Advanced Orbital Mechanics

Catalog description

This course is an introduction to the mathematics and practices in orbital mechanics as applied to spacecraft mission design and operation. The major topics are: the n-body problem, the two-body problem, Keplerian orbits, the Kepler problem (position as a function of time), three-dimensional specifications of Keplerian orbits (classical orbital elements and modified equinoctial elements), Lambert's problem (determining a conic section that joins two specified points for a given time of flight), impulsive transfers, the Hohmann transfer and its extension to other problems, spherical trigonometry and its use in plane-change maneuvers and in gravitational modelling, the sphere of influence, the patched-conic approximation, the circular restricted three-body problem, linear orbit theory (relative motion between vehicles in neighboring orbits), gravitational modelling via spherical harmonics, perturbation methods (Encke's method and variation of elements), orbit determination, tracking kinematics, and time systems.