Study Of Orbital Dynamics Near Asteroid And Application In Gravity Tractor

Asteroid detection has caused extreme concern in scientific field in recent years, thus numerous missions about asteroid detection has been operated or in the process among several countries. The missions that have been done or in the process give an enormous impetus to creation of a brand new field in celestial mechanics---research of orbital dynamics of spacecraft around asteroid. Due to the unique properties of asteroid, such as its small mass, irregular shape, and complicated self-rotation, the difference between orbital dynamic of spacecraft in the gravitational field of traditional planet and that of asteroid is pretty big. Therefore the traditional orbital theory which is based on the circumstance of planet is unable to solve the orbital dynamic around asteroid accurately, unless proper improvement is applied in traditional method or some new method is introduced for substitution.This academic dissertation focuses on the research of orbital dynamic of spacecraft orbiting the asteroid and its application in gravity tractor, the main contents of which contains these respects:Firstly, the modeling of gravitational field of irregularly-shaped asteroid is studied, and follows an introduction of commonly used method and property of modeling of gravitational-field of asteroid. As the scarcity of data of fly-by orbit, the accurate spherical harmonic coefficients are unable to obtain from a spherical harmonic functional model, and using polyhedral model can only help obtain computational results, which is inconvenient for orbital analysis and design. In order to solve the problems above, this paper proposes a new method based on polyhedral model to determine the spherical harmonic coefficients of gravitational field of irregularly-shaped asteroid. The proposed method combines the advantages of polyhedral model and determining spherical harmonic coefficients of gravitational field, takes the data of asteroid's shape as the information source of determining spherical harmonic coefficients of gravitational field. By fully taking advantages of astro-observation on the ground and existed shape-information of asteroid obtained from fly-by mission, the relative high-accurate spherical harmonic coefficients can be obtained before the launch of detecting mission.Secondly, the orbit around equilibrium point of asteroid in a bigger mass is studied. In order to study the properties of orbital motion around equilibrium point, a method based on the first-order analytical solution is proposed, in which the linearized first-order analytical solution is given to analyze the properties of orbital motion around stable and unstable equilibrium point. In connection with the unstable ones, an orbital control law based on low-thrust engine is given, which can enable the spacecraft to orbit around the nominal orbit given by first-order analytical solution. To determine the stable region around the stable ones, the 1:1 orbital resonance theory is adopted to derive the formula of width of stable region.Subsequently, a special periodical orbit exists around equilibrium point of asteroid (halo-orbit) is studied, due to the strong nonlinearity around equilibrium point, adopting analytical method is very difficult to determine halo orbit, and numerical searching algorithm highly depends on the initial guess, which means hard to convergence. To solve the problems above, a hybrid searching algorithm based on the third-analytical solution is proposed, in which the Lindstedt-Poincarémethod is introduced in the first place to solve the third-order analytical solution of halo orbit, then the differential correction method is adopted to revise the initial value given by third-order analytical solution, thus the accurate computational solution of halo orbit can be obtained finally. This method combines the advantages of analytical method and computational method, thereby the high computational efficiency can be assured and of course the certainty of convergence of algorithm.Finally, displaced orbit in two-body system and three-body system is researched respectively. The analysis of hover-orbit in two-body system indicates that during the labor of gravity tractor, the reduction of fuel can cause its orbital destabilization. In order to maintain the stabilization of orbit of gravity tractor, this paper proposes three different methods to solve the fuel-reduction problem, and analyzes the orbital properties of these three methods, also the comparison of effects of these three methods on the asteroid traction respectively is made. A hover orbit based on the idea of average is proposed to figure out whether there exists such a hover orbit of spacecraft in three body system including sun, asteroid and spacecraft, in which the Hill equation is introduced to describe the orbit of gravity orbit in three-body system, and by using average-method to progress the motion equation, the fast variable is casted aside to obtain the average solution, which can not only determine the hover orbit of spacecraft with respect to asteroid and also analyze the stability of this orbit and its stable region.