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A note on independent variables for restricted three-body problems

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Abstract

In studies of the elliptic restricted three-body problem, the true anomaly of the motion of the primaries is often used as the independent variable. The equations of motion then show invariancy in form from the circular case. It is of interest whether other independent variables exist, such that the invariant form of the equations is maintained. It is found that true anomaly is the only such variable.

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References

  • Szebehely, V. G.: 1967,Theory of Orbits, Academic Press, New York, pp. 589–594.

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  • Szebehely, V. and Giacaglia, G. O.: 1964, ‘On the Elliptic Restricted Problem’,Astron. J. 69, 230.

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Authors and Affiliations

  1. Dept. of Aerospace Engineering, The University of Michigan, Ann Arbor, Mich., USA

    T. A. Heppenheimer

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  1. T. A. Heppenheimer
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Heppenheimer, T.A. A note on independent variables for restricted three-body problems. Celestial Mechanics 4, 326–328 (1971). https://doi.org/10.1007/BF01231394

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  • DOI: https://doi.org/10.1007/BF01231394

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