Orbit determination with the Keplerian integrals

2021/11/03 by Gronchi, Giovanni Federico · 1 citation
#Earth and Planetary Astrophysics (astro-ph.EP) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2111.02406

Abstract

We review two initial orbit determination methods for too short arcs (TSAs) of optical observations of a solar system body. These methods employ the conservation laws of Kepler's problem, and allow to attempt the linkage of TSAs referring to quite far epochs, differing by even more than one orbital period of the observed object. The first method (\tt Link2) concerns the linkage of 2 TSAs, and leads to a univariate polynomial equation of degree 9. An optimal property of this polynomial is proved using Gröbner bases theory. The second method (\tt Link3) is thought for the linkage of 3 TSAs, and leads to a univariate polynomial equation of degree 8. A numerical test is shown for both algorithms.

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• Preliminary orbits with over-determined systems of Keplerian conservation laws

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