Falling Down A Hole
Through The Center of The Earth

Sam Stekol

This presentation provides a mathematical description of a negligibly small particle theoretically drilling its own path through the Earth. We chart the path of this particle by analyzing a differential equation that dictates the motion of the particle. We then obtain the equations for the particle's acceleration, velocity, and position. We assume a homogeneously dense Earth rotating at a constant speed and ignore all effects of resistance on the particle. We demonstrate that the particle satisfies analogues of Kepler's three laws, using various coordinate systems.