On the Distance Function Between Two Keplerian Elliptic Orbits

Details On the Distance Function Between Two Keplerian Elliptic Orbits On the Distance Function Between Two Keplerian Elliptic Orbits

Oct 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999cemda..75...75k&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 75, Issue 2, p. 75-83 (1999).

Astronomy and Astrophysics

Astronomy

8

Distance Function, Elliptic Orbits, Critical Points, Gröbner Basis, Computer Algebra, Distance Function, Elliptic Orbits, Critical Points, Gr&Ouml, Bner Basis, Computer Algebra

Scientific paper

The problem of finding critical points of the distance function between two Keplerian elliptic orbits is reduced to the determination of all real roots of a trigonometric polynomial of degree 8. The coefficients of the polynomial are rational functions of orbital parameters. Using computer algebra methods we show that a polynomial of a smaller degree with such properties does not exist. This fact shows that our result cannot be improved and it allows us to construct an optimal algorithm to find the minimal distance between two Keplerian orbits.

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