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SUBROUTINE sla_PV2EL (PV, DATE, PMASS, JFORMR,
: JFORM, EPOCH, ORBINC, ANODE, PERIH,
: AORQ, E, AORL, DM, JSTAT)
*+
* - - - - - -
* P V 2 E L
* - - - - - -
*
* Heliocentric osculating elements obtained from instantaneous position
* and velocity.
*
* Given:
* PV d(6) heliocentric x,y,z,xdot,ydot,zdot of date,
* J2000 equatorial triad (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)
* 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 PMASS
* -2 = illegal JFORMR
* -3 = position/velocity out of 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:
*
* 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 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 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.
*
* Reference: Sterne, Theodore E., "An Introduction to Celestial
* Mechanics", Interscience Publishers, 1960
*
* Called: sla_DRANRM
*
* P.T.Wallace Starlink 13 February 1999
*
* Copyright (C) 1999 Rutherford Appleton Laboratory
*-
IMPLICIT NONE
DOUBLE PRECISION PV(6),DATE,PMASS
INTEGER JFORMR,JFORM
DOUBLE PRECISION EPOCH,ORBINC,ANODE,PERIH,AORQ,E,AORL,DM
INTEGER JSTAT
* Seconds to days
DOUBLE PRECISION DAY
PARAMETER (DAY=86400D0)
* Gaussian gravitational constant (exact)
DOUBLE PRECISION GCON
PARAMETER (GCON=0.01720209895D0)
* Sin and cos of J2000 mean obliquity (IAU 1976)
DOUBLE PRECISION SE,CE
PARAMETER (SE=0.3977771559319137D0,
: CE=0.9174820620691818D0)
* Minimum allowed distance (AU) and speed (AU/day)
DOUBLE PRECISION RMIN,VMIN
PARAMETER (RMIN=1D-3,VMIN=1D-8)
* How close to unity the eccentricity has to be to call it a parabola
DOUBLE PRECISION PARAB
PARAMETER (PARAB=1D-8)
DOUBLE PRECISION X,Y,Z,XD,YD,ZD,R,V2,V,RDV,GMU,HX,HY,HZ,
: HX2PY2,H2,H,OI,BIGOM,AR,ECC,S,C,AT,U,OM,
: GAR3,EM1,EP1,HAT,SHAT,CHAT,AE,AM,DN,PL,
: EL,Q,TP,THAT,THHF,F
INTEGER JF
DOUBLE PRECISION sla_DRANRM
* Validate arguments PMASS and JFORMR.
IF (PMASS.LT.0D0) THEN
JSTAT = -1
GO TO 999
END IF
IF (JFORMR.LT.1.OR.JFORMR.GT.3) THEN
JSTAT = -2
GO TO 999
END IF
* Provisionally assume the elements will be in the chosen form.
JF = JFORMR
* Rotate the position from equatorial to ecliptic coordinates.
X = PV(1)
Y = PV(2)*CE+PV(3)*SE
Z = -PV(2)*SE+PV(3)*CE
* Rotate the velocity similarly, scaling to AU/day.
XD = DAY*PV(4)
YD = DAY*(PV(5)*CE+PV(6)*SE)
ZD = DAY*(-PV(5)*SE+PV(6)*CE)
* Distance and speed.
R = SQRT(X*X+Y*Y+Z*Z)
V2 = XD*XD+YD*YD+ZD*ZD
V = SQRT(V2)
* Reject unreasonably small values.
IF (R.LT.RMIN.OR.V.LT.VMIN) THEN
JSTAT = -3
GO TO 999
END IF
* R dot V.
RDV = X*XD+Y*YD+Z*ZD
* Mu.
GMU = (1D0+PMASS)*GCON*GCON
* Vector angular momentum per unit reduced mass.
HX = Y*ZD-Z*YD
HY = Z*XD-X*ZD
HZ = X*YD-Y*XD
* Areal constant.
HX2PY2 = HX*HX+HY*HY
H2 = HX2PY2+HZ*HZ
H = SQRT(H2)
* Inclination.
OI = ATAN2(SQRT(HX2PY2),HZ)
* Longitude of ascending node.
IF (HX.NE.0D0.OR.HY.NE.0D0) THEN
BIGOM = ATAN2(HX,-HY)
ELSE
BIGOM=0D0
END IF
* Reciprocal of mean distance etc.
AR = 2D0/R-V2/GMU
* Eccentricity.
ECC = SQRT(MAX(1D0-AR*H2/GMU,0D0))
* True anomaly.
S = H*RDV
C = H2-R*GMU
IF (S.NE.0D0.AND.C.NE.0D0) THEN
AT = ATAN2(S,C)
ELSE
AT = 0D0
END IF
* Argument of the latitude.
S = SIN(BIGOM)
C = COS(BIGOM)
U = ATAN2((-X*S+Y*C)*COS(OI)+Z*SIN(OI),X*C+Y*S)
* Argument of perihelion.
OM = U-AT
* Capture near-parabolic cases.
IF (ABS(ECC-1D0).LT.PARAB) ECC=1D0
* Comply with JFORMR = 1 or 2 only if orbit is elliptical.
IF (ECC.GE.1D0) JF=3
* Functions.
GAR3 = GMU*AR*AR*AR
EM1 = ECC-1D0
EP1 = ECC+1D0
HAT = AT/2D0
SHAT = SIN(HAT)
CHAT = COS(HAT)
* Ellipse?
IF (ECC.LT.1D0 ) THEN
* Eccentric anomaly.
AE = 2D0*ATAN2(SQRT(-EM1)*SHAT,SQRT(EP1)*CHAT)
* Mean anomaly.
AM = AE-ECC*SIN(AE)
* Daily motion.
DN = SQRT(GAR3)
END IF
* "Major planet" element set?
IF (JF.EQ.1) THEN
* Longitude of perihelion.
PL = BIGOM+OM
* Longitude at epoch.
EL = PL+AM
END IF
* "Comet" element set?
IF (JF.EQ.3) THEN
* Perihelion distance.
Q = H2/(GMU*EP1)
* Ellipse, parabola, hyperbola?
IF (ECC.LT.1D0) THEN
* Ellipse: epoch of perihelion.
TP = DATE-AM/DN
ELSE
* Parabola or hyperbola: evaluate tan ( ( true anomaly ) / 2 )
THAT = SHAT/CHAT
IF (ECC.EQ.1D0) THEN
* Parabola: epoch of perihelion.
TP = DATE-THAT*(1D0+THAT*THAT/3D0)*H*H2/(2D0*GMU*GMU)
ELSE
* Hyperbola: epoch of perihelion.
THHF = SQRT(EM1/EP1)*THAT
F = LOG(1D0+THHF)-LOG(1D0-THHF)
TP = DATE-(ECC*SINH(F)-F)/SQRT(-GAR3)
END IF
END IF
END IF
* Return the appropriate set of elements.
JFORM = JF
ORBINC = OI
ANODE = sla_DRANRM(BIGOM)
E = ECC
IF (JF.EQ.1) THEN
PERIH = sla_DRANRM(PL)
AORL = sla_DRANRM(EL)
DM = DN
ELSE
PERIH = sla_DRANRM(OM)
IF (JF.EQ.2) AORL = sla_DRANRM(AM)
END IF
IF (JF.NE.3) THEN
EPOCH = DATE
AORQ = 1D0/AR
ELSE
EPOCH = TP
AORQ = Q
END IF
JSTAT = 0
999 CONTINUE
END
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