palUe2el

Universal elements to heliocentric osculating elements

Description:

Transform universal elements into conventional heliocentric osculating elements.

Invocation

void palUe2el ( const double u[13], int jformr, int jform, double epoch, double orbinc, double anode, double perih, double aorq, double e, double aorl, double dm, int jstat );

Arguments

u = const double [13] (Given)
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
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 combined mass

  • 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)

See Also