Passive and periodic circular-like formations at critical inclination around an oblate earth

Passive and periodic formations minimize the active control of long-term satellite formation flying. Among different passive and periodic formations, the circular-like ones have potential applications in many formation flying missions. This paper shows that such formations under J₂ perturbation are only possible at the critical inclination. It is revealed that strict constraints for both the reference and member satellite orbits are necessary: the reference orbit must be at the critical inclination with a nonzero eccentricity and an argument of perigee not on the equator plane, while every member satellite orbit subjects to four constraints: the same inclination, semi-major axis and eccentricity with the reference orbit, as well as a same small bias in the along-track direction. Further study leads to a geometrical design approach in the rest 2 dimensional constraint space. Results in this paper are valid in arbitrary elliptic orbits under J₂ perturbation.