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kepleq

 Procedure Abstract Required_Reading Keywords Declarations Brief_I/O Detailed_Input Detailed_Output Parameters Exceptions Files Particulars Examples Restrictions Literature_References Author_and_Institution Version

Procedure

KEPLEQ ( Solve Kepler's Equation --- Equinoctial Form )

DOUBLE PRECISION FUNCTION KEPLEQ (ML,H,K)

Abstract

Solve the equinoctial version of Kepler's equation.

None.

SPK

Declarations

IMPLICIT NONE

DOUBLE PRECISION  ML
DOUBLE PRECISION  H
DOUBLE PRECISION  K

Brief_I/O

VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
ML         I   Mean longitude.
H          I   h component of equinoctial elements.
K          I   k component of equinoctial elements.

The function returns the solution to the equinoctial version of
Kepler's equation, given the mean longitude and the h and k
components of the equinoctial elements.

Detailed_Input

ML       is the mean longitude of some body following two body
motion. (Mean longitude = Mean anomaly + argument of
periapse + longitude of ascending node.)

H        is the h component of the equinoctial element set
( h = ECC*SIN( arg of periapse + long ascending node) )

K        is the k component of the equinoctial element set
( k = ECC*COS( arg of periapse + long ascending node) )

Detailed_Output

The function returns the solution to the equinoctial version of
Kepler's equation, given the mean longitude and the h and k
components of the equinoctial elements.

The solution is the value of F such that

ML = F + H * COS(F) - K * SIN(F)

Note that ECC = DSQRT ( K*K + H*H )

None.

Exceptions

1)  If the sum of the squares of H and K is not less than .9,
the error SPICE(ECCOUTOFBOUNDS) is signaled.

2)  If the iteration for a solution to the equinoctial Kepler's
equation does not converge in 10 or fewer steps, the error
SPICE(NOCONVERGENCE) is signaled.

None.

Particulars

This routine solves the equinoctial element version of
Kepler's equation.

ML = F + H * COS(F) - K * SIN(F)

Here F is an offset from the eccentric anomaly E.

F = E - argument of periapse - longitude of ascending node.

where E is eccentric anomaly.

None.

None.

Literature_References

  W. Owen and R. Vaughan, "Optical Navigation Program
Mathematical Models," JPL Engineering Memorandum 314-513,
August 9, 1991.

Author_and_Institution

J. Diaz del Rio    (ODC Space)
W.L. Taber         (JPL)

Version

SPICELIB Version 1.0.1, 26-AUG-2021 (JDR)

Edited the header to comply with NAIF standard. Updated
\$Procedure section for consistency with KPSOLV routine.

SPICELIB Version 1.0.0, 11-DEC-1996 (WLT)
Fri Dec 31 18:36:29 2021