Stable orbits in the proximity of an asteroid: solutions for the Hayabusa 2 mission

This thesis studies the dynamics that arise in the surroundings of a small asteroid with the objective of identifying feasible trajectories for use in the Japanese mission Hayabusa 2. Hayabusa 2, which is expected to be launched at the end of year 2014, will travel to near earth asteroid 1999 JU3 and rendezvous with it. The main purpose of the mission is to collect a sample of the asteroid’s rock and carry it back to the earth for a detailed analysis. The spacecraft, however, will remain close to the asteroid for approximately 1.5 years, and it will perform several other types of scientific observations. All of the operations will be carried out from a controlled hovering position, that is, a fixed point between the earth the asteroid, close to the latter. This study aims at finding orbital strategies, different from hovering, that can enhance the scientific returns of this phase. In particular, orbits passing repeatedly close to the asteroid would provide a wealth of information on the gravitational field, and thus the internal structure, that would not be available through simple hovering. A first part of this work is focused on the circular augmented Hill’s 3–body problem, a formulation similar to the restricted 3-body problem that well describes the asteroidal environment, including solar radiation pressure. In this system we perform a grid search that results in a collection of several periodic orbits. We study a group of these orbits in detail, constructing their whole families with numerical continuation and analyzing their stability properties. The orbit families are also subject to a comparison on the basis of the characteristics most appropriate to Hayabusa 2. The result of this part is the identification of a type of orbit that is most feasible for the Japanese mission. Not treated in the above part are the two other important properties of the dynamical system, that is, the inhomogeneity of the asteroid’s mass and the ellipticity of its orbit around the sun. These are considered in the second part as perturbations, and a linear quadratic regulator (LQR) is set up in order to actively eliminate them. We show that the LQR is capable of stabilizing the periodic orbits against these and other effects, using thrusts attainable, in theory, with electric propulsion. The final part of this thesis addresses the need for trajectories that are stable in the elliptic Hill’s problem without any control. Rather then looking for periodic orbits in this more complex system, we use the results from the circular case to identify non-periodic repetitive trajectories that are nonetheless stable. The result in a map of the space of initial conditions containing a wide group of trajectories that neither impact nor escape from the asteroids for long periods of time. Among these trajectories, some are especially suitable for the purposes and instrument requirements of Hayabusa 2.