diff options
Diffstat (limited to 'src/slalib/ue2el.f')
| -rw-r--r-- | src/slalib/ue2el.f | 194 |
1 files changed, 194 insertions, 0 deletions
diff --git a/src/slalib/ue2el.f b/src/slalib/ue2el.f new file mode 100644 index 0000000..d7187d9 --- /dev/null +++ b/src/slalib/ue2el.f @@ -0,0 +1,194 @@ + SUBROUTINE sla_UE2EL (U, JFORMR, + : JFORM, EPOCH, ORBINC, ANODE, PERIH, + : AORQ, E, AORL, DM, JSTAT) +*+ +* - - - - - - +* U E 2 E L +* - - - - - - +* +* Transform universal elements into conventional heliocentric +* osculating elements. +* +* Given: +* U d(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 (r0) +* (7-9) velocity at reference epoch (v0) +* (10) heliocentric distance at reference epoch +* (11) r0.v0 +* (12) date (t) +* (13) universal eccentric anomaly (psi) of date, approx +* +* JFORMR i requested element set (1-3; Note 3) +* +* Returned: +* JFORM d element set actually returned (1-3; Note 4) +* EPOCH d epoch of elements (TT MJD) +* ORBINC d inclination (radians) +* ANODE d longitude of the ascending node (radians) +* PERIH d longitude or argument of perihelion (radians) +* AORQ d mean distance or perihelion distance (AU) +* E d eccentricity +* AORL d mean anomaly or longitude (radians, JFORM=1,2 only) +* DM d daily motion (radians, JFORM=1 only) +* JSTAT i status: 0 = OK +* -1 = illegal combined mass +* -2 = illegal JFORMR +* -3 = position/velocity out of 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: +* +* Option JFORM=1, suitable for the major planets: +* +* EPOCH = epoch of elements (TT MJD) +* ORBINC = inclination i (radians) +* ANODE = longitude of the ascending node, big omega (radians) +* PERIH = longitude of perihelion, curly pi (radians) +* AORQ = mean distance, a (AU) +* E = eccentricity, e +* AORL = mean longitude L (radians) +* DM = daily motion (radians) +* +* Option JFORM=2, suitable for minor planets: +* +* EPOCH = epoch of elements (TT MJD) +* ORBINC = inclination i (radians) +* ANODE = longitude of the ascending node, big omega (radians) +* PERIH = argument of perihelion, little omega (radians) +* AORQ = mean distance, a (AU) +* E = eccentricity, e +* AORL = mean anomaly M (radians) +* +* Option JFORM=3, suitable for comets: +* +* EPOCH = epoch of perihelion (TT MJD) +* ORBINC = inclination i (radians) +* ANODE = longitude of the ascending node, big omega (radians) +* PERIH = argument of perihelion, little omega (radians) +* AORQ = perihelion distance, q (AU) +* E = eccentricity, e +* +* 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 6: 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 curly pi 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 " epoch of perihelion (MJD, TT) +* i " inclination (radians) +* Omega " longitude of the ascending node (radians) +* curly pi " longitude of perihelion (radians) +* omega " argument of perihelion (radians) +* a " mean distance (AU) +* q " perihelion distance (AU) +* e " eccentricity +* L " longitude (radians, 0-2pi) +* M " mean anomaly (radians, 0-2pi) +* n " 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 Inc., 1960. Section 6.7, p199. +* +* 2 Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983. +* +* Called: sla_PV2EL +* +* P.T.Wallace Starlink 18 March 1999 +* +* Copyright (C) 1999 Rutherford Appleton Laboratory +*- + + IMPLICIT NONE + + DOUBLE PRECISION U(13) + INTEGER JFORMR,JFORM + DOUBLE PRECISION EPOCH,ORBINC,ANODE,PERIH,AORQ,E,AORL,DM + INTEGER JSTAT + +* Gaussian gravitational constant (exact) + DOUBLE PRECISION GCON + PARAMETER (GCON=0.01720209895D0) + +* Canonical days to seconds + DOUBLE PRECISION CD2S + PARAMETER (CD2S=GCON/86400D0) + + INTEGER I + DOUBLE PRECISION PMASS,DATE,PV(6) + + +* Unpack the universal elements. + PMASS = U(1)-1D0 + DATE = U(3) + DO I=1,3 + PV(I) = U(I+3) + PV(I+3) = U(I+6)*CD2S + END DO + +* Convert the position and velocity etc into conventional elements. + CALL sla_PV2EL(PV,DATE,PMASS,JFORMR,JFORM,EPOCH,ORBINC,ANODE, + : PERIH,AORQ,E,AORL,DM,JSTAT) + + END |