Solar sail capture trajectories at Mercury

Mercury is an ideal environment for future planetary exploration by solar sail since it has proved difficult to reach with conventional propulsion and hence remains largely unexplored. In addition, its proximity to the Sun provides a solar sail acceleration of order ten times the sail characteristic acceleration at 1 AU. Conventional capture techniques are shown to be unsuitable for solar sails and a new method is presented. It is shown that capture is bound by upper and lower limits on the orbital elements of the approach orbit and that failure to be within limits results in a catastrophic collision with the planet. These limits are presented for a range of capture inclinations and sail characteristic accelerations. It is found that sail hyperbolic excess velocity is a critical parameter during capture at Mercury, with only a narrow allowed band in order to avoid collision with the planet. The new capture methodis demonstrated for a Mercury sample return mission

Binary Collisions and the Slingshot Effect

We derive the equations for the gravity assist manoeuvre in the general 2D case without the constraints of circular planetary orbits or widely different masses as assumed by Broucke, and obtain the slingshot conditions and maximum energy gain for arbitrary mass ratios of two colliding rigid bodies. Using the geometric view developed in an earlier paper by the authors the possible trajectories are computed for both attractive or repulsive interactions yielding a further insight on the slingshot mechanics and its parametrization. The general slingshot manoeuvre for arbitrary masses is explained as a particular case of the possible outcomes of attractive or repulsive binary collisions, and the correlation between asymptotic information and orbital parameters is obtained in general.Comment: 12 pages, 7 figures, accepted for publication Dec'07, Celestial Mechanics and Dynamical Astronom

Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming

In this paper an optimisation algorithm based on Differential Dynamic Programming is applied to the design of rendezvous and fly-by trajectories to near Earth objects. Differential dynamic programming is a successive approximation technique that computes a feedback control law in correspondence of a fixed number of decision times. In this way the high dimensional problem characteristic of low-thrust optimisation is reduced into a series of small dimensional problems. The proposed method exploits the stage-wise approach to incorporate an adaptive refinement of the discretisation mesh within the optimisation process. A particular interpolation technique was used to preserve the feedback nature of the control law, thus improving robustness against some approximation errors introduced during the adaptation process. The algorithm implements global variations of the control law, which ensure a further increase in robustness. The results presented show how the proposed approach is capable of fully exploiting the multi-body dynamics of the problem; in fact, in one of the study cases, a fly-by of the Earth is scheduled, which was not included in the first guess solution