Chapter 13, Problem 76P

You’re working on the script of a movie whose plot involves a hole drilled straight through Earth’s center and out the other side. You’re asked to determine what will happen if a person falls into the hole. You find that the gravitational acceleration inside Earth points toward Earth’s center, with magnitude given approximately by g(r) = g₀(r/R_E), where g₀ is the surface value, r is the distance from Earth’s center, and R_E is Earth's radius. What do you report for the person’s motion, including equations and values for any relevant parameters?