Procedure

     HYPTOF ( Hyperbolic time of flight )

     SUBROUTINE HYPTOF ( MA, ECC, F )

Abstract

     Solve the time of flight equation MA = e sinh(F) - F for the
     hyperbolic eccentric anomaly F, given the mean anomaly, MA,
     and the eccentricity, e.

Required_Reading

     None.

Keywords

     CONIC

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION      MA
     DOUBLE PRECISION      ECC
     DOUBLE PRECISION      F

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     MA         I   Mean anomaly at epoch.
     ECC        I   Eccentricity.
     F          O   Hyperbolic eccentric anomaly.

Detailed_Input

     MA       is the hyperbolic mean anomaly of an orbiting body at
              some epoch t,

                                   3 1/2
                 MA = (t-T)(mu/(-a) )

              where T is the time of periapsis passage, a is
              the semi-major axis of the orbit, and mu is the
              gravitational parameter of the primary body.

     ECC      is the eccentricity of the orbit.

Detailed_Output

     F        is the corresponding eccentric anomaly. This is the
              solution to the time of flight equation

                 MA = e sinh(F) - F

Parameters

     None.

Exceptions

     1)  If the eccentricity (ECC) is less than one, the error
         SPICE(WRONGCONIC) is signaled.

Files

     None.

Particulars

     Iterate to solve

        f(F,MA,e) = e sinh(F) - F - MA = 0

Examples

     ELLTOF, HYPTOF, and PARTOF are used by CONICS.

Restrictions

     None.

Literature_References

     [1]  R. Bate, D. Mueller, and J. White, "Fundamentals of
          Astrodynamics," Dover Publications Inc., 1971.

Author_and_Institution

     N.J. Bachman       (JPL)
     J. Diaz del Rio    (ODC Space)
     W.L. Taber         (JPL)
     I.M. Underwood     (JPL)

Version

    SPICELIB Version 3.2.0, 14-APR-2021 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard.

    SPICELIB Version 3.1.0, 13-JUL-2007 (NJB)

        Bug fix: MAXLOG is now saved.

    SPICELIB Version 3.0.0, 14-DEC-1994 (WLT)

        A counter was placed in the loop which bisects to a
        solution to the hyperbolic version of Kepler's equation.
        This addition forces the loop to terminate. On some platforms
        the loop would not terminate without this additional
        check. This was due to the compiler performing tests on
        extended precision registers.

    SPICELIB Version 2.0.1, 10-MAR-1992 (WLT)

        Comment section for permuted index source lines was added
        following the header.

    SPICELIB Version 2.0.0, 19-APR-1990 (WLT)

        A bad initial guess at bracketing the solution to the
        hyperbolic time of flight equation was corrected so that
        floating point overflows are now avoided. In addition, the
        Newton's method used before has been replaced by simply
        bisection.

    SPICELIB Version 1.0.0, 31-JAN-1990 (IMU)