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Research Article Open access CC BY 4.0

Analytic Inversion of Closed form Solutions of the Satellite’s J2 Problem

Alessio Bocci, Giovanni Mingari Scarpello

Asian Research Journal of Mathematics · pp. 50–68 · Published 21 Jul 2021

10.9734/arjom/2021/v17i530299

Abstract

This report provides some closed form solutions -and their inversion- to a satellite’s bounded motion on the equatorial plane of a spheroidal attractor (planet) considering the J2 spherical zonal harmonic. The equatorial track of satellite motion- assuming the co-latitude φ fixed at π/2- is investigated: the relevant time laws and trajectories are evaluated as combinations of elliptic integrals of first, second, third kind and Jacobi elliptic functions. The new feature of this report is: from the inverse t = t(c) we get the period T of some functions c(t) of mechanical interest and then we construct the relevant c(t) expansion in Fourier series, in such a way performing the inversion. Such approach-which led to new formulations for time laws of a J2 problem- is benchmarked by applying it to the basic case of keplerian motion, finding again the classic results through our different analytic path.

J2 problem bounded satellite motion Fourier series elliptic integrals Jacobi elliptic functions

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Cited by 1

The Differential Equations of Gravity-free Double Pendulum: Lauricella Hypergeometric Solutions and Their Inversion

A. Bocci, G. Scarpello · Asian Research Journal of Mathematics · 2021

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