This paper uses an optimal control method based on LQR to control satellite formation flying, and makes simulation for earth oblateness perturbation (J2 force) in the low earth orbits (LEO).

By use of wavelet power spectrum analysis and discrete wavelet transform,the periods and characteristics of J2 time series of GRACE time-variable gravity models from CNES/GRGS、CSR、GFZ are analyzed and extracted,and then they are compared with the corresponding results of J2 time series from SLR tracking data.

In this paper,the minimum-fuel,time-fixed optimal multiple-impulse rendezvous between non-coplanar elliptic orbits considering the J2 perturbation effects was mainly studied.

Two impulsive control strategys for formation keeping were put forward with regard to the problem that satellites formation could be destroyed under J2 perturbation.

In order to explore the effect of J2 perturbation,the non-singular orbit elements are imported.

The effect of J_2 perturbation on ellipse forming flying was also discussed.

The continuous and discrete control methods to keep the position of micro-satellite forming flying that flied in ellipse orbit when J_2 perturbation was in consideration were derived by using Lyapunov potential function in this paper.

The J2 invariant perturbation conditions were developed to describe the relative movement of satellites in formation with small eccentricities.