SLA_PV2UE - Position/Velocity to Universal Elements

From d54fe7c1f704a63824c5bfa0ece65245572e9b27 Mon Sep 17 00:00:00 2001 From: Joseph Hunkeler Date: Wed, 4 Mar 2015 21:21:30 -0500 Subject: Initial commit --- src/slalib/sun67.htx/node157.html | 203 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 203 insertions(+) create mode 100644 src/slalib/sun67.htx/node157.html (limited to 'src/slalib/sun67.htx/node157.html') diff --git a/src/slalib/sun67.htx/node157.html b/src/slalib/sun67.htx/node157.html new file mode 100644 index 0000000..08c25e9 --- /dev/null +++ b/src/slalib/sun67.htx/node157.html @@ -0,0 +1,203 @@ + + + + +SLA_PV2UE - Position/Velocity to Universal Elements + + + + + + + + + + + + +

+ +

+
+ Next: SLA_PVOBS - Observatory Position & Velocity +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PV2EL - Orbital Elements from Position/Velocity +

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 $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$ , 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 (t₀)
(4-6)		position at reference epoch ( ${\rm \bf r}_0$ )
(7-9)		velocity at reference epoch ( ${\rm \bf v}_0$ )
(10)		heliocentric distance at reference epoch
(11)		${\rm \bf r}_0.{\rm \bf v}_0$
(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. +

+ +

+
+ Next: SLA_PVOBS - Observatory Position & Velocity +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PV2EL - Orbital Elements from Position/Velocity +

+SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999
E-mail:ptw@star.rl.ac.uk +

+ + -- cgit