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General time elements for the two body problem

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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.

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Authors and Affiliations

  1. Dept. of Mathematics, Georgetown University, 20057, Washington D.C., USA

    Arnold Stokes

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  1. Arnold Stokes
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Additional information

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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Stokes, A. General time elements for the two body problem. Celestial Mechanics 17, 137–144 (1978). https://doi.org/10.1007/BF01371326

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  • DOI: https://doi.org/10.1007/BF01371326

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