Motion of the planets: the calculation and visualization in Mathcad

TL;DR

This paper demonstrates how Mathcad can be used to solve and visualize the motion of multiple planets under gravity, discussing numerical accuracy and illustrating Kepler's laws with animations.

Contribution

It introduces a method for solving planetary motion problems using Mathcad, including visualization and analysis of numerical accuracy.

Findings

Mathcad effectively visualizes planetary motion and Kepler's laws.

Numerical methods' accuracy limits are discussed.

Animations enhance understanding of orbital dynamics.

Abstract

This article describes use of Mathcad mathematical package to solve problem of the motion of two, three and four material points under the influence of gravitational forces on the planar motion and in three-dimensional space. The limits of accuracy of numerical methods for solving ordinary differential equations are discussed. Usual concept of Kepler hours with uneven movement arrows illustrates Kepler's second law. Mathcad animation tools are used to illustrate solutions and links with animations are provided.