prop2b_c |

Table of contents## Procedureprop2b_c ( Propagate a two-body solution ) void prop2b_c ( SpiceDouble gm, ConstSpiceDouble pvinit[6], SpiceDouble dt, SpiceDouble pvprop[6] ) ## AbstractCompute the state of a massless body at time t_0 + dt by applying the two-body force model to a given central mass and a given body state at time t_0. ## Required_ReadingNone. ## KeywordsCONIC EPHEMERIS UTILITY ## Brief_I/OVARIABLE 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_Inputgm 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 an 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_Outputpvprop is the two-body propagation of the initial state `dt' units of time past the epoch of the initial state. ## ParametersNone. ## Exceptions1) If `gm' is not positive, the error SPICE(NONPOSITIVEMASS) is signaled by a routine in the call tree of this routine. 2) If the position of the initial state is the zero vector, the error SPICE(ZEROPOSITION) is signaled by a routine in the call tree of this routine. 3) If the velocity of the initial state is the zero vector, the error SPICE(ZEROVELOCITY) is signaled by a routine in the call tree of this routine. 4) If the cross product of the position and velocity of `pvinit' has squared length of zero, the error SPICE(NONCONICMOTION) is signaled by a routine in the call tree of this routine. 5) If `dt' is so large that there is a danger of floating point overflow during computation, the error SPICE(DTOUTOFRANGE) is signaled by a routine in the call tree of this routine and a message is generated describing the problem. 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. ## FilesNone. ## ParticularsThis 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]. ## ExamplesThe numerical results shown for these examples may differ across platforms. The results depend on the SPICE kernels used as input, the compiler and supporting libraries, and the machine specific arithmetic implementation. 1) Use the two-body force model to propagate the state of a massless body orbiting the Earth at 100,000,000 km after half a period. In circular two-body motion, the orbital speed is s = sqrt(mu/r) where mu is the central mass. After tau/2 = pi*r/s seconds (half period), the state should equal the negative of the original state. Example code begins here. /. Program prop2b_ex1 ./ #include <stdio.h> #include <math.h> #include "SpiceUsr.h" int main( ) { /. Local variables. ./ SpiceDouble mu; SpiceDouble pvinit [ 6 ]; SpiceDouble r; SpiceDouble speed; SpiceDouble state [ 6 ]; SpiceDouble t; /. Initial values. ./ mu = 3.9860043543609598E+05; r = 1.0e+08; speed = sqrt( mu / r ); t = pi_c()*r/speed; pvinit[0] = 0.0; pvinit[1] = r/sqrt(2.0); pvinit[2] = r/sqrt(2.0); pvinit[3] = 0.0; pvinit[4] = -speed/sqrt(2.0); pvinit[5] = speed/sqrt(2.0); /. Calculate the state of the body at 0.5 period after the epoch. ./ ## Restrictions1) Users should be sure that `gm', `pvinit' and `dt' are all in the same system of units ( for example MKS ). ## Literature_References[1] J. Danby, "Fundamentals of Celestial Mechanics," 2nd Edition, pp 168-180, Willman-Bell, 1988. ## Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) W.L. Taber (JPL) E.D. Wright (JPL) ## Version-CSPICE Version 1.1.1, 01-NOV-2021 (JDR) Edited -Examples section to comply with NAIF standard. Added complete code example. -CSPICE Version 1.1.0, 24-JUL-2001 (NJB) Changed prototype: 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) (WLT) ## Index_EntriesPropagate state vector using two-body force model |

Fri Dec 31 18:41:10 2021