Accession Number : ADA267512


Title :   Energy Potential Analysis of Zero Velocity Curves in the Restricted Three-Body Problem


Descriptive Note : Master's thesis


Corporate Author : AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH


Personal Author(s) : Tuason, Christopher M


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a267512.pdf


Report Date : May 1993


Pagination or Media Count : 64


Abstract : The restricted problem of three bodies is a more tractable case than the general three-body problem. Two primary celestial bodies are restricted to a circular orbit while a third body of negligible mass orbits in the plane of motion established by the primaries. Among many other practical applications, these restrictions forms a rough approximation to the Earth-Moon-spacecraft problem. This study analyzes the restricted problem by superposition of the energy potential wells that arise from the gravitational and inertial forces of the primaries in their circular motion. Three-dimensional computer graphics are used to illustrate the surfaces that are created by the potential of the primaries. Zero velocity curves, also known as Hill's curves, describe the boundary between regions of possible motion and forbidden regions for the third body. These curves are the principle qualitative aspect of the restricted problem. A curve of zero velocity is found by taking a cross-section of the potential surface at a specific energy level corresponding to the Jacobian constant of the third body. The topology of a zero velocity curve may change depending on the energy of the third body.


Descriptors :   *N BODY PROBLEM , INERTIA , THESES , PROBLEM SOLVING , THREE DIMENSIONAL , LIMITATIONS , COMPUTER GRAPHICS , GRAVITY


Subject Categories : Celestial Mechanics


Distribution Statement : APPROVED FOR PUBLIC RELEASE