  The $N$-body problem is of historical significance because it was the first
implementation of the Newtonian dynamical laws for the description of our Solar
System. Motivated by this, the project's goal is to revisit this problem for
small $N$ and find a solution for the trajectories of specific two-body and
three-body configurations as well as the planetary orbits of our Solar System
using a fourth order Runge-Kutta explicit iterative method. We find an adequate
agreement in our results with planetary trajectories found online.
