The Assessment Of The Semi-analytical Method In The Long-term Orbit Prediction Of Earth Satellites

This Master Dissertation is based on a project during my graduate student learning. It studies the performance of the semi-analytical method used in the long-term prediction in Earth satellite orbits and assesses the accuracy and speed applied in different kinds of orbits.The introduction is in the first chapter. Firstly, introduce the background of this dissertation. To understand the long-term evolution and distribution of the objects in space, we need to make the orbit prediction. Taking the accuracy and speed into account, it is proper to use the semi-analytical method. Although it is not a new method, there are seldomly seen papers which quantitatively report the performance. This situation makes some difficulties when we use the semi-analytical method in practical work. For these reasons, we quantitatively assess the accuracy and speed of the semi-analytical method in usual Earth satellite orbits. The results can help us understand its feasibility in the long-term orbit prediction. Secondly, we introduce the research situation home and abroad. Finally, show the time system, coordinate system, perturbation equations and the unit system.The second chapter describes the satellite prediction methods. To solve the perturbation equations there are three ways:numerical, analytical and semi-analytical. Numerical method uses numerical integrator to calculate the orbital elements step by step which has a high accuracy but costs much time. Analytical one will give an explicit solution formulas of the orbital elements under the two-body problem with perturbations. It will directly give the results of the end point and have a fast speed. Nevertheless, it is better to use the formulas within 103 units of time and it limits the time length of the prediction. The semi-analytical method uses the numerical integrator to calculate the averaged system whose accuracy is higher than the analytical one and speed is faster than the numerical one. The key point of the semi-analytical method is how to get the averaged perturbation accelerations. We introduce the analytical average and the numerical average respectively and explain the reason why we choose the analytical average in the semi-analytical method.The third chapter explains the treatment of each perturbation in the semi-analytical method. This chapter successively introduces the details of the non-spherical gravitation, third body, solar radiation pressure and atmospheric drag in the semi-analytical method. When adding a new perturbation acceleration, the semi-analytical method will be applied to different altitudes of satellites to understand the dynamic characteristics of the new perturbation and its influence on the accuracy and speed.The forth chapter applies the semi-analytical method to different kinds of orbits with the full force model. Firstly, a simple example is given to analyze the suitable degrees and orders of the non-spherical gravitation for different altitudes of orbits. Then study the accuracy of the semi-analytical method with different initial pairs of a,i under the full force model. We apply the method to kinds of orbits, like low Earth orbit (without atmospheric drag), low Earth orbit (with atmospheric drag),12-hours medium Earth orbit and 24-hours geostationary Earth orbit. By comparing a large number of examples, it is found that the osculating element error of a,e,i is O(10’3), and the error of Ω. is within 10°. Although in most situations the semi-analytical method with the first and second order accelerations works well, there still exist some special cases where the performance is not satisfactory. Some of these cases are accompanied by special dynamic phenomena, some of which are attributed to the treatment method. The former, we give the explanation in this chapter; the latter, we will put forward a reasonable solution in the fifth chapter.The fifth chapter discusses the special issues in our implementation process of the semi-analytical method. Firstly, we explain the reason for the accuracy degradation problem around i=90°. Then give the solution for high eccentricity orbit. Thirdly, we discuss the necessity for the additional perturbation of the coordinate system in the semi-analytical method. In the end, we explain the reason for the "island" structure in the LEO error map.For different kinds of Earth satellite orbits, this dissertation quantitatively shows the performance of the semi-analytical method for the long-term prediction of the 100-year scale. Of course, here are only some basic discussions, the application of the semi-analytical method is far more than these. The method can also be used in the areas like the fast estimation of debris distribution after collision, the orbit determination and correlation in the spatial object cataloging and so on. Hoping this work can give some useful reference to the people in related fields.