Research On The Dynamics And Applications Of The Collinear Libration Point In The Earth-Moon Systems

The paper focuses on the dynamics and applications of the collinear libration point in the real Earth-Moon systems,including the onboard orbit prediction of the probe around the L1 and L2,and the dynamics of the point L3 which are seldom studied now.Studies on the onboard orbit prediction can be referenced by futures missions which utilize the points L1 and L2 in Earth-Moon systems.And studies on the point L3 enrich current theories on the dynamics around collinear libration points of the Earth-Moon system,and may be also useful for future mission which utilize this point.With increasing number of probes,autonomous navigation of probes can greatly save the efforts of stations on the ground,and meanwhile is necessary for some missions requiring real-time manipulations.Based on this background,we carried out the work of onboard orbit prediction of probes around the points L1 and L2.In the real Earth-Moon system,considering the inherent instability of orbital motions around L1 and L2,and limited onboard computation and storage resources,we propose a way to fulfill the goal of onboard orbit prediction.First,we analyze various perturbation forces on the probe around L1 and L2 in the real Earth-Moon system,and truncate the force model at a given accuracy.Then we simplify the ephemeris of the Moon and the Sun which is necessary for the third-body perturbation.The analytical ephemeris suffered from low accuracy,which is fetal to our problem here due to the strong instability.The numerical ephemeris,while is accurate enough,suffers the problem of a large onboard storage.In this thesis,we solve this problem from two ways.The first way is to construct a semi-analytical ephemeris using FFT analysis based on the real motions of the Moon,and using analytical ephemeris for the Sun and the planets.The error of using this semi-analytical ephemeris,when compared with that using the numerical ephemeris,is less than 1×10-4(with the unit as the mean distance between the Earth and the Moon)in position in a prediction time of 2-3 days.The second way is to use simplified numerical ephemeris.We remove many factors of the numerical ephemeris which are unnecessary for the orbit prediction of probes around the L1 and L2 points,and greatly reduces the storage of the simplified ephemeris.For example,the simplified DE 405 ephemeris needs a storage of about 3M while the simplified DE 406 ephemeris only needs a storage of 800K.The second half of the thesis is devoted to the dynamics around the collinear libration point L3 of the real Earth-Moon system.About the points L1 and L2,there are already some work on them.However,studies on the point L3 is relatively less.This is due to the fact that currently no such missions around this point are planned.However,there are already some potential applications of this point in some theoretical studies.In the future when missions in the Earth-Moon point are common to space agencies,we think this point may have special applications just as the Ll and L2 due to their special positions in space.So it is of some value to make some preliminary study.Actually,that is exactly the reason that drives the current study.In this part of the work,we have performed some analysis different from previous studies.More specific:(1)we use the real motions of the Moon and the Sun.In order to get the analytical representation of these motions,FFT analysis is used;(2)Compared with some previous studies using the similar approach as ours,our equations of motion are in a more complete form;(3)We directly present analytical formulae truncated at order three of the averaged system,along with short-period corrections to the averaged system.Compared with the results of the circular restricted three-body problem of the Earth-Moon system,the analytical solutions diverges much slower due to the fact that the frequency is more accurately computed by considering the perturbations from the Moon's orbit eccentricity and the Sun's gravitational perturbation.