The J2 Relative Perturbation Analysis of Satellite Formation under the Requirement of Relative Position Maintenance with Millimeter-Level Accuracy

Abstract

With high-precision DEM (Digital Elevation Model) and GMTI (Ground Moving Target Indicator) as the demand background, the influence of J2 zonal harmonic term perturbation on the relative motion of the millimeter-level short-range leader-follower satellites in near-circular orbit is studied through the relative perturbation method. An equation of motion that can describe the motion of the leader-follower satellites under the influence of J2 perturbation in near-circular orbit is derived, and the characteristics of the trajectory of in-plane periodic motion are analyzed. A study shows that under the influence of the relative perturbation of the J2 term, the in-plane periodic motion of the leader-follower satellites in near-circular orbit is a symmetrical closed “drop-shaped” trajectory with a period of 2π/n. By comparing with the results of numerical simulations, the correctness of the conclusions obtained in this paper is verified. According to the research results, it can be known that only using a thruster as the actuator to maintain the relative position can no longer meet the requirements of the long-term mm-level relative position maintenance. In the future, a new technical approach needs to be explored to achieve the long-term relative position maintenance with millimeter-level control accuracy.