ISBN-10: 0120121034

ISBN-13: 9780120121038

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Extra resources for Advances in Computers, Vol. 3

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3) The computation of the position and velocity a t a given time from the two-body formulas will itself lead to errors. This is especially true for the limiting case of nearly parabolic orbits. Thus when great accuracy is required, it will not be clear whether the integration or the analytic formulas introduce the largest error. The first two objections, but not the third, can be partially removed by basing the comparison on a three dimensional problem for which an analytic solution is known. Among such problems are the restricted three-body problem and the problem of a vehicle moving under the attraction of two fixed centers of gravitation.

The Delaunay I1 results are somewhat poorer. The major part of this error can be attributed directly to small errors in the mean anomaly as computed by the Delaunay formulas. The error is thus almost entirely along the path of the motion rather than perpendicular to it. 035". The error Ax in any position component x can be obtained from the formula AM Ax=-X n where AM is the error in the mean anomaly, n is the mean motion in degrees per second and x is the velocity in feet per second. r n = -2n =T 155(60)’ x - -20,500 fps and 18,500 ft.

Numerical integration over this revolution leads to the difference equation ~ . + l- Yn = f ( t n , yn> = fn. , vfn = fn - fn-k. The coefficients X, are given as j t h degree polynomials in l / k . 18) while those given b y Thomas [44]use the Gauss-Jackson central difference formulas. 18) was obtained with extremely high precision. On the other hand experiments by Thomas using a machine with a 12-digit word length and based on Cowell’s method led to optimistic conclusions. Because of the possible application of this approach to the satellite lifrtimc problem, further investigation of its capabilities appear warranted.

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