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/node187.html | 378 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 378 insertions(+) create mode 100644 src/slalib/sun67.htx/node187.html (limited to 'src/slalib/sun67.htx/node187.html') diff --git a/src/slalib/sun67.htx/node187.html b/src/slalib/sun67.htx/node187.html new file mode 100644 index 0000000..9b71eb3 --- /dev/null +++ b/src/slalib/sun67.htx/node187.html @@ -0,0 +1,378 @@ + + + + +SLA_UE2EL - Universal to Conventional Elements + + + + + + + + + + + + +
+ +next + +up + +previous +
+ Next: SLA_UE2PV - Pos/Vel from Universal Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_TPV2C - Plate centre from and x,y,z +

+

+

SLA_UE2EL - Universal to Conventional Elements +   +

+
+
ACTION: +
Transform universal elements into conventional heliocentric +osculating elements. +

CALL: +
CALL sla_UE2EL ( + U, JFORMR, + JFORM, EPOCH, ORBINC, ANODE, PERIH, + AORQ, E, AORL, DM, JSTAT) +

+

+
GIVEN: +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
UD(13)universal orbital elements (updated; 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
   
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 ``universal'' elements are those which define the orbit for the +purposes of the method of universal variables (see reference 2). +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 universal elements are 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. +
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. +
+

+
REFERENCES: +
+
1. +
Sterne, Theodore E., An Introduction to Celestial Mechanics, +Interscience Publishers, 1960. Section 6.7, p199. +
2. +
Everhart, E. & Pitkin, E.T., Am. J. Phys. 51, 712, 1983. +
+
+ +next + +up + +previous +
+ Next: SLA_UE2PV - Pos/Vel from Universal Elements +
+Up: SUBPROGRAM SPECIFICATIONS +
+ Previous: SLA_TPV2C - Plate centre from and x,y,z +

+

+

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