火卫二动力学模型与精密定轨研究

Precision Orbit Determination for the Dynamics Model of Deimos

模型充分考虑了火卫二与火星的二体运动模型、火星重力场、太阳系主要天体的三体摄动、广义相对论效应、火星固体潮、火卫二天平动等影响火卫二运动的因素,建立了火卫二动力学模型,并将人造卫星精密定轨的方法扩展至自然天体火卫二,建立了针对动力学模型数据拟合的平差模型。分别利用轨道研究中主流的8阶RKF (Runge-Kutta-Fehlberg)、12阶ABM(Adams-Bashforth-Moulton)和Gauss-Radau三种积分算法求解火卫二轨道,比较计算效率,将轨道计算中使用的完整相对论模型与简化相对论模型的计算结果进行了对比。数值实验结果表明:建立的火卫二动力学模型以及平差模型稳定可靠;在同等实验条件下,三种积分算法计算结果精度相当,12阶ABM积分算法的计算效率最高;两种相对论模型计算结果相当。

This paper comprehensively considers factors influencing the motion of Deimos,such as the two-body motion model between Deimos and Mars,Mars’gravity field,the three-body perturbation from major celestial bodies in the solar system,general relativity effects,Martian solid tides,and the libration of Deimos.A dynamical model for Deimos is established,and the methodology of precise satellite orbit determination,originally designed for artificial satellites,is extended to the natural satellite Deimos.Additionally,an adjustment model for fitting dynamic model data is developed.In the process of model establishment,this paper compares the computational efficiency of three mainstream integration algorithms in orbital research,namely the 8-order Runge-Kutta-Fehlberg(RKF),12-order Adams-Bashforth-Moulton,and Gauss-Radau methods when solving Deimos’orbit.Simultaneously,a comparison is made between the results obtained using the complete general relativity model and a simplified relativistic model that treats Deimos’orbit as circular.Numerical experimental results indicate that the established dynamical model and adjustment model for Deimos are stable and reliable.Moreover,under equivalent experimental conditions,the computational accuracy of the three integration algorithms is comparable,with the 12th-order Adams-Bashforth-Moulton method demonstrating the highest computational efficiency.The results from both relativistic models are comparable,and the simplified model can be directly utilized when considering computational efficiency.This work lays the foundation for the subsequent development of a new dynamical model for Martian satellites,incorporating complete rotation,and the construction of accurate Deimos ephemerides.