Hill's Boundary Curves for a Special Case of the Restricted Four-Body Problem and Different Values of the Finite Masses.

Abstract

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Hill's Boundary Curves for a Special Case of the Restricted Four-Body Problem and Different Values of the Finite Masses. Eckstein, Martin C. Abstract For the special case of the restricted four-body problem, where the three finite masses are located at the angle points of an equilateral triangle, the values of the Jacobian constant were calculated by means of a suitable computational schedule. The trace of Hill's boundary curves was determined in the xy plane in the neighborhood of the mass triangle. The procedure was applied to 2 t different combinations of values of the three finite masses, the sum of which was always t. The possibilities of motion of the infinitesimal mass and its dependency upon the values of the finite masses have been discussed. It turns out that the possibilities of motion may be completely different even if the initial conditions (or the Jacobian constant) are the same. The regions of the xy plane, inside of which the motion of the infinitesimal mass is possible according to its Jacobian constant, were regarded and discussed with respect to their dependency on the combination of the three values of the finite masses. A separate discussion has been made for Hill's boundary curves in the vicinity of a finite, but very small mass (0.0000t); and of Hill's boundary curves in the vicinity of the libration points. The connection between the stability of motion of the infinitesimal mass around the libration points and the shape of Hill's boundary curves in their vicinity has been discussed. Publication: The Astronomical Journal Pub Date: September 1963 DOI: 10.1086/109062 Bibcode: 1963AJ.....68Q.535E full text sources ADS |