ORBITAL PERTURBATION DIFFERENTIAL EQUATIONS WITH NON‐LINEAR CORRECTIONS FOR CHAMP‐LIKE SATELLITE

Directly from the second order differential equations of satellite motion, the linearized orbital perturbation differential equations for CHAMP-like satellites are derived after introducing the reference orbit, and then introducing the omitted terms into the linearized orbital perturbation differential equations, the orbital perturbation differential equations with nonlinear corrections are derived. The accuracies for the orbital perturbation differential equations are estimated and the following results are obtained: if the measurement errors of the satellite positions and the non-gravitational accelerations are less than 3 cm and 3 × 10−10 m·s−2 respectively, the linearized orbital perturbation differential equations and the equations with nonlinear corrections can hold the accuracies 3 × 10−10 m·s−2 only when ρ ≤ 4.7 m and ρ ≤ 4.14 × 103 m respectively, where ρ is the distance between the satellite orbit and the reference one. Hence, compared with the linearized orbital perturbation differential equations, the equations with nonlinear corrections are suitable to establish normal system of equations of the gravity field's spherical harmonic coefficients in long time span. The solving method for the orbital perturbation differential equations is also given with the help of the superposition principle in the paper. At last, some imitation examples for CHAMP and GRACE missions are computed, and the results illustrate that the orbital perturbation differential equations with nonlinear corrections have higher accuracies than the linearized ones.