Table of contents
CSPICE_PROP2B computes 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.
Given:
gm a scalar double precision defining the gravitational constant of
the primary.
help, gm
DOUBLE = Scalar
pvinit the double precision state 6-vector describing the initial state
of the massless body (secondary) at some epoch.
help, pvinit
DOUBLE = Array[6]
dt the double precision scalar time step in TDB seconds from the
epoch.
help, dt
DOUBLE = Scalar
the call:
cspice_prop2b, gm, pvinit, dt, pvprop
returns:
pvprop a double precision 6-vector defining the state of the body at a
time 'dt' from the epoch as determined by the classical two-body
force model.
help, pvprop
DOUBLE = Array[6]
None.
Any numerical results shown for this example may differ between
platforms as the results depend on the SPICE kernels used as input
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.
PRO prop2b_ex1
;;
;; Initial values.
;;
mu = 3.9860043543609598E+05
r = 1.d08
speed = sqrt( mu / r )
t = cspice_pi()*r/speed
pvinit= [ 0.d, r/sqrt(2.d), r/sqrt(2.d) , $
0.d, -speed/sqrt(2.d), speed/sqrt(2.d) ]
;;
;; Calculate the state of the body at 0.5 period
;; after the epoch.
;;
cspice_prop2b, mu, pvinit, t, state
;;
;; The 'state' vector should equal '-pvinit'
;;
print, 'State at t0: '
print, FORMAT='(" R (km):",3F17.5)', pvinit[0:2]
print, FORMAT='(" V (km/s):",3F17.5)', pvinit[3:5]
print, ' '
print, 'State at tau/2: '
print, FORMAT='(" R (km):",3F17.5)', state[0:2]
print, FORMAT='(" V (km/s):",3F17.5)', state[3:5]
END
When this program was executed on a Mac/Intel/IDL8.x/64-bit
platform, the output was:
State at t0:
R (km): 0.00000 70710678.11865 70710678.11865
V (km/s): 0.00000 -0.04464 0.04464
State at tau/2:
R (km): -0.00000 -70710678.11865 -70710678.11865
V (km/s): 0.00000 0.04464 -0.04464
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].
1) 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.
6) If any of the input arguments, `gm', `pvinit' or `dt', is
undefined, an error is signaled by the IDL error handling
system.
7) If any of the input arguments, `gm', `pvinit' or `dt', is not
of the expected type, or it does not have the expected
dimensions and size, an error is signaled by the Icy
interface.
8) If the output argument `pvprop' is not a named variable, an
error is signaled by the Icy interface.
None.
1) Users should be sure that `gm', `pvinit' and `dt' are all in the
same system of units ( for example MKS ).
ICY.REQ
[1] J. Danby, "Fundamentals of Celestial Mechanics," 2nd Edition,
pp 168-180, Willman-Bell, 1988.
J. Diaz del Rio (ODC Space)
E.D. Wright (JPL)
-Icy Version 1.0.2, 01-NOV-2021 (JDR)
Edited -Examples section to comply with NAIF standard. Added
example's task description.
Added -Parameters, -Exceptions, -Files, -Restrictions,
-Literature_References and -Author_and_Institution sections.
Removed reference to the routine's corresponding CSPICE header from
-Abstract section.
Added arguments' type and size information in the -I/O section.
-Icy Version 1.0.1, 15-AUG-2011 (EDW)
Edits to comply with NAIF standard for Icy headers.
-Icy Version 1.0.0, 16-JUN-2003 (EDW)
Propagate state vector using two-body force model
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