Analytical propagation on relative motion of geostationary earth orbit satellites with orbital perturbations

An accurate description of the relative motion of satellites is critical for space missions in the complex geostationary earth orbit space environment. Here, a new relative motion model is established considering major perturbations. To avoid the singularity of the classical orbital elements, a set of quasi-non-singular orbital elements are used to represent the relative motion states, which is further extended by considering the SRP coefficient difference. On the basis of existing classical model, an analytical model is derived by taking the Taylor expansion of the time derivative of the perturbation functions to the first order in the neighbourhood of the reference satellite, which contains the earth's oblateness perturbation, the third-body perturbations and the solar radiation pressure perturbation. This method avoids solving the complex differential equations of relative motion directly and provides a general framework for including arbitrary perturbations into the model. The new model is verified in uncontrolled natural relative motion scenarios and position-keeping control scenario, respectively. The results show that the proposed model has high accuracy and strong competitiveness.