Computer Simulation of Stable Orbits in the Three-Body Problem

Abstract

The role of computer modeling in the study of physical and astronomical processes and phenomena is difficult to overestimate. Today, computer modeling is in demand in various scientific fields and, in comparison with noncomputer modeling methods and full-scale testing, allows the creation of prototypes for the studied objects, processes, or systems that function in a given specific environment. Taking into account the complexity of the models being created and conducting experiments in real conditions, computer modeling allows, depending on the factors and conditions of the functioning of objects in a virtual environment, analysis, making various forecasts for the future, studying the interaction between objects, and presenting the results obtained in a convenient graphic, textual, or tabular forms. The article discusses particular mathematical solutions to the three-body problem proposed by mathematicians from different countries from the 18th to the 21st centuries. The presented project allows us to touch on knowledge from various fields (physics, astronomy, mathematics, and history) and implement a mathematical model of the system using the state vector of three bodies and integrating a system of differential equations using a program based on the explicit Runge–Kutta method of the eighth order of accuracy.