An optimization approach to search for quasi-critical inclinations for direct and retrograde orbits Applications for artificial satellites around Io

摘要

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 degrees and 116.56 degrees 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 C-22 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.