This document summarizes an N-body simulation of celestial mechanics. Newton's second law was used to model the gravitational force between point masses. The equations of motion were integrated using a leap frog method to simulate the motion of bodies in the solar system over 25.5 years. While the total energy and angular momentum were conserved to a high degree, some error accumulated in the calculated positions of planets compared to ephemeris data, due to approximations in the model. Additional simulations demonstrated orbits in binary star and three-body systems.