For my computational project I would like to investigate two particular topics in celestial mechanics: the precession of the perihelion of Mercury and Kirkwood gaps. Astronomy is a very precise science, but nevertheless deviations from the accepted laws exist, and sometimes the exact results are poorly known; in these situations computational answers are the most useful and feasible. One such deviation from the accepted laws (here, Kepler’s laws) is the precession, or the rotation of the orientation axes of its orbit, of the planet Mercury- that is, the point at which Mercury is closest to the Sun rotates moves, most likely due to the gravitational effect from the other planets. This precession can be calculated using computational methods. A similar situation arises with the asteroids that orbit in our solar system- something, most likely the gravity of other planets, is causing a deviation from known laws, only here, the asteroids are conspicuously absent from certain orbital radii. The gaps, mostly caused by Jupiter, are referred to as Kirkwood gaps and are found at particular orbital resonances with Jupiter (i.e. 2/1, 3/1, 5/2 resonances). The same process occurs with the rings around a planet such as Saturn- for some orbital radii there is no such ring. The occurrence of such gaps, in orbital location and at resonance point, can be found via computational methods.