### SLA_UE2PV

Pos/Vel from Universal Elements

ACTION:
Heliocentric position and velocity of a planet, asteroid or comet, starting from orbital elements in the “universal variables” form.
CALL:
CALL sla_UE2PV (DATE, U, PV, JSTAT)
##### GIVEN:
 DATE D date (TT Modified Julian Date = JD$-$2400000.5)

##### GIVEN and RETURNED:
 U D(13) universal orbital elements (updated; Note 1) (1) combined mass ($M+m$) (2) total energy of the orbit ($\alpha$) (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 ($\psi$) of date, approx

##### RETURNED:
 PV D(6) heliocentric $\left[\phantom{\rule{0.3em}{0ex}}x,y,z,ẋ,ẏ,ż\phantom{\rule{0.3em}{0ex}}\right]$, equatorial, J2000 (AU, AU/s; Note 1) JSTAT I status: 0 = OK $-$1 = radius vector zero $-2$ = failed to converge

NOTES:
(1)
The “universal” elements are those which define the orbit for the purposes of the method of universal variables (see reference). 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.
(2)
The companion routine is sla_EL2UE. This takes the conventional orbital elements and transforms them into the set of numbers needed by the present routine. A single prediction requires one one call to sla_EL2UE followed by one call to the present routine; for convenience, the two calls are packaged as the routine sla_PLANEL. Multiple predictions may be made by again calling sla_EL2UE once, but then calling the present routine multiple times, which is faster than multiple calls to sla_PLANEL.

It is not obligatory to use sla_EL2UE to obtain the parameters. However, it should be noted that because sla_EL2UE performs its own validation, no checks on the contents of the array U are made by the present routine.

(3)
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).
(4)
The universal elements supplied in the array U are in canonical units (solar masses, AU and canonical days). The position and velocity are not sensitive to the choice of reference frame. The sla_EL2UE routine in fact produces coordinates with respect to the J2000 equator and equinox.
(5)
The algorithm was originally adapted from the EPHSLA program of D. H. P. Jones (private communication, 1996). The method is based on Stumpff’s Universal Variables.
REFERENCE:
Everhart, E. & Pitkin, E.T., Am. J. Phys. 51, 712, 1983.