Sudden loss of mass from a binary gravitating system

Abstract

A recent discussion by Mitalas is generalized to treat sudden mass loss from a binary system in an originally elliptical orbit. Emphasis is placed on characterizing the orbits by angular momentum and energy, and it is shown that none of the changes in the relative orbit depends on which object loses part of its mass; indeed, in principle, each could lose a different fraction. Time averages are introduced so that the orbital changes, which depend on where in orbit the mass loss occurs, can be suitably averaged over a statistical ensemble of initial systems. Although I present several results that appear to be new (such as a unique relation between the increase in the semimajor axis and the change in eccentricity, independent of the orbital phase at the moment of mass loss), the main thrust is to choose and manipulate variables yielding the greatest economy of description and the greatest power of computation. (All calculations were easily done on a pocket calculator.) Graphs are presented showing the fraction of systems that on the average will be disrupted, the mean orbital changes for the survivors (which can easily turn out to have smaller mean eccentricity than the progenitors), and the extreme limits for the change in eccentricity.