Topocentric RA,Dec of a Solar-System object from universal elements
’ s east longitude (radians) ’ s
geodetic latitude (radians) (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
-1 = radius vector zero
-2 = failed to converge
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 " universal" elements are those which define the orbit for the purposes of the method of universal
variables (see reference 2). They consist of the combined mass of the two bodies, an epoch, and the
position and velocity vectors (arbitrary reference frame) at that epoch. The parameter set used here
includes also various quantities that can, in fact, be derived from the other information.
This approach is taken to avoiding unnecessary computation and loss of accuracy. The
supplementary quantities are (i) alpha, which is proportional to the total energy of the orbit, (ii) the
heliocentric distance at epoch, (iii) the outwards component of the velocity at the given
epoch, (iv) an estimate of psi, the " universal eccentric anomaly" at a given date and (v) that
date.
The universal elements are with respect to the J2000 equator and equinox.
Sterne, Theodore E., " An Introduction to Celestial Mechanics" , Interscience Publishers Inc., 1960.
Section 6.7, p199.
Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.