Interplanetary Trajectory Design using Dynamical Systems Theory

Interplanetary Trajectory Design using Dynamical Systems Theory

Van der Ham, L.

Noomen, R. (mentor)

Aerospace Engineering

Earth Observation and Space Systems

Astrodynamics & Satellite Systems

2012-03-15

Instead of the two-body problem commonly used in interplanetary trajectory design, also three bodies can be considered: the satellite, a planet and the Sun. Knowing that planet and Sun orbit one another in almost circular orbits, and the mass of the satellite is negligible compared to the mass of these bodies, the model of the circular restricted three-body problem (CR3BP) can be used. Dynamical Systems Theory (DST) concerns itself with the analysis of differential equations, as the equations of motion in the CR3BP are. After finding the Lagrange libration points, the region about these points can be examined. Periodic orbits and asymptotic orbits are two of the four types of motion in these regions. The asymptotic paths form manifolds and create a natural highway to travel from and to the area around equilibrium points. Extending the manifolds far from the periodic orbits for many Sun-planet systems shows a network of manifold tubes, which is referred to as the Interplanetary Superhighway and may be an energy efficient way of transfer. Zooming in on two consecutive Sun-planet systems the transfer from one to another can be examined. The actual four-body problem is approximated by two coplanar coupled three-body problems. The high-trust maneuver requiring the minimal instantaneous velocity increment, to get from one CR3BP to the next, is to be found. On the intersection of manifolds, different positions for executing the maneuver are available. Furthermore the mutual geometry of the two systems changes with the chosen epoch. So for changing place and time of the maneuver, the minimal velocity increment is computed and analyzed. Finally the optimal maneuver is used in the design of a mission; a transfer from one planet to another.

space
trajectory design
dynamical systems theory
circular restricted three-body problem
interplanetary space flight

http://resolver.tudelft.nl/uuid:98c55fe3-cd59-4c61-817e-9caa6ac835b6

2012-03-20

Student theses

master thesis

(c) 2012 Van der Ham, L.