Mathematics – Probability
Scientific paper
Jan 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993phdt........45b&link_type=abstract
Ph.D. Thesis Texas Univ., Austin, TX.
Mathematics
Probability
Orbital Mechanics, Swingby Technique, Three Body Problem, Transfer Orbits, Two Body Problem, Aerobraking, Comets, Jupiter (Planet), Lagrangian Equilibrium Points, Lunar Orbits, Planetary Orbits
Scientific paper
This dissertation deals with the general topic of transfer orbits in the two- and three-body problems. To begin with, we study what is called Henon's problem. It is the problem of transferring a spacecraft from one body back to the same body, after a certain time. We also generalize to the problem of transferring to the corresponding Lagrangian points L4 or L5. This problem is solved first by using two-body equations and the Lambert problem. Families of transfers with small Delta V are found. Next, this problem is studied using the planar restricted circular three-body problem with the global Lamaitre's regularization as the model for the simulations. Transfers with near-zero Delta V to the Lagrangian points exist in this model. Next, we study the swing-by maneuvers. The fundamentals of the theory and some practical applications are presented, including a classification of Jupiter or moon swing-bys. The effect of the atmospheric drag is later included, and we study aerobraking in swing-by-maneuvers. We also study the effect of a swing-by with Jupiter on comets. A large range of initial conditions has been used for the incoming comets. The main questions considered are: the probability of capture of a comet in the solar system; the distribution of captured comets according to pericenter distance and semimajor axis; and the percentage of captured comets that will have a short period. Another important problem is the question of time-free minimum Delta V transfers between any two elliptical coplanar orbits. A set of analytical equations to solve this problem for a multi-impulsive maneuver is derived and solved. Comparisons between those maneuvers are made. Then, the Lambert problem is studied.
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