Numerical solution of differential equations system of two gravitating bodies by the Euler method

Authors: Belkina E.V., Loginova A.A.
Published in issue: #1(30)/2019
DOI: 10.18698/2541-8009-2019-1-428
Category: Physics | Chapter: Mathematical physics
Keywords: numerical integration, Euler method, Runge rule, law of universal gravitation, differential equations, gravitational problem, interaction of two bodies, error estimate
Published: 23.01.2019

A system of 12 differential equations describing the interaction of two gravitating bodies was integrated in this work. The considered problem is a special case of two bodies gravitational problem. To account for the forces acting on the body, Newton’s law of universal gravitation is used. Graphs of coordinates and speeds depending on time are obtained. The estimation of numerical integration error is performed using the Runge rule. The problem was solved for specific values of input parameters; in the general case, it is possible to find the solution for different source data depending on the task.

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