palPv2el palPv2el - Position velocity to heliocentirc osculating elements

Description:
Heliocentric osculating elements obtained from instantaneous position and velocity.

Invocation:
void palPv2el ( const double pv[6], double date, double pmass, int jformr, int $*$jform, double $*$epoch, double $*$orbinc, double $*$anode, double $*$perih, double $*$aorq, double $*$e, double $*$aorl, double $*$dm, int $*$jstat );

Arguments:

pv = const double [6] (Given)
Heliocentric x,y,z,xdot,ydot,zdot of date, J2000 equatorial triad (AU,AU/s; Note 1)
date = double (Given)
Date (TT Modified Julian Date = JD-2400000.5)
pmass = double (Given)
Mass of the planet (Sun=1; Note 2)
jformr = int (Given)
Requested element set (1-3; Note 3)
jform = int $*$ (Returned)
Element set actually returned (1-3; Note 4)
epoch = double $*$ (Returned)
Epoch of elements (TT MJD)
orbinc = double $*$ (Returned)
inclination (radians)
anode = double $*$ (Returned)
longitude of the ascending node (radians)
perih = double $*$ (Returned)
longitude or argument of perihelion (radians)
aorq = double $*$ (Returned)
mean distance or perihelion distance (AU)
e = double $*$ (Returned)
eccentricity
aorl = double $*$ (Returned)
mean anomaly or longitude (radians, JFORM=1,2 only)
dm = double $*$ (Returned)
daily motion (radians, JFORM=1 only)
jstat = int $*$ (Returned)
status: 0 = OK
  • -1 = illegal PMASS

  • -2 = illegal JFORMR

  • -3 = position/velocity out of range


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 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 AORL = mean anomaly M (radians)

Option JFORM=3, suitable for comets:

EPOCH = epoch of 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


JFORMR JFORM meaning

1 1 OK - elements are in the requested format 1 2 never happens 1 3 orbit not elliptical

2 1 never happens 2 2 OK - elements are in the requested format 2 3 orbit not elliptical

3 1 never happens 3 2 never happens 3 3 OK - elements are in the requested format


JFORM 1 2 3 EPOCH t0 t0 T ORBINC i i i ANODE Omega Omega Omega PERIH curly pi omega omega AORQ a a q E e e e AORL L M - DM n - -

where:

t0 is the epoch of the elements (MJD, TT) T " epoch of perihelion (MJD, TT) i " inclination (radians) Omega " longitude of the ascending node (radians) curly pi " longitude of perihelion (radians) omega " argument of perihelion (radians) a " mean distance (AU) q " perihelion distance (AU) e " eccentricity L " longitude (radians, 0-2pi) M " mean anomaly (radians, 0-2pi) n " daily motion (radians)