GRAVITATIONAL COUPLING IN THE EARTHS INTERIOR REVISITED

Gravitational coupling within the Earth had been dismissed until about 10 years ago. Inappropriate application of Newton's theorem to the Earth is cited as a reason for this dismissal. For the theorem a new proof is given, a by-product of which is an exact expression for the gravitational potential within a homogeneous ellipsoidal shell of different outer and inner flattening. The gravitational torque on a spheroid inside such a shell can be analytically calculated. When applied to a simplified model of the earth, the gravitational torque between the mantle and the inner core is found to be enormous*, confirming earlier calculations for realistic earth models based on integration of the Clairaut figure equation. The torque is found to be dominated by a contribution arising from a thin layer surrounding the inner core.