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 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).
pvprop is the two-body propagation of the initial state dt units of time past the epoch of the initial state.
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 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.
Users should be sure that gm, pvinit and dt are all in the same system of units ( for example MKS ).
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.
W.L. Taber (JPL) N.J. Bachman (JPL) E.D. Wright (JPL)
 `Fundamentals of Celestial Mechanics', Second Edition by J.M.A. Danby; Willman-Bell, Inc., P.O. Box 35025 Richmond Virginia; pp 168-180
-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