[rv, pv] = ERFA.plan94(date1, date2, np)Approximate heliocentric position and velocity of a nominated major planet: Mercury, Venus, EMB, Mars, Jupiter, Saturn, Uranus or Neptune (but not the Earth itself).
n.b. Not IAU-endorsed and without canonical status.
date1 double TDB date part A (Note 1)
date2 double TDB date part B (Note 1)
np int planet (1=Mercury, 2=Venus, 3=EMB, 4=Mars,
5=Jupiter, 6=Saturn, 7=Uranus, 8=Neptune)
pv double[2][3] planet p,v (heliocentric, J2000.0, au,au/d)
int status: -1 = illegal NP (outside 1-8)
0 = OK
+1 = warning: year outside 1000-3000
+2 = warning: failed to converge
- The date date1+date2 is in the TDB time scale (in practice TT can be used) and is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TDB)=2450123.7 could be expressed in any of these ways, among others:
date1 date2
2450123.7 0.0 (JD method)
2451545.0 -1421.3 (J2000 method)
2400000.5 50123.2 (MJD method)
2450123.5 0.2 (date & time method)
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience. The limited accuracy of the present algorithm is such that any of the methods is satisfactory.
-
If an np value outside the range 1-8 is supplied, an error status (function value -1) is returned and the pv vector set to zeroes.
-
For np=3 the result is for the Earth-Moon Barycenter. To obtain the heliocentric position and velocity of the Earth, use instead the ERFA function eraEpv00.
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On successful return, the array pv contains the following:
pv[0][0] x }
pv[0][1] y } heliocentric position, au
pv[0][2] z }
pv[1][0] xdot }
pv[1][1] ydot } heliocentric velocity, au/d
pv[1][2] zdot }
The reference frame is equatorial and is with respect to the mean equator and equinox of epoch J2000.0.
- The algorithm is due to J.L. Simon, P. Bretagnon, J. Chapront, M. Chapront-Touze, G. Francou and J. Laskar (Bureau des Longitudes, Paris, France). From comparisons with JPL ephemeris DE102, they quote the following maximum errors over the interval 1800-2050:
L (arcsec) B (arcsec) R (km)
Mercury 4 1 300
Venus 5 1 800
EMB 6 1 1000
Mars 17 1 7700
Jupiter 71 5 76000
Saturn 81 13 267000
Uranus 86 7 712000
Neptune 11 1 253000
Over the interval 1000-3000, they report that the accuracy is no worse than 1.5 times that over 1800-2050. Outside 1000-3000 the accuracy declines.
Comparisons of the present function with the JPL DE200 ephemeris give the following RMS errors over the interval 1960-2025:
position (km) velocity (m/s)
Mercury 334 0.437
Venus 1060 0.855
EMB 2010 0.815
Mars 7690 1.98
Jupiter 71700 7.70
Saturn 199000 19.4
Uranus 564000 16.4
Neptune 158000 14.4
Comparisons against DE200 over the interval 1800-2100 gave the following maximum absolute differences. (The results using DE406 were essentially the same.)
L (arcsec) B (arcsec) R (km) Rdot (m/s)
Mercury 7 1 500 0.7
Venus 7 1 1100 0.9
EMB 9 1 1300 1.0
Mars 26 1 9000 2.5
Jupiter 78 6 82000 8.2
Saturn 87 14 263000 24.6
Uranus 86 7 661000 27.4
Neptune 11 2 248000 21.4
- The present ERFA re-implementation of the original Simon et al. Fortran code differs from the original in the following respects:
* C instead of Fortran.
* The date is supplied in two parts.
* The result is returned only in equatorial Cartesian form;
the ecliptic longitude, latitude and radius vector are not
returned.
* The result is in the J2000.0 equatorial frame, not ecliptic.
* More is done in-line: there are fewer calls to subroutines.
* Different error/warning status values are used.
* A different Kepler's-equation-solver is used (avoiding
use of double precision complex).
* Polynomials in t are nested to minimize rounding errors.
* Explicit double constants are used to avoid mixed-mode
expressions.
None of the above changes affects the result significantly.
- The returned status indicates the most serious condition encountered during execution of the function. Illegal np is considered the most serious, overriding failure to converge, which in turn takes precedence over the remote date warning.
eraAnpm normalize angle into range +/- pi
Reference: Simon, J.L, Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., and Laskar, J., Astron.Astrophys., 282, 663 (1994).
This revision: 2021 May 11
Copyright (C) 2013-2021, NumFOCUS Foundation. Derived, with permission, from the SOFA library.