Extension of the critical inclination
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 J _{2} 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 J _{2} and J _{4} is analyzed. Besides, when given certain values of J _{2} and J _{4}, 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.
 Publication:

Astrophysics and Space Science
 Pub Date:
 July 2011
 DOI:
 10.1007/s105090110685y
 arXiv:
 arXiv:1108.4639
 Bibcode:
 2011Ap&SS.334..115L
 Keywords:

 Critical inclination;
 Frozen orbit;
 Gravity;
 Mean element theory;
 Spherical harmonic;
 Venus;
 Astrophysics  Earth and Planetary Astrophysics;
 Physics  Space Physics
 EPrint:
 24 pages, 13 figures, accepted for publication in Astrophysics &