Continental drift and the rotation of the earth-a new and critical evaluation

Abstract

Abstraet. Sconzo has proposed that the continental drift of a land mass like Greenland can make a detectable change in the Earth's rotation rate through a change in the Earth's moment of inertia. The correction of theoretical and numerical errors in his paper results in a change in the length of the day of only 3.5 x 10-s s cy-1, a rate which is 6 orders of magnitude less than the value he gives. Continental drift does not appear to cause an important change in the length of the day. TheorySconzo (1980) considers a land mass in the form of a circular cap at the surface of a spherical Earth of radius R = 6.38 x 106 m. This mass has a mean density /~ = 2.8 x 103 kgm -3 and thickness W = 50 km contained between geocentric radii R o and R~ = R o + W. The cap has a geocentric angular radius o = 8 ~ and a center at latitude q5 o = 70 ~ This cap is considered to be moving southward at 10 m cy-t so dq~o/dt = -1.57 • 10 -6 radcy -1 where t is time.(1 cy = 100 yr.)Sconzo mentions that this cap floats on the mantle material, but he overlooks the effect that the displaced mantle material has on I, the earth's moment of inertia about its axis of rotation. If the cap extends to a depth W below the mantle's outer radius which we take to be R, we must writewhere I c is the moment of inertia of the cap, I~ is the moment of inertia of the Earth if the cap was removed and the resulting hole in the mantle was filled with materialOf the same density #m as the mantle, and I m is the moment of inertia of the material which then fills the hole. I E is independent of the cap position. Isostatic equilibrium requires that the cap displace a volume of mantle material equal to its own weight, soSconzo's Equation (1) requires the insertion of a cos 3 q5 factor in the second integral, where q5 is latitude, to correct a typographic error. His formulas for I c are otherwise correct as the following much simpler derivation shows. One divides the cap into coaxial circular ring elements extending between geocentric radii p and (p + dp) and geocentric angles 0 and (0 + dO) measured from the center of the cap. Then Celestial Mechanics 29 (1981) 89-91. 0008-8714/81/0251-0089500.45.