Index Page prop2b_c

A B C D E F G H I J K L M N O P Q R S T U V W X

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

#### Procedure

       void prop2b_c ( SpiceDouble         gm,
                       ConstSpiceDouble    pvinit[6],
                       SpiceDouble         dt,
                       SpiceDouble         pvprop[6] )

#### Abstract

       Given a central mass and the state of massless body at time t_0,
       this routine determines the state as predicted by a two-body
       force model at time t_0 + dt.

#### Required_Reading

       None.

#### Keywords

       CONIC
       EPHEMERIS
       UTILITY

#### Brief_I/O

       Variable  I/O  Description
       --------  ---  --------------------------------------------------
       gm         I   Gravity of the central mass.
       pvinit     I   Initial state from which to propagate a state.
       dt         I   Time offset from initial state to propagate to.
       pvprop     O   The propagated state.

#### Detailed_Input

       gm         is the gravitational constant G times the mass M of the
                  central body.

       pvinit     is the state at some specified time relative to the
                  central mass.  The mass of the object is assumed to
                  be negligible when compared to the central mass.

       dt         is a offset in time from the time of the initial
                  state to which the two-body state should be
                  propagated. (The units of time and distance must be
                  the same in gm, pvinit, and dt).

#### Detailed_Output

       pvprop     is the two-body propagation of the initial state
                  dt units of time past the epoch of the initial state.

#### Parameters

       None.

#### Exceptions

       1) If gm is not positive, the error SPICE(NONPOSITIVEMASS) will
          be signalled.

       2) If the position of the initial state is the zero vector, the
          error SPICE(ZEROPOSITION) will be signalled.

       3) If the velocity of the initial state is the zero vector, the
          error SPICE(ZEROVELOCITY) will be signalled.

       4) If the cross product of the position and velocity of pvinit
          has squared length of zero, the error SPICE(NONCONICMOTION)
          will be signalled.

       5) The value of dt must be "reasonable".  In other words, dt
          should be less than 10**20 seconds for realistic solar system
          orbits specified in the MKS system.  (The actual bounds
          on dt are much greater but require substantial computation.)
          The "reasonableness" of dt is checked at run-time.  If dt is
          so large that there is a danger of floating point overflow
          during computation, the error SPICE(DTOUTOFRANGE) is
          signalled and a message is generated describing the problem.

#### Files

       None.

#### Particulars

       This routine uses a universal variables formulation for the
       two-body motion of an object in orbit about a central mass. It
       propagates an initial state to an epoch offset from the
       epoch of the initial state by time dt.

       This routine does not suffer from the finite precision
       problems of the machine that are inherent to classical
       formulations based on the solutions to Kepler's equation:

             n( t - T ) = E - e Sin(E)         elliptic case
             n( t - T ) = e sinh(F) - F        hyperbolic case

       The derivation used to determine the propagated state is a
       slight variation of the derivation in Danby's book
       `Fundamentals of Celestial Mechanics' [1] .

#### Examples

       When the eccentricity of an orbit is near 1, and the epoch
       of classical elements is near the epoch of periapse, classical
       formulations that propagate a state from elements tend to
       lack robustness due to the finite precision of floating point
       machines. In those situations it is better to use a universal
       variables formulation to propagate the state.

       By using this routine, you need not go from a state to elements
       and back to a state. Instead, you can get the state from an
       initial state.

       If pv is your initial state and you want the state 3600
       seconds later, the following call will suffice.

            Look up gm somewhere

            dt = 3600.0;

            prop2b_c ( gm, pv, dt, pvdt );

       After the call, pvdt will contain the state of the
       object 3600 seconds after the time it had state pv.

#### Restrictions

       Users should be sure that gm, pvinit and dt are all in the
       same system of units ( for example MKS ).

#### Literature_References

       [1] `Fundamentals of Celestial Mechanics', Second Edition
           by J.M.A. Danby;  Willman-Bell, Inc., P.O. Box 35025
           Richmond Virginia;  pp 168-180

#### Author_and_Institution

       W.L. Taber     (JPL)
       N.J. Bachman   (JPL)
       E.D. Wright    (JPL)

#### Version

       -CSPICE Version 1.1.0, 24-JUL-2001   (NJB)

           Changed protoype:  input pvinit is now type
           (ConstSpiceDouble [6]). Implemented interface macro for
           casting input pvinit to const.

       -CSPICE Version 1.0.1, 20-MAR-1998 (EDW)

          Minor correction to header.

       -CSPICE Version 1.0.0, 08-FEB-1998   (EDW)

#### Index_Entries

        Propagate state vector using two-body force model

#### Link to routine prop2b_c source file prop2b_c.c

    Wed Apr  5 17:54:41 2017