Study Of The Numerical Methods For Satellite Dynamics Equations And Application Of Satellite Laser Ranging Technique To Precise Orbit Determination

The differential equations that describe the artificial satellite motion are very complicated, and it is impossible to get the analytic express of solution. Its analytic solution such as small parameter power series solution cannot meet the orbit determination accuracy that artificial satellite application needs. So this makes numerical method in ordinary differential equations for the satellite dynamics occupy very important position.This paper studied the numerical methods in celestial motion equations from the applied aspect. First, now in all common numerical methods for the satellite dynamics equations the most important problem that needs to be improved is stability problem. Whether are a single-step methods or multi-step methods, the error in calculating every step will spread and accumulate. When the error accumulation can be controlled, the relativemethod is just stable.Numerical stability is relative with the choice of step-size. The weakness of fixed step-size is that step-size is not variable regardless the curvature of each point of the integral curve change or not, which will affirmatively bring serious error in these points that the value of curvature is bigger. And, this kind of error will accumulate in calculating process. If the change of step-size is controlled by the value of curvature of integral curve, the result can avoid such an error accumulation. From this viewpoint, we fulfilled to control the step-size with the curvature of integral curve. The step-size is smaller in calculating these points that the value of the curvature is bigger and the step-size is bigger in calculating these points that the value of the curvature is smaller, which is rather reasonable choice and is also a creative point in this paper.The next in order, it is well known that the formula of Taylor series method is simple and its stability is good, but its high level derivative is not easy to be gotten and so it is difficult in practice. This paper points out that the values of the right function at arbitrarily points can express the high level derivatives of at , and gives out the formulas. So we translated the numerical methods for artificial satellite motion equation into the iterative method for a set of nonlinear equations. This kind of integrator is high accurate and great stable.Author also did some research work for the application of Satellite Laser　Ranging(SLR) technique to precise orbit determination. We calculated theorbit elements of Lageos-1 with using the worldwide SLR data and the orbit accuracy attain 1 cm, meanwhile calculated the coordinates of Changchun SLR Station. Some conclusions were gotten by analyzing the data processing results of Changchun SLR Station. Further more, author designed an implementary project for daytime observation at Changchun SLR Station.