Analysis of the Critical Inclination in Orbit of Planetary Moons
Jean Paulo dos Santos Carvalho1; Brenda Melo Ferreira1; Denilson Paulo Souza dos Santos2
1 UFRB; 2 UNESP
Resumo
One of the first authors to analyze the problem of critical inclination was Brouwer \cite{Brouwer} in 1959. But even today, several papers are analyzing this problem.Here, we present an approach to analyze the critical inclination of orbits around the planetary moons considering the $J_{2}$ and $C_{22}$ terms of the their non-uniform distribution of mass. The main focus is in the development of the equation due to the $C_{22}$ term (equatorial ellipticity), where the explicit dependence of time is not eliminated, rather, we use a mathematical expression to maintain this time dependence in the equations. Applications are made for several moons of our solar system. We show that the value of the critical inclination depends on the longitude of the ascending node and of the time. The value of the $J_{2}/C_{22}$ ratio, condition of the hydrostatic equilibrium, affects the result of the critical inclination.
Palavras-chave: Astrodynamics; Critical Inclination; Non-sphericity; Artificial Satellite