palPlante palPlante - Topocentric RA,Dec of a Solar-System object from heliocentric orbital elements

Description:
Topocentric apparent RA,Dec of a Solar-System object whose heliocentric orbital elements are known.

Invocation:
void palPlante ( double date, double elong, double phi, int jform, double epoch, double orbinc, double anode, double perih, double aorq, double e, double aorl, double dm, double $*$ra, double $*$dec, double $*$r, int $*$jstat );

Arguments:

date = double (Given)
TT MJD of observation (JD-2400000.5)
elong = double (Given)
Observer's east longitude (radians)
phi = double (Given)
Observer's geodetic latitude (radians)
jform = int (Given)
Element set actually returned (1-3; Note 6)
epoch = double (Given)
Epoch of elements (TT MJD)
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)
ra = double $*$ (Returned)
Topocentric apparent RA (radians)
dec = double $*$ (Returned)
Topocentric apparent Dec (radians)
r = double $*$ (Returned)
Distance from observer (AU)
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 sla_PERTEL may be used to update the element-set (and its associated osculating epoch) by applying planetary perturbations.


The JPL Horizons elements (heliocentric, J2000 ecliptic and equinox) correspond to SLALIB arguments as follows.

Major planets:

JFORM = 1 EPOCH = JDCT-2400000.5 ORBINC = IN (in radians) ANODE = OM (in radians) PERIH = OM$+$W (in radians) AORQ = A E = EC AORL = MA$+$OM$+$W (in radians) DM = N (in radians)

Epoch of osculation = JDCT-2400000.5

Minor planets:

JFORM = 2 EPOCH = JDCT-2400000.5 ORBINC = IN (in radians) ANODE = OM (in radians) PERIH = W (in radians) AORQ = A E = EC AORL = MA (in radians)

Epoch of osculation = JDCT-2400000.5

Comets:

JFORM = 3 EPOCH = Tp-2400000.5 ORBINC = IN (in radians) ANODE = OM (in radians) PERIH = W (in radians) AORQ = QR E = EC

Epoch of osculation = JDCT-2400000.5

The MPC elements correspond to SLALIB arguments as follows.

Minor planets:

JFORM = 2 EPOCH = Epoch-2400000.5 ORBINC = Incl. (in radians) ANODE = Node (in radians) PERIH = Perih. (in radians) AORQ = a E = e AORL = M (in radians)

Epoch of osculation = Epoch-2400000.5

Comets:

JFORM = 3 EPOCH = T-2400000.5 ORBINC = Incl. (in radians) ANODE = Node. (in radians) PERIH = Perih. (in radians) AORQ = q E = e

Epoch of osculation = Epoch-2400000.5