Eur. Phys. J. Special Topics 229, 1429–1440 (2020)
https://doi.org/10.1140/epjst/e2020-900189-y

Regular Article

An optimization approach to search for quasi-critical inclinations for direct and retrograde orbits

Applications for artificial satellites around Io

¹ Space Mechanics and Control Division, National Institute for Space Research, São José dos Campos, São Paulo, Brazil
² Institute of Science and Technology, Federal University of São Paulo, São José dos Campos, São Paulo, Brazil
³ Center for Science and Technology in Energy and Sustainability, Federal University of Recôncavo of the Bahia, Feira de Santana, Bahia, Brazil

^a e-mail: livia.thibes@gmail.com

Received: 31 August 2019
Received in final form: 26 December 2019
Published online: 29 May 2020

Abstract

When only the secular terms due to the central body oblateness are considered in the gravitational potential, the critical inclination classical values are about 63.43° and 116.56° for the direct and retrograde orbits, respectively. If sectoral terms are included into disturbing function, the equations of motion become coupled, then searching for critical inclinations is not a trivial problem. Thus, for the purpose of overcoming this difficulty and to shed light on the effect of inserting the C₂₂ sectoral hamornic in the Hamiltonian function, the quasi-critical inclinations concept is revised and its solution is proposed as an optimization problem. In this sense, the present article makes the following contributions to the quasi-critical inclination problem: (i) applying the nonlinear optimization tools to solve this problem; (ii) through this technique, obtaining quasi-critical inclinations for the retrograde case for the first time; (iii) using this technique to find direct and retrograde orbits around Io, a very important body to be studied in the future.