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 second introductory chapter, the concept of gravitational potential is presented and then developed up to the level usually encountered in applications of stellar dynamics, such as the computation of the gravitational fields of disks and heterogeneous triaxial ellipsoids, the construction of the far-field multipole expansion of the gravitational field of generic mass distributions, and finally the expansion to orthogonal functions of the Green function for the Laplace operator.