Orbit state deviation prediction model with second-order correction due to the J2 term

Abstract

The analytic orbit state deviation prediction model derived based on the State Space Perturbation Method (SSPM) has proven effective and efficient to predict the impact error of ballistic missile caused by the J2 term. However, the accuracy of this analytic model declines when the prediction point is located in the ascending portion of an orbit with large eccentricity. To deal with this problem, a second-order correction algorithm is proposed in this paper by deriving the partial derivatives of the analytic integral function with respect to the reference two-body orbit parameters. Three application scenarios are adopted to verify the accuracy of the proposed orbit state deviation prediction model, namely orbit injection point deviation prediction of carrier rocket, impact deviation prediction of ballistic missile and re-entry point deviation prediction of space shuttle. The accuracy of the proposed model is compared with the one without second-order correction as well as the Kozai’s solution. Simulation results show that the proposed model has high precision in each case.