Orbit Research Based On Regular Method

With development of science and technology, it needs more and more support subjects for deep space exploration and other research in astronomy. One of the important supports is precise orbit of artificial satellites and natural satellites in solar system. Collision problem is one of the special difficulties of theory in orbit determination which need to resolve. It will be effective by using KS regularization method to solve this problem.To observe satellites is the first step for getting precise positions of the satellites. The observations for artificial satellites will supply precise orbit prediction. At the same time, the planet mass and more precise natural satellites’ orbit could get from the observations of natural satellites. Most of the natural satellites data are valuable for orbit determination and deep space exploration. The precision of observation could improve the orbit accuracy of satellites; simultaneously it requires improving the method of orbit determination. It needs to expand new method for resolving kinds of problem in orbit determination.One of the special problems in satellite’s orbit computation is the collision problem. This problem exists in movements of lots of earth-approaching objects, asteroids and comets. When a satellite movement follows perturbed two-body problem, the cubic distance of two bodies is inversely proportional to the acceleration of satellite. The distance of the two bodies is a singular point in the equation of movement, and it will bring some problems in orbit determination. In Kepler’s equation, the big eccentricity could make the distance of two bodies tend to zero, so the error of orbit determination will increase rapidly. The big eccentricity problem belongs to a kind of collision problem. In solar system, most irregular satellites have the features of big eccentricity and big inclination, the orbit problems may be solved by the method of solving collision problem.One of the methods of solving collision problem is to avoid the singular point in computation of satellite orbit. In 1965, Kustaanheimo and Stiefel set up a method named KS regularization method to avoid singular point in collision problem. This method also could solve big eccentricity problem in two-body problem. The KS regularization method could transfer three-dimensional physical space into four-dimensional parameter space by using fictitious time replace physical time. It analyzed the KS regularization method and used the method in Phoebe orbit which belongs to big eccentricity of satellite orbit. The study on KS regularization method with Phoebe orbit is kind of the foundation for other satellites with big eccentricity.There are several aspects in this dissertation:First, the numerical integration of satellites orbit is based on perturbed two-body problem. The forces which act on satellite except center gravitation also contain the gravitation of sun, major planet, main satellites, and primary oblateness. Usually, the method of numerical integration of satellites orbit consist of Adams-Cowell, Gragg-Bulirsh-Stoer、Runge-Kutta-Fehlberg and Runge-Kutta-Nystrom. These methods will be used in different situation with different conditions.Second, KS regular method could reduce the error propagation, and then resolve the problem of orbit stability. Based on research of Phoebe, KS regularization method is used in determination of Phobe orbit. The three-dimensional physical space transferred to four-dimensional parameter space. The result indicates that: the difference between the orbits which use KS regular method and which do not use regular method is around a hundred kilometer. The precious of the orbit of Phoebe which has far distance from earth is appropriate. Based on this work, it will spread this method to determine other big eccentricity satellites or comet, asteroid.Third, it is used a novel technology of orbit determination which called Paired Observation Combination for Both Stations(POCBS) in artificial satellites. In this paper it lists the observations of Uranian major satellites and Phoebe. In 1998-2007, there are 2358 observations of Uranian major satellites. The bias between observations and theory is 50-100 mas both in right ascension and declination. In 2005-2008, there are 1173 observations of Phoebe, and the observed positions with the JPL ephemeris shows the accuracy is about 100 mas. The observations appear to be consistent with the ephemeris within only about 50 mas. At the same time, it analyzes the difference of planet position between different planet ephemerides.