The Gravitational Potential in Close Binary Star Systems

The gravitational potential for close binary systems is usually calculated assuming both stars to be point masses. Deupree and Karakas recently examined the internal structure of both members of a binary system under the assumption that the gravitational potential for each member is the gravitational potential produced by its own mass distribution and by a point source companion. Here we examine the validity of using a point source potential for the companion by calculating the total gravitational potential of each member by using the mass distributions of both stars. We find that the potential differences produced by the mass distribution of the companion are always within one percent of the point source potential.