A study of single- and double-averaged second-order models to evaluate third-body perturbation considering elliptic orbits for the perturbing body
type: Item
instance of: scholarly article
title: A study of single- and double-averaged second-order models to evaluate third-body perturbation considering elliptic orbits for the perturbing body
zbMATH Open document ID: 1296.70016
DOI: 10.1155/2013/260830
author: R. C. Domingos
author: R. Vilhena de Moraes
author: A. F. Bertachini de Almeida Prado
published in: Mathematical Problems in Engineering
publication date: 2014-10-13T00:00:00Z
review text: Summary: The equations for the variations of the Keplerian elements of the orbit of a spacecraft perturbed by a third body are developed using a single average over the motion of the spacecraft, considering an elliptic orbit for the disturbing body. A comparison is made between this approach and the more used double averaged technique, as well as with the full elliptic restricted three-body problem. The disturbing function is expanded in Legendre polynomials up to the second order in both cases. The equations of motion are obtained from the planetary equations, and several numerical simulations are made to show the evolution of the orbit of the spacecraft. Some characteristics known from the circular perturbing body are studied: circular, elliptic equatorial, and frozen orbits. Different initial eccentricities for the perturbed body are considered, since the effect of this variable is one of the goals of the present study. The results show the impact of this parameter as well as the differences between both models compared to the full elliptic restricted three-body problem. Regions below, near, and above the critical angle of the third-body perturbation are considered, as well as different altitudes for the orbit of the spacecraft.
Mathematics Subject Classification ID: 70F15
Mathematics Subject Classification ID: 70M20
zbMATH DE Number: 6354578
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/260830
OpenAlex ID: W2029055809
Wikidata QID: Q59025315
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description: scientific article; zbMATH DE number 6354578