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/node156.html | 323 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 323 insertions(+) create mode 100644 src/slalib/sun67.htx/node156.html (limited to 'src/slalib/sun67.htx/node156.html') diff --git a/src/slalib/sun67.htx/node156.html b/src/slalib/sun67.htx/node156.html new file mode 100644 index 0000000..ab897bc --- /dev/null +++ b/src/slalib/sun67.htx/node156.html @@ -0,0 +1,323 @@ + + + + +SLA_PV2EL - Orbital Elements from Position/Velocity + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_PV2UE - Position/Velocity to Universal Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PRENUT - Precession/Nutation Matrix +

+

+

SLA_PV2EL - Orbital Elements from Position/Velocity +   +

+
+
ACTION: +
Heliocentric osculating elements obtained from instantaneous +position and velocity. +

CALL: +
CALL sla_PV2EL ( + PV, DATE, PMASS, JFORMR, JFORM, EPOCH, ORBINC, + ANODE, PERIH, AORQ, E, AORL, DM, JSTAT) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + +
PVD(6)heliocentric $[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$, equatorial, J2000
(AU, AU/s; Note 1)
DATEDdate (TT Modified Julian Date = JD-2400000.5)
PMASSDmass of the planet (Sun = 1; Note 2)
JFORMRIrequested element set (1-3; Note 3)
+

+
RETURNED: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
JFORMIelement set actually returned (1-3; Note 4)
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)
JSTATIstatus:
0 = OK
-1 = illegal PMASS
-2 = illegal JFORMR
-3 = position/velocity out of allowed range
+

+
NOTES: +
+
1. +
The PV 6-vector is with respect to the mean equator and equinox of +epoch J2000. The orbital elements produced are with respect to +the J2000 ecliptic and mean equinox. +
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. +
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 $( 0 \leq e \leq 10 )$
+
4. +
It may not be possible to generate elements in the form + requested through JFORMR. The caller is notified of the form + of elements actually returned by means of the JFORM argument: +


+ 		 JFORMR 		 JFORM 		 meaning 
+ 
+		      1 		      1 		 OK: elements are in the requested format
+		      1 		      2 		 never happens
+		      1 		      3 		 orbit not elliptical
+		      2 		      1 		 never happens
+		      2 		      2 		 OK: elements are in the requested format
+		      2 		      3 		 orbit not elliptical
+		      3 		      1 		 never happens
+		      3 		      2 		 never happens
+		      3 		      3 		 OK: elements are in the requested format        
+
+
5. +
The arguments returned for each value of JFORM (cf Note 5: + JFORM may not be the same as JFORMR) are as follows: +


+ 		 JFORM 		 1 		 2 		 3 
+ 
+		 EPOCH 		 t0 t0 T 
+		 ORBINC 		 i i i 
+		 ANODE 		 $\Omega$ $\Omega$ $\Omega$ 
+		 PERIH 		 $\varpi$ $\omega$ $\omega$ 
+		 AORQ 		 a a q 
+		 E 		 e e e 
+		 AORL 		 L M -
+		 DM 		 n - 		 -        
+
+

+where: + 


+ 		 t0 is the epoch of the elements (MJD, TT)
+		 T is the epoch of perihelion (MJD, TT)
+		 i is the inclination (radians)
+		 $\Omega$ is the longitude of the ascending node (radians)
+		 $\varpi$ is the longitude of perihelion (radians)
+		 $\omega$ is the argument of perihelion (radians)
+		 a is the mean distance (AU)
+		 q is the perihelion distance (AU)
+		 e is the eccentricity
+		 L is the longitude (radians, $0-2\pi$)		 M is the mean anomaly (radians, $0-2\pi$)		 n is the daily motion (radians)
+		 - 		 means no value is set        
+
+
6. +
At very small inclinations, the longitude of the ascending node + ANODE becomes indeterminate and under some circumstances may be + set arbitrarily to zero. Similarly, if the orbit is close to + circular, the true anomaly becomes indeterminate and under some + circumstances may be set arbitrarily to zero. In such cases, + the other elements are automatically adjusted to compensate, + and so the elements remain a valid description of the orbit. +
+

+
REFERENCE: +
Sterne, Theodore E., An Introduction to Celestial Mechanics, +Interscience Publishers, 1960. +
+
+ +next + +up + +previous +
+ Next: SLA_PV2UE - Position/Velocity to Universal Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_PRENUT - Precession/Nutation Matrix +

+

+

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