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

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 $\ast$ra, double $\ast$dec, double $\ast$r, int $\ast$jstat );

date = double (Given)

elong = double (Given)

phi = double (Given)

jform = int (Given)

epoch = double (Given)

orbinc = double (Given)

anode = double (Given)

perih = double (Given)

aorq = double (Given)

e = double (Given)

aorl = double (Given)

dm = double (Given)

ra = double $\ast$ (Returned)

dec = double $\ast$ (Returned)

r = double $\ast$ (Returned)

jstat = int $\ast$ (Returned)

• DATE is the instant for which the prediction is required. It is in the TT timescale (formerly Ephemeris Time, ET) and is a Modified Julian Date (JD-2400000.5).

• The longitude and latitude allow correction for geocentric parallax. This is usually a small effect, but can become important for near-Earth asteroids. Geocentric positions can be generated by appropriate use of routines palEpv (or palEvp) and palUe2pv.

• The elements are with respect to the J2000 ecliptic and equinox.

• A choice of three different element-set options is available:

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.

• Each of the three element sets defines an unperturbed heliocentric orbit. For a given epoch of observation, the position of the body in its orbit can be predicted from these elements, which are called " osculating elements" , using standard two-body analytical solutions. However, due to planetary perturbations, a given set of osculating elements remains usable for only as long as the unperturbed orbit that it describes is an adequate approximation to reality. Attached to such a set of elements is a date called the " osculating epoch" , at which the elements are, momentarily, a perfect representation of the instantaneous position and velocity of the body.

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.

• Two important sources for orbital elements are Horizons, operated by the Jet Propulsion Laboratory, Pasadena, and the Minor Planet Center, operated by the Center for Astrophysics, Harvard.

The JPL Horizons elements (heliocentric, J2000 ecliptic and equinox) correspond to PAL/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