Analytical propagation for third-body perturbed orbits

TY - JOUR

T1 - Analytical propagation for third-body perturbed orbits

AU - NIE, Tao

AU - LI, Jinfeng

AU - ZHANG, Shijie

AU - REN, Jiadong

AU - XU, Rui

N1 - Publisher Copyright: © 2025

PY - 2026/4

Y1 - 2026/4

N2 - With the increasing complexity of space missions, traditional Keplerian models no longer satisfy the precision requirements for spacecraft orbital calculations in modern deep space exploration and lunar transfer missions. Unlike J2 perturbations, third-body perturbations induce long-period oscillations in orbital eccentricity and inclination, resulting in significant nonlinear changes in long-term orbital evolution that present challenges for deriving analytical solutions. This paper proposes an analytical method for spacecraft orbit propagation under third-body perturbations, which divides the calculation into long-term and periodic components. The long-period terms are determined by solving the mean orbital dynamics using elliptical integrals, while the periodic terms are computed using von Zeipel theory. The proposed method enables the analytical computation of satellite orbital states at arbitrary epochs. This method accounts for the perturbing body's orbital eccentricity and inclination, making it applicable to all scenarios, including both circulating and librating orbit types. The effectiveness of the proposed method is verified through numerical simulations. This analytical propagation method provides robust support for orbital optimization and autonomous control in deep space exploration missions.

AB - With the increasing complexity of space missions, traditional Keplerian models no longer satisfy the precision requirements for spacecraft orbital calculations in modern deep space exploration and lunar transfer missions. Unlike J2 perturbations, third-body perturbations induce long-period oscillations in orbital eccentricity and inclination, resulting in significant nonlinear changes in long-term orbital evolution that present challenges for deriving analytical solutions. This paper proposes an analytical method for spacecraft orbit propagation under third-body perturbations, which divides the calculation into long-term and periodic components. The long-period terms are determined by solving the mean orbital dynamics using elliptical integrals, while the periodic terms are computed using von Zeipel theory. The proposed method enables the analytical computation of satellite orbital states at arbitrary epochs. This method accounts for the perturbing body's orbital eccentricity and inclination, making it applicable to all scenarios, including both circulating and librating orbit types. The effectiveness of the proposed method is verified through numerical simulations. This analytical propagation method provides robust support for orbital optimization and autonomous control in deep space exploration missions.

KW - Autonomous control

KW - Elliptic integral

KW - Orbit propagation

KW - Third-body perturbation

KW - Von Zeipel

UR - https://www.scopus.com/pages/publications/105029512468

U2 - 10.1016/j.cja.2025.103865

DO - 10.1016/j.cja.2025.103865

M3 - Article

AN - SCOPUS:105029512468

SN - 1000-9361

VL - 39

JO - Chinese Journal of Aeronautics

JF - Chinese Journal of Aeronautics

IS - 4

M1 - 103865

ER -