Orbit Analysis, Design And Control In Deep Space

This paper studies the issues about orbit analysis and orbit design in deep space explorations. There are two parts—Mars explorations and asteroid explorations. Each part includes two types of orbits, the transfer orbits and the orbits around target bodies.The chemical propulsion system and the electric propulsion system are used to design the Earth-Mars transfer orbits. For the former, the launch windows of low-energy orbits in the simplified two-body model are chosen for the restrictions of fuel and the launch capacity of the rocket. Then the classical patched conic method is employed to obtain the two-body transfer orbits of three sections. Afterwards, the relations of how the variables influence each other are studied before we can judge quickly whether the suitable orbit can be given or not. However, for the low-thrust transfer orbit, the transfer time has only to be matched with low-thrust. The whole Earth-Mars low-thrust orbit is divided into three parts according to the property of low-thrust orbit. The transfer time within the gravisphere of either the Earth or the Mars is so long that the optimal control strategy minimizing the time is adopted. The approximate solution is obtained by solving the approximate differential equations. Therefore, the optimal control problem is simplified into orbit integrations. For the Sun-centered section, the optimal fuel orbit is preferred. After that, the three sections can be patched smoothly by adjusting the transfer time slightly.The orbits around the Mars should be studied after the probe is captured by the Mars. Similar to the Earth, the Mars rotates fast. However, the gravitational field of the Mars is quite different from that of the Earth. The coefficient J2,2is very close to J2and other coefficients are also larger compared with those of the Earth, so the coupled perturbations especially that of J2and J2,2cannot be neglected in analytical solution. Besides, both of the two natural satellites of the Mars are close to the Mars, hence their perturbations for the high-altitude satellites are not negligible. Nevertheless, there are no publications concerning the analytical ephemerides of the two natural satellites. Both of the two problems need to be solved. In this paper, the analytical formulae of the coupled perturbations and the natural satellites’perturbations are derived, and the analytical solution of the Mars probe is constructed. Then the analytical solutions of the two natural satellites are given. After simplifying the formulae and abandoning the short-period terms, the coefficients of the analytical ephemerides can be obtained. At last, the numerical solutions are provided to verify the precisions of the analytical solution and the analytical ephemerides. The results show that the position error of the low-altitude satellite is about500m with the duration of1-2d. For the natural satellites, the appropriate duration is about180d for Phobos and Deimos if the error needed to be within O(10-4).Most of small body explorations are of the type of multiple targets and multitasking, so the paper uses three asteroids as the target bodies, flying by the first one and circling around or accompanying the second one and the third one. Different from the planets, the design of the transfer orbit is relatively simple for the gravitational scopes of most asteroids are so small that can be neglected. However, the difficulty is to find out the optimal launch window of exploring multiple asteroids. This paper divided the whole transfer orbit into two sections reasonably according to the restrictions and the properties of task type. For each section, the chemical propulsion orbit with low energy and moderate duration is obtained and then optimized using low-thrust. On the basis of the methods above, two kinds of orbits are given with chemical propulsion and electric propulsion—the low-thrust orbit and the orbit with both high and low thrust. Besides, the methods and software are also applicable for other deep space orbit design.The gravity fields of the asteroids are mostly very small and irregular, so it is necessary to study the orbits around them with special treatment. In the paper, two kinds of intermediate orbits for asteroid explorations are proposed. One is around the collinear libration points of the Sun-asteroid restricted three-body problem. The other is around the asteroid itself. The first kind of intermediate orbit is applicable to asteroids with known masses, while the second is suitable for asteroids with unknown or negligible masses. Analytical solutions of these two intermediate orbits in the simplified models are introduced first, and then numerical algorithms are used to refine them to obtain the true orbits in the real force model. At last, the problem of station-keeping is addressed. Both of low-thrust control and solar sail control are used. The solar sail control strategy includes varying the solar sail area and varying the pitch angle and the yaw angle. The linear optimal feedback control law is considered, and numerical simulations are made to both kinds of intermediate orbits. The results show that both kinds of orbits are feasible. For low-thrust control strategy, the cost is reasonable and mainly depends on the initial insertion error. For the other one, the technique of varying the pitch angle and the yaw angle is better than varying the solar sail area.