palPlanel

Transform conventional elements into position and velocity

Description:

Heliocentric position and velocity of a planet, asteroid or comet, starting from orbital elements.

Invocation

void palPlanel ( double date, int jform, double epoch, double orbinc, double anode, double perih, double aorq, double e, double aorl, double dm, double pv[6], int jstat );

Arguments

date = double (Given)
Epoch (TT MJD) of osculation (Note 1)
jform = int (Given)
Element set actually returned (1-3; Note 3)
epoch = double (Given)
Epoch of elements (TT MJD) (Note 4)
orbinc = double (Given)
inclination (radians)
anode = double (Given)
longitude of the ascending node (radians)
perih = double (Given)
longitude or argument of perihelion (radians)
aorq = double (Given)
mean distance or perihelion distance (AU)
e = double (Given)
eccentricity
aorl = double (Given)
mean anomaly or longitude (radians, JFORM=1,2 only)
dm = double (Given)
daily motion (radians, JFORM=1 only)
u = double [13] (Returned)
Universal orbital elements (Note 1) (0) combined mass (M+m) (1) total energy of the orbit (alpha) (2) reference (osculating) epoch (t0) (3-5) position at reference epoch (r0) (6-8) velocity at reference epoch (v0) (9) heliocentric distance at reference epoch (10) r0.v0 (11) date (t) (12) universal eccentric anomaly (psi) of date, approx
jstat = int (Returned)
status: 0 = OK
  • -1 = illegal JFORM

  • -2 = illegal E

  • -3 = illegal AORQ

  • -4 = illegal DM

  • -5 = numerical error

Notes:

Option JFORM = 1, suitable for the major planets:

EPOCH = epoch of elements (TT MJD) ORBINC = inclination i (radians) ANODE = longitude of the ascending node, big omega (radians) PERIH = longitude of perihelion, curly pi (radians) AORQ = mean distance, a (AU) E = eccentricity, e (range 0 to <1) AORL = mean longitude L (radians) DM = daily motion (radians)

Option JFORM = 2, suitable for minor planets:

EPOCH = epoch of elements (TT MJD) ORBINC = inclination i (radians) ANODE = longitude of the ascending node, big omega (radians) PERIH = argument of perihelion, little omega (radians) AORQ = mean distance, a (AU) E = eccentricity, e (range 0 to <1) AORL = mean anomaly M (radians)

Option JFORM = 3, suitable for comets:

EPOCH = epoch of elements and perihelion (TT MJD) ORBINC = inclination i (radians) ANODE = longitude of the ascending node, big omega (radians) PERIH = argument of perihelion, little omega (radians) AORQ = perihelion distance, q (AU) E = eccentricity, e (range 0 to 10)

Unused arguments (DM for JFORM=2, AORL and DM for JFORM=3) are not accessed.

Therefore, for any given problem there are up to three different epochs in play, and it is vital to distinguish clearly between them:

. The epoch of observation: the moment in time for which the position of the body is to be predicted.

. The epoch defining the position of the body: the moment in time at which, in the absence of purturbations, the specified position (mean longitude, mean anomaly, or perihelion) is reached.

. The osculating epoch: the moment in time at which the given elements are correct.

For the major-planet and minor-planet cases it is usual to make the epoch that defines the position of the body the same as the epoch of osculation. Thus, only two different epochs are involved: the epoch of the elements and the epoch of observation.

For comets, the epoch of perihelion fixes the position in the orbit and in general a different epoch of osculation will be chosen. Thus, all three types of epoch are involved.

For the present routine:

. The epoch of observation is the argument DATE.

. The epoch defining the position of the body is the argument EPOCH.

. The osculating epoch is not used and is assumed to be close enough to the epoch of observation to deliver adequate accuracy. If not, a preliminary call to palPertel may be used to update the element-set (and its associated osculating epoch) by applying planetary perturbations.

See Also

Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.