void prop2b_c ( SpiceDouble gm,
SpiceDouble pvprop )
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.
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.
gm is the gravitational constant G times the mass M of the
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).
pvprop is the two-body propagation of the initial state
dt units of time past the epoch of the initial state.
1) If gm is not positive, the error SPICE(NONPOSITIVEMASS) will
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.
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'  .
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
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.
Users should be sure that gm, pvinit and dt are all in the
same system of units ( for example MKS ).
 `Fundamentals of Celestial Mechanics', Second Edition
by J.M.A. Danby; Willman-Bell, Inc., P.O. Box 35025
Richmond Virginia; pp 168-180
W.L. Taber (JPL)
N.J. Bachman (JPL)
E.D. Wright (JPL)
-CSPICE Version 1.1.0, 24-JUL-2001 (NJB)
Changed protoype: input pvinit is now type
(ConstSpiceDouble ). 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)
Propagate state vector using two-body force model