General time elements for the two body problem |
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| Authors: | Arnold Stokes |
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| Institution: | (1) Dept. of Mathematics, Georgetown University, 20057 Washington D.C., USA |
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| Abstract: | When integrating a perturbed two-body problem, very often the propagation of the numerical error is reduced by using a new time variables defined by dt/ds=|q|
n
, (|q| is the radial distance,t the time). This paper introduces a time element for such transformations, i.e., a new variablet
n is defined so that dt
n/ds=1+ (perturbing terms) andt=F
n(tn), whereF
n is a known function. The time element equation should be useful in reducing the error in the determination of the timet.F
n is given explicitly forn=1, 3/2, 2, 5/2 and 3, and a general expression is given for other values.The work was performed while the author was an NRC Senior Research Associate, Goddard Space Flight Center, Greenbelt, Md., U.S.A. |
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| Keywords: | |
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