  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
