Extension of the critical inclination

TL;DR

This paper extends the concept of critical inclination in satellite theory beyond the traditional J2 dominance, analyzing how additional gravitational harmonics and orbital parameters influence its solutions, with implications for orbit correction methods.

Contribution

It introduces a generalized analysis of critical inclination considering J2 and J4 harmonics, revealing multiple solutions and deviations from traditional values.

Findings

Critical inclination can have multiple solutions under certain conditions.

Values of J2 and J4 significantly affect the critical inclination.

Extended analysis applicable to celestial bodies beyond Earth.

Abstract

The critical inclination is of special interest in artificial satellite theory. The critical inclination can maintain minimal deviations of eccentricity and argument of pericentre from the initial values, and orbits at this inclination have been applied to some space missions. Most previous researches about the critical inclination were made under the assumption that the oblateness term J2 is dominant among the harmonic coefficients. This paper investigates the extension of the critical inclination where the concept of the critical inclination is different from that of the traditional sense. First, the study takes the case of Venus for instance, and provides some preliminary results. Then for general cases, given the values of argument of pericentre and eccentricity, the relationship between the multiplicity of the solutions for the critical inclination and the values of J2 and J4 is analyzed. Besides, when given certain values of J2 and J4, the relationship between the multiplicity of the solutions for the critical inclination and the values of semimajor axis and eccentricity is studied. The results show that for some cases, the value of the critical inclination is far away from that of the traditional sense or even has multiple solutions. The analysis in this paper could be used as starters of correction methods in the full gravity field of celestial bodies