This project involves the application of molecular dynamics (MD) to a simple two-dimensional planetary system consisting of two planets and a fixed star. The primary focus is to construct a MD code using Newton’s law of universal gravitation as the interaction law and the Verlet algorithm for solving the initial value problem. The project examines the gravitational interaction described by Newton’s laws, focusing on the law of universal gravitation and its application to the planetary system. It further explores the principle of equivalence, the concept of conservative force, and the effective potential energy of the system. The discussion also covers the reduction of a single planet motion to one dimension, which offers insights into the trajectory of the planetary system. Finally, the project outlines the numerical approach using the Verlet algorithm for simulating the motion of the planets. The comprehensive understanding of the gravitational interactions and the computational techniques provide a solid foundation for the study of complex dynamical systems.

In this chapter we describe motion caused by central forces, especially the orbits of planets, moons, and artificial satellites due to central gravitational forces. Historically, this is the most important testing ground of Newtonian mechanics. In fact, it is not clear how the science of mechanics would have developed if the earth had been covered with permanent clouds, obscuring the moon and planets from view. And Newton’s laws of motion with central gravitational forces are still very much in use today, such as in designing spacecraft trajectories to other planets. Our treatment here of motion in central gravitational forces is followed in the next chapter with a look at motion due to electromagnetic forces, which can also be central in special cases, but are commonly much more varied, partly because they involve both electric and magnetic forces. Throughout this chapter we focus on nonrelativistic regimes. The setting where large speeds are involved and gravitational forces are particularly large is the realm of general relativity, where Newtonian gravity fails to capture the correct physics. We explore such extreme scenarios in the capstone Chapter 10.