Fall Through Earth's Center

The imaginary problem of the time it takes for a small mass to fall through a “well”, or tunnel, or hole, passing through the center of the Earth is solved using simplifying assumptions. Those assumptions include that the Earth has a uniform density throughout, there is no air resistance, and no effects of rotation. The differential equation to be solved is compared to familiar cases involving simple differential equation to obtain the solution. Of particular interest, it is shown that the expression for the period of the fall, i.e. the time of one cycle, is exactly the same for the period of a hypothetical satellite skimming the Earth’s surface as derived from the expression for Kepler’s 3rd Law of Planetary Motion. Both time periods are calculated to be about 82 min. A simple approximate derivation of the fall time is also developed employing an average "g" taken to be 1/2 (9.8) m per second squared. Andrew R. Ochadlick Jr. received a Ph.D. in Physics from the State University of New York at Albany (SUNYA) and is a career physicist with university, government and industry R&D experience and teaching experience at the undergraduate and graduate level. He may be reached at [email protected] .