Introduction to the Roche Model

Abstract

The goal of this work is to examine the Roche Model created by the French astronomer and mathematician Édouard Roche, its implications for the study of close binary systems, and to analyze a simplified form of the problem, in order to understand, in practical and at an undergraduate research level, its properties, their equipotentials and the Roche limit. The article introduces a first part of initiation into the concepts of binary systems, potential energy, and the two body problem, and presents the linearization tools necessary to investigate the problem. The second part of the article focuses on contextualizing the problem and why there was a reason, in the past, to create a new mathematical model for the study of close binary stars. Finally, all the concepts presented in the previous sections will be used to study, in a substantially simplified way, a binary system with a function that defines its equipotentials.