Marek Rouchal, Martin Wilck and others --> +<HTML> +<HEAD> +<TITLE>Ephemerides</TITLE> +<META NAME="description" CONTENT="Ephemerides"> +<META NAME="keywords" CONTENT="sun67"> +<META NAME="resource-type" CONTENT="document"> +<META NAME="distribution" CONTENT="global"> +<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso_8859_1"> +<LINK REL="STYLESHEET" HREF="sun67.css"> +<LINK REL="next" HREF="node225.html"> +<LINK REL="previous" HREF="node223.html"> +<LINK REL="up" HREF="node197.html"> +<LINK REL="next" HREF="node225.html"> +</HEAD> +<BODY > +<BR> <HR> +<A NAME="tex2html2693" HREF="node225.html"> +<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A> +<A NAME="tex2html2691" HREF="node197.html"> +<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A> +<A NAME="tex2html2685" HREF="node223.html"> +<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="previous_motif.gif"></A> <A HREF="sun67.html#stardoccontents"><IMG ALIGN="BOTTOM" BORDER="0" + SRC="contents_motif.gif"></A> +<BR> +<B> Next:</B> <A NAME="tex2html2694" HREF="node225.html">Radial Velocity and Light-Time Corrections</A> +<BR> +<B>Up:</B> <A NAME="tex2html2692" HREF="node197.html">EXPLANATION AND EXAMPLES</A> +<BR> +<B> Previous:</B> <A NAME="tex2html2686" HREF="node223.html">Geocentric Coordinates</A> +<BR> <HR> <P> +<P><!--End of Navigation Panel--> +<H2><A NAME="SECTION000518000000000000000"> +Ephemerides</A> +</H2> +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. +<P> +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 <IMG WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0" + SRC="img316.gif" + ALT="$2\hspace{-0.05em}^{'\hspace{-0.1em}'}$">), 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.) +<P> +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 (<IMG WIDTH="17" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img131.gif" + ALT="$5\hspace{-0.05em}^{'\hspace{-0.1em}'}$">) and distance accuracy a little worse. +<P> +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 <IMG WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img82.gif" + ALT="$30\hspace{-0.05em}^{'\hspace{-0.1em}'}$"> in direction +and 1000 km in distance. +<P> +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 <IMG WIDTH="39" HEIGHT="25" ALIGN="MIDDLE" BORDER="0" + SRC="img317.gif" + ALT="$\pm100$"> years for Pluto). +The routine +sla_PLANET produces heliocentric position and +velocity in the form of equatorial <IMG WIDTH="106" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img51.gif" + ALT="$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$"> 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 <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img3.gif" + ALT="$[\,\alpha,\delta\,]$"> and angular size as seen by a +terrestrial observer. +<P> +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 <I>essential</I> in the case of the Moon, where the observer's +position on the Earth can affect the Moon's <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img3.gif" + ALT="$[\,\alpha,\delta\,]$"> by up to +<IMG WIDTH="18" HEIGHT="13" ALIGN="BOTTOM" BORDER="0" + SRC="img318.gif" + ALT="$1^\circ$">. 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: +<P><PRE> + * 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 +</PRE> +<P> +The output produced is as follows: +<P><PRE> + geocentric: +03 06 55.59 +15 03 39.0 + topocentric: +03 09 23.79 +15 40 51.5 +</PRE> +<P>(An easier but +less instructive method of estimating the topocentric apparent place of the +Moon is to call the routine +sla_RDPLAN.) +<P> +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: +<P><PRE> + * 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 +</PRE> +<P> +The output produced (the Ephemeris Time on the day in question, and +the closest approach in arcseconds) is as follows: +<P><PRE> + 21:19 33.7 +</PRE> +<P> +For comparison, accurate predictions based on the JPL DE102 ephemeris +give a separation about <IMG WIDTH="17" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img319.gif" + ALT="$8\hspace{-0.05em}^{'\hspace{-0.1em}'}$"> less than +the above estimate, occurring about half an hour earlier +(see <I>Sky and Telescope,</I> April 1987, p357). +<P> +The following program demonstrates +sla_RDPLAN. +<PRE> + * 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 +</PRE> +Entering the following data (for 1927 June 29 at <IMG WIDTH="49" HEIGHT="17" ALIGN="BOTTOM" BORDER="0" + SRC="img320.gif" + ALT="$5^{\rm h}\,25^{\rm m}$"> ET +and the position of Preston, UK.): +<PRE> + 1927 6 29 + 5 25 + -2 42 + 53 46 +</PRE> +produces the following report: +<PRE> + 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 +</PRE> +Inspection of the Sun and Moon data reveals that +a total solar eclipse is in progress. +<P> +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. +<P> +The SLALIB planetary-prediction +routines that work with orbital elements are +sla_PLANTE (the orbital-elements equivalent of +sla_RDPLAN), which predicts the topocentric <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img3.gif" + ALT="$[\,\alpha,\delta\,]$">, and +sla_PLANEL (the orbital-elements equivalent of +sla_PLANET), which predicts the heliocentric <IMG WIDTH="106" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img51.gif" + ALT="$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$"> with respect to the +J2000 equinox and equator. In addition, the routine +sla_PV2EL does the inverse of +sla_PLANEL, transforming <IMG WIDTH="106" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img51.gif" + ALT="$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$"> into <I>osculating elements.