2023/12/22 by Erica Scantamburlo, Scantamburlo, Erica, Giovanni F. Gronchi +3
Computer Science · Physics and Astronomy · #Advanced Frequency and Time Standards #FOS: Physical sciences #Mathematical Physics (math-ph) #Polynomial and algebraic computation #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2312.14764
openalex publication_date 2023/12/22 · openalex created_date 2023/12/26 · openalex updated_date 2026/07/28
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 \mathfrakv of degree 8 in the unknown topocentric distance at the mean epoch of the VSA. Through Gröbner bases theory, we show that the degree of \mathfrakv 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.