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On linking coefficient of two Keplerian orbits

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Abstract

We define a function of the set of pairs of Keplerian ellipses so that the sign of the function will be a topological invariant of their configuration. The sign is negative if and only if the related ellipses are linked. Two modifications of the coefficient which are more reliable in the case of closed to coplanar orbits are proposed. Explicit formulae representing the linking coefficients as functions of orbital elements are deduced. Extension in the case of unbounded orbits is obtained. We suggest different ways to use these coefficients for determining intersections of pairs of osculating Keplerian orbits. If we study dynamical behaviour of geometric configuration of pairs of Keplerian orbits, we can fix the moments of their intersections. These moments correspond exactly to the vanishing of linking coefficients.

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References

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Authors and Affiliations

  1. St. Petersburg University, e‐mail, Russia

    Konstantin V. Kholshevnikov

  2. Petersburg Branch of the Steklov Mathematical, Institute of the Russian Academy of Sciences, e‐mail, Russia

    Nikolay N. Vassiliev

Authors
  1. Konstantin V. Kholshevnikov
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  2. Nikolay N. Vassiliev
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Kholshevnikov, K.V., Vassiliev, N.N. On linking coefficient of two Keplerian orbits. Celestial Mechanics and Dynamical Astronomy 75, 67–74 (1999). https://doi.org/10.1023/A:1008384004589

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  • DOI: https://doi.org/10.1023/A:1008384004589

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