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/node91.html | 330 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 330 insertions(+) create mode 100644 src/slalib/sun67.htx/node91.html (limited to 'src/slalib/sun67.htx/node91.html') diff --git a/src/slalib/sun67.htx/node91.html b/src/slalib/sun67.htx/node91.html new file mode 100644 index 0000000..2beedff --- /dev/null +++ b/src/slalib/sun67.htx/node91.html @@ -0,0 +1,330 @@ + + + + +SLA_EL2UE - Conventional to Universal Elements + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_EPB - MJD to Besselian Epoch +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EG50 - B1950 to Galactic +

+

+

SLA_EL2UE - Conventional to Universal Elements +   +

+
+
ACTION: +
Transform conventional osculating orbital elements +into ``universal'' form. +

CALL: +
CALL sla_EL2UE ( + DATE, JFORM, EPOCH, ORBINC, ANODE, + PERIH, AORQ, E, AORL, DM, + U, JSTAT) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
DATEDepoch (TT MJD) of osculation (Note 3)
JFORMIchoice of element set (1-3; Note 6)
EPOCHDepoch of elements (t0 or T, TT MJD)
ORBINCDinclination (i, radians)
ANODEDlongitude of the ascending node ($\Omega$, radians)
PERIHDlongitude or argument of perihelion +($\varpi$ or $\omega$,
radians)
AORQDmean distance or perihelion distance (a or q, AU)
EDeccentricity (e)
AORLDmean anomaly or longitude +(M or L, radians,
JFORM=1,2 only)
DMDdaily motion (n, radians, JFORM=1 only)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
UD(13)universal orbital elements (Note 1)
(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
   
JSTATIstatus:
0 = OK
-1 = illegal JFORM
-2 = illegal E
-3 = illegal AORQ
-4 = illegal DM
-5 = numerical error
+

+
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_UE2PV. This takes the set of numbers + that the present routine outputs and uses them to derive the + object's position and velocity. A single prediction requires one + call to the present routine followed by one call to sla_UE2PV; + for convenience, the two calls are packaged as the routine + sla_PLANEL. Multiple predictions may be made by again calling the + present routine once, but then calling sla_UE2PV multiple times, + which is faster than multiple calls to sla_PLANEL. +
3. +
DATE is the epoch of osculation. It is in the TT timescale + (formerly Ephemeris Time, ET) and is a Modified Julian Date + (JD-2400000.5). +
4. +
The supplied orbital elements are with respect to the J2000 + ecliptic and equinox. The position and velocity parameters + returned in the array U are with respect to the mean equator and + equinox of epoch J2000, and are for the perihelion prior to the + specified epoch. +
5. +
The universal elements returned in the array U are in canonical + units (solar masses, AU and canonical days). +
6. +
Three different element-format options are supported, as + follows.
+

+JFORM=1, suitable for the major planets: +


+ 		 EPOCH 		 = 		 epoch of elements t0 (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 longitude of perihelion $\varpi$ (radians)
+		 AORQ 		 = 		 mean distance a (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e < 1 )$ 
+		 AORL 		 = 		 mean longitude L (radians)
+		 DM 		 = 		 daily motion n (radians)        
+
+

+JFORM=2, suitable for minor planets: +


+ 		 EPOCH 		 = 		 epoch of elements t0 (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 argument of perihelion $\omega$ (radians)
+		 AORQ 		 = 		 mean distance a (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e < 1 )$ 
+		 AORL 		 = 		 mean anomaly M (radians)        
+
+

+JFORM=3, suitable for comets: +


+ 		 EPOCH 		 = 		 epoch of perihelion T (TT MJD)
+		 ORBINC 		 = 		 inclination i (radians)
+		 ANODE 		 = 		 longitude of the ascending node $\Omega$ (radians)
+		 PERIH 		 = 		 argument of perihelion $\omega$ (radians)
+		 AORQ 		 = 		 perihelion distance q (AU)
+		 E 		 = 		 eccentricity e $( 0 \leq e \leq 10 )$
+
7. +
Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are + not accessed. +
8. +
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. +
+
+ +next + +up + +previous +
+ Next: SLA_EPB - MJD to Besselian Epoch +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_EG50 - B1950 to Galactic +

+

+

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