Drilling down into the earth from the surface, one eventually encounters magma, glowing molten rock, at a radius r from the center of the earth. Assuming the earth is a constant density sphere of mass M and radius R, find the gravitational frequency shift of the light emitted by the magma when it reaches the earth's surface.

Drilling down into the earth from the surface, one eventually encounters magma, glowing molten rock, at a radius r from the center of the earth. Assuming the earth is a constant density sphere of mass M and radius R, find the gravitational frequency shift of the light emitted by the magma when it reaches the earth's surface.