地球场的广义相对论效应对人造卫星轨道的影响

THE RELATIVISTIC EFFECT OF THE EARTH GRAVITY FIELD ON ORBIT OF A ARTIFICIAL SATELLITE

从计及J2项的地球重力场度规出发,我们导出在这样的度规场中人造卫星的摄动加速度及在径向横向和轨道面法向等方向的摄动函数,进而计算了轨道根数一阶导数的平均值,讨论了在这种重力场中卫星的轨道特性。其主要结论是: 1.球形地球的广义相对论摄动仅对近地点角距ω和平近点角τ产生长期项,而地球J2项的广义相对论效应不仅对这两个根数有长期摄动,而且对升交点角距Ω也有长期摄动。值得注意的是这两种广义相对论效应对半长轴a,偏心率e及倾角i都没有长期摄动; 2.球形地球的广义相对论效应对倾角i和升交点角距Ω仅有短周期摄动,但地球J2项的广义相对论效应除了对它们有短周期摄动外,还有长周期摄动,对Ω甚至还有长期摄动。

Starting from the metric of the Earth gravity, field containing J2 term we derived pertubation acceleration and the perturbation functions in the directions of radius, vertical, normal of orbit plan for a artificial satellite. Through the method of evaluating the average values of the perturbation functions of. the orbit elements, we discussed the orbit characateristic of the artificial satellite in such metric lield. The main conclusions are as follows, (1) The relativistic effect of sphere Earth produces the secular perturbations only to the argument of pericenter ω and L, but the relativistic effect of J2, term of the Earth produces the secular perturbations to the longitude of asci.nding rode Ω, besides ω and L. It is noted that these two relativistic effects do not produce secular perturbation to semi-major axis a, eccentricity e and inclination i; (2) The relativistic effect of sphere Earth only has short period perturbations to the inclination i and the longitude of ascinding rode Q, but the relativistic effect of J2 term of the Earth produces the long period perturbations to them besides the short period perturbation.