Effect of Initial Orbital Elements on Orbital Evolution of MEO BDS-3 Satellite with Considering the Lunisolar Secular Resonance

This paper investigates the effect of initial orbital elements on the orbital evolution of the Medium Earth Orbit (MEO) satellites of the third generation of the BEIDOU Navigation Satellite System (BDS-3), considering the lunisolar secular resonance. The double-averaged Hamiltonian dynamical model is used to simulate the long-term evolution of the orbits for 24 BDS-3 MEO satellites in the absence of active control. The simulation results show that some satellites could enter the Earth’s atmosphere as their eccentricities increase. On the contrary, some other satellites have stable orbits during the long-term evolution. The effects of different $${{e}_{0}}$$ , $${{i}_{0}}$$ , $${{\omega }_{0}}$$ , and $${{\Omega }_{0}}$$ on the long-term evolution are investigated, respectively. The results show that when $${{e}_{0}}$$ is larger, the eccentricity reaches $${{e}_{{{\text{max}}}}}$$ faster; and the variations in $${{e}_{0}}$$ or $${{\omega }_{0}}$$ don’t change the values of the resonance angle in resonance. However, both the change of $${{i}_{0}}$$ and $${{\Omega }_{0}}$$ will change the values of the resonance angle in resonance. The maximum eccentricity method is used to study the influences of different initial conditions (including initial orbital elements and initial epoch) on the long-term evolution of MEO satellites. The results show that the changes of $${{i}_{0}}$$ , $${{\omega }_{0}}$$ , and $${{\Omega }_{0}}$$ affect the distribution of $${{e}_{{{\text{max}}}}}$$ in the $$\left( {{{\Omega }_{0}}, {{\omega }_{0}}} \right)$$ space. In the $$\left( {{{\Omega }_{0}},{{\omega }_{0}}} \right)$$ space, if the initial $${{\Omega }_{{\text{M}}}}$$ changes, the shape of the $${{e}_{{{\text{max}}}}}$$ map changes, but the maximum value of $${{e}_{{{\text{max}}}}}$$ barely changes. Apart from the region with large values of $${{e}_{{{\text{max}}}}}$$ in the $$\left( {{{\Omega }_{0}},{{\omega }_{0}}} \right)$$ space, there are also regions with small values of $${{e}_{{{\text{max}}}}}$$ , where the differences between $${{e}_{{{\text{max}}}}}$$ and $${{e}_{0}}$$ are minimal.