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Paper: Distance Between Two Arbitrary Unperturbed Orbits
Volume: 316, Order and Chaos in Stellar and Planetary Systems
Page: 110
Authors: Kholshevnikov, K.V.; Baluyev, R.V.
Abstract: The problem of finding critical points of the distance function between two keplerian elliptic orbits (hence finding distance between them in a sense of set theory) is reduced to determination of all real roots of a trigonometric polynomial of degree eight (Kholshevhikov & Vassiliev 1999). A polynomial of smaller degree with such properties does not exist in non-degenerate cases. Here we extend the results to all 9 cases of conic section ordered pairs. Note, that ellipse—hyperbola and hyperbola—ellipse cases are not equivalent as we exclude the variable marking the position on the second curve.
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