Procedure

     ELLTOF ( Elliptic time of flight )

     SUBROUTINE ELLTOF ( MA, ECC, E )

Abstract

     Solve the time of flight equation MA = E - e sin(E) for the
     elliptic eccentric anomaly E, given mean anomaly the MA and
     the eccentricity ECC.

Required_Reading

     None.

Keywords

     CONIC

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION      MA
     DOUBLE PRECISION      ECC
     DOUBLE PRECISION      E

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     MA         I   Mean anomaly at epoch.
     ECC        I   Eccentricity.
     E          O   Elliptic eccentric anomaly.

Detailed_Input

     MA       is the elliptic 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

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

                 MA = E - e sin(E)

Parameters

     None.

Exceptions

     1)  If the eccentricity (ECC) is outside the range [0,1),
         the error SPICE(WRONGCONIC) is signaled.

Files

     None.

Particulars

     Iterate to solve

        f(E,MA,e) = E - e sin(E) - 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.

     [2]  E. W. Ng, "A General Algorithm for the Solution of Kepler's
          Equation for Elliptic Orbits", Cel. Mech. 20, pp.243-249,
          1979.

Author_and_Institution

     J. Diaz del Rio    (ODC Space)
     K.R. Gehringer     (JPL)
     W.L. Taber         (JPL)
     I.M. Underwood     (JPL)

Version

    SPICELIB Version 1.2.0, 14-APR-2021 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard.

    SPICELIB Version 1.1.0, 29-FEB-1996 (KRG)

        The declaration for the SPICELIB function PI is now
        preceded by an EXTERNAL statement declaring PI to be an
        external function. This removes a conflict with any
        compilers that have a PI intrinsic function.

    SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)

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

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