</I> +<P> +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. +<P> +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 <TT>JFORM</TT>: +<BR> +<P><TABLE CELLPADDING=3 BORDER="1"> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><TT>JFORM=1</TT></TD> +<TD ALIGN="CENTER" NOWRAP><TT>JFORM=2</TT></TD> +<TD ALIGN="CENTER" NOWRAP><TT>JFORM=3</TT></TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><I>t<SUB>0</SUB></I></TD> +<TD ALIGN="CENTER" NOWRAP><I>t<SUB>0</SUB></I></TD> +<TD ALIGN="CENTER" NOWRAP><I>T</I></TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><I>i</I></TD> +<TD ALIGN="CENTER" NOWRAP><I>i</I></TD> +<TD ALIGN="CENTER" NOWRAP><I>i</I></TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><IMG WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0" + SRC="img99.gif" + ALT="$\Omega$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0" + SRC="img99.gif" + ALT="$\Omega$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0" + SRC="img99.gif" + ALT="$\Omega$"></TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><IMG WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img100.gif" + ALT="$\varpi$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img101.gif" + ALT="$\omega$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img101.gif" + ALT="$\omega$"></TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><I>a</I></TD> +<TD ALIGN="CENTER" NOWRAP><I>a</I></TD> +<TD ALIGN="CENTER" NOWRAP><I>q</I></TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><I>e</I></TD> +<TD ALIGN="CENTER" NOWRAP><I>e</I></TD> +<TD ALIGN="CENTER" NOWRAP><I>e</I></TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><I>L</I></TD> +<TD ALIGN="CENTER" NOWRAP><I>M</I></TD> +<TD ALIGN="CENTER" NOWRAP> </TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><I>n</I></TD> +<TD ALIGN="CENTER" NOWRAP> </TD> +<TD ALIGN="CENTER" NOWRAP> </TD> +</TR> +</TABLE> +<BR> +<BR> +<BR> +<BR> +<BR> +<BR> +The symbols have the following meanings: +<PRE><TT> + <I>t<SUB>0</SUB></I> epoch at which the elements were correct + <I>T</I> epoch of perihelion passage + <I>i</I> inclination of the orbit + <IMG WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0" + SRC="img99.gif" + ALT="$\Omega$"> longitude of the ascending node + <IMG WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img100.gif" + ALT="$\varpi$"> longitude of perihelion (<IMG WIDTH="81" HEIGHT="27" ALIGN="MIDDLE" BORDER="0" + SRC="img321.gif" + ALT="$\varpi = \Omega + \omega$">) <IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img101.gif" + ALT="$\omega$"> argument of perihelion + <I>a</I> semi-major axis of the orbital ellipse + <I>q</I> perihelion distance + <I>e</I> orbital eccentricity + <I>L</I> mean longitude (<IMG WIDTH="87" HEIGHT="27" ALIGN="MIDDLE" BORDER="0" + SRC="img322.gif" + ALT="$L = \varpi + M$">) <I>M</I> mean anomaly + <I>n</I> mean motion +</TT></PRE> +<P> +The mean motion, <I>n</I>, tells sla_PLANEL the mass of the planet. +If it is not available, it should be claculated +from <I>n<SUP>2</SUP></I> <I>a<SUP>3</SUP></I> = <I>k<SUP>2</SUP></I> (1+<I>m</I>), where <I>k</I> = 0.01720209895 and +m is the mass of the planet (<IMG WIDTH="59" HEIGHT="27" ALIGN="MIDDLE" BORDER="0" + SRC="img323.gif" + ALT="$M_\odot = 1$">); <I>a</I> is in AU. +<P> +Conventional elements are not the only way of specifying an orbit. +The <IMG WIDTH="106" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img51.gif" + ALT="$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$"> state vector is an equally valid specification, +and the so-called <I>method of universal variables</I> 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. +<P> +The universal elements are the <IMG WIDTH="106" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img51.gif" + ALT="$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$"> 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. +<P> +The routines +sla_EL2UE and +sla_UE2EL transform conventional elements into the +universal form and <I>vice versa.</I> +The routine +sla_PV2UE takes an <IMG WIDTH="106" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img51.gif" + ALT="$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$"> and forms the set of universal +elements; +sla_UE2PV takes a set of universal elements and predicts the <IMG WIDTH="106" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img51.gif" + ALT="$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$"> for a specified epoch. +The routine +sla_PERTUE provides updated universal elements, +taking into account perturbations from the major planets. +<P> +<BR> <HR> +<A NAME="tex2html2693" HREF="node225.html"> +<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A> +<A NAME="tex2html2691" HREF="node197.html"> +<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A> +<A NAME="tex2html2685" HREF="node223.html"> +<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="previous_motif.gif"></A> <A HREF="sun67.html#stardoccontents"><IMG ALIGN="BOTTOM" BORDER="0" + SRC="contents_motif.gif"></A> +<BR> +<B> Next:</B> <A NAME="tex2html2694" HREF="node225.html">Radial Velocity and Light-Time Corrections</A> +<BR> +<B>Up:</B> <A NAME="tex2html2692" HREF="node197.html">EXPLANATION AND EXAMPLES</A> +<BR> +<B> Previous:</B> <A NAME="tex2html2686" HREF="node223.html">Geocentric Coordinates</A> +<BR> <HR> <P> +<P><!--End of Navigation Panel--> +<ADDRESS> +<I>SLALIB --- Positional Astronomy Library<BR>Starlink User Note 67<BR>P. T. Wallace<BR>12 October 1999<BR>E-mail:ptw@star.rl.ac.uk</I> +</ADDRESS> +</BODY> +</HTML> |