SLA_PLANTU

$[α, δ]$ from Universal Elements

ACTION:: Topocentric apparent $[α, δ]$ of a Solar-System object whose heliocentric universal orbital elements are known.
CALL:: CALL sla_PLANTU (DATE, ELONG, PHI, U, RA, DEC, R, JSTAT)

DATE	D	TT MJD of observation (JD $-$ 2400000.5)

ELONG,PHI	D	observer’s longitude (east +ve) and latitude

		radians)

U	D(13)	universal orbital elements

(1)		combined mass ( $M + m$ )
(2)		total energy of the orbit ( $α$ )
(3)		reference (osculating) epoch ( $t_{0}$ )
(4-6)		position at reference epoch ( $r_{0}$ )
(7-9)		velocity at reference epoch ( $v_{0}$ )
(10)		heliocentric distance at reference epoch
(11)		$r_{0} . v_{0}$
(12)		date ( $t$ )
(13)		universal eccentric anomaly ( $ψ$ ) of date, approx

RA,DEC	D	topocentric apparent $[α, δ]$ (radians)

R	D	distance from observer (AU)

JSTAT	I	status:

		0 = OK

		$-$ 1 = radius vector zero

		$-$ 2 = failed to converge

NOTES:

(1): DATE is the instant for which the prediction is required. It is in the TT time scale (formerly Ephemeris Time, ET) and is a Modified Julian Date (JD $-$ 2400000.5).
(2): 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 the routines sla_EVP (or sla_EPV) and sla_UE2PV.
(3): 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) $α$ , 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 $ψ$ , the “universal eccentric anomaly” at a given date and (v) that date.
(4): The universal elements are with respect to the J2000 ecliptic and equinox.

REFERENCES:

(1): Sterne, Theodore E., An Introduction to Celestial Mechanics, Interscience Publishers, 1960. Section 6.7, p199.
(2): Everhart, E. & Pitkin, E.T., Am. J. Phys. 51, 712, 1983.