Imagine a slick pebble that relentlessly drills its own hole as it drops toward Earth’s center, then continues onward. Affected only by Earth’s gravity and its rotation, what path would the frictionless pebble follow? How close to Earth’s center would it get?
These are among the intriguing questions that Andrew J. Simoson of King College in Bristol, Tenn., considers in an article in the June Mathematics Magazine.