Procedure

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

     DOUBLE PRECISION FUNCTION KEPLEQ (ML,H,K)

Abstract

     Solve the equinoctial version of Kepler's equation.

Required_Reading

     None.

Keywords

     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 )

Parameters

     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.

Files

     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.

Examples

     None.

Restrictions

     None.

Literature_References

     [1]  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)