### SLA_PV2UE

Position/Velocity to Universal Elements

ACTION:
Construct a universal element set based on an instantaneous position and velocity.
CALL:
CALL sla_PV2UE (PV, DATE, PMASS, U, JSTAT)
##### GIVEN:
 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) DATE D date (TT Modified Julian Date = JD$-$2400000.5) PMASS D mass of the planet (Sun = 1; Note 2)

##### RETURNED:
 U D(13) universal orbital elements (Note 3) (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 JSTAT I status: 0 = OK $-$1 = illegal PMASS $-$2 = too close to Sun $-$3 = too slow

NOTES:
(1)
The PV 6-vector can be with respect to any chosen inertial frame, and the resulting universal-element set will be with respect to the same frame. A common choice will be mean equator and ecliptic of epoch J2000.
(2)
The mass, PMASS, is important only for the larger planets. For most purposes (e.g. asteroids) use 0D0. Values less than zero are illegal.
(3)
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.
REFERENCE:
Everhart, E. & Pitkin, E.T., Am. J. Phys. 51, 712, 1983.