The problem that follow involve straight-line motion. The time t is in seconds unless othe...

The problem that follow involve straight-line motion. The time t is in seconds unless otherwise stated.

Problem

Suppose that a circular tunnel of radius R could be dug beneath the equator. In principle, a satellite could be placed in orbit about the center of the earth within the tunnel. The acceleration due to gravity in the tunnel would be gR/RE. where g is the acceleration due to gravity at sea level and RE is the earth’s radius. Determine the velocity of the satellite and show that the time required to complete one orbit is independent of the radius R. (See Example 13.10.)