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arXiv · 2312.14764

Orbit determination from one position vector and a very short arc of optical observations

Erica Scantamburlo·Giovanni F. Gronchi·Giulio Baù
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Abstract

In this paper we address the problem of computing a preliminary orbit of a celestial body from one topocentric position vector and a very short arc (VSA) of optical observations. Using the conservation laws of the two-body dynamics, we write the problem as a system of 8 polynomial equations in 6 unknowns. We prove that this system is generically consistent, namely it admits solutions at least in the complex field. From this system we derive a univariate polynomial $\mathfrak{v}$ of degree 8 in the unknown topocentric distance at the mean epoch of the VSA. Through Gr\"obner bases theory, we show that the degree of $\mathfrak{v}$ is minimum among the degrees of all the univariate polynomials solving this problem. The proposed method is relevant for different purposes, e.g. the computation of a preliminary orbit of an Earth satellite with radar and optical observations, the detection of maneuvres of an Earth satellite, and the recovery of asteroids which are lost due to a planetary close encounter. We also show some numerical tests in the case of asteroids undergoing a close encounter with the Earth.

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Erica Scantamburlo, Giovanni F. Gronchi, Giulio Baù. 2023-12-22. Orbit determination from one position vector and a very short arc of optical observations. https://arxiv.org/abs/2312.14764

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