Correcting Semi-Major to Reduce Effect of J2 Perturbation on Formation Flying

After the relative motion coordinate frame is defined, linear equations of relative motion described by small orbital element bias are developed with respect to it. And then the differential expressions of relative position drifts due to J₂ perturbation are established. Integrating them along the orbit, the drifts without effects of true anomaly are obtained. A cost function denoting the magnitude of drifts is selected. The optimal solution to the function is the optimal correction of semi-major. The calculating formula is available. Numerical simulations are employed to check the fidelity of the approach. Comparisons of illustrations show that the approach has more advantages in reducing the relative position drifts and better shape the relative orbit