Page 399 - Global Tectonics

THE MECHANISM OF PLATE TECTONICS 381

the universal gravitational constant was decreasing Moon has been progressively partitioned between the
with time as the universe expanded and its constituent two bodies, by a mechanism known as tidal interaction,
matter became more widely dispersed. Gravitational in such a way as to reduce the rotational energy of the
forces are responsible for binding the Earth into a system. At present the stage has been reached in which
spherical form, and since the gravitational constant the Moon spins very slowly and must consequently lie
directly controls the magnitude of the force of attrac- at a greater distance from the Earth than in the past, so
tion between masses, its decrease would imply a pro- that momentum is conserved in its orbital motion. The
gressive relaxation of the binding forces and an increase tidal interaction of the Moon on the Earth is similarly
in the Earth’s radius. causing the latter’s angular rotation to decelerate. Since
The most recent versions of the expanding Earth the number of rotations in a complete orbit of the Sun
hypothesis correlate the period of rapid expansion with determines the number of days in a year, the year in the
the break-up and fragmentation of Pangea in the past past would have consisted of more days than at present.
200 Ma. These argue that continental reconstructions This also implies that the length of the day has progres-
can be arranged more accurately on a globe of smaller sively increased.
radius, and propose that during this period the surface Transfer of angular momentum from Earth to Moon
area of the Earth increased by a factor of 2.5 implying thus causes an increase in the length of the day. A
an increase in the radius from 63% of its present value further contributor to this phenomenon would be an
−1
and a mean radial expansion rate of about 12 mm a . increase in the Earth’s moment of inertia, which would
There are two methods available that can be used to allow angular momentum to be conserved by a slower
test the expanding Earth hypothesis directly. rate of rotation. Knowledge of the length of the lunar
month would allow an estimate to be made of the lunar
contribution to the Earth’s rotational deceleration and
allow any change in its moment of inertia to be
12.3.1 Calculation of the isolated.
ancient moment of inertia of Information on the rotational history of the Earth–
Moon system has been provided from a detailed exam-
the Earth ination of fossil organisms whose patterns of growth
are strongly affected by diurnal effects. In particular,
The moment of inertia of a rigid body about a given certain rugose corals of Middle Devonian age (390 Ma)
2
axis is defi ned as Σmr , where m is the mass of each have been shown to exhibit epithecal banding which
small element of the body and r the distance of the can be attributed to daily, monthly, and yearly cycles of
element from the axis of rotation. The moment of growth (Scrutton, 1967). Such studies have indicated
2
inertia of a uniform sphere is given by 2MR /5, where that the Middle Devonian year comprised 400 ± 7 days,
M is the mass of the sphere and R its radius. Newton’s and was divided into 13 lunar months of 30.5 days. The
laws of mechanics for linear motion state that the average increase in the length of day up to present times
−1
momentum (mass × velocity) of a system is conserved is 20 s Ma .
unless an external force acts upon it. These laws apply The length of the lunar month in Devonian times
equally to angular (rotational) motion, in that angular allows an estimate to be made of the Moon’s angular
momentum (moment of inertia × angular velocity) is momentum at that time, and hence the deceleration of
conserved unless the system is acted upon by an exter- the Earth’s rotation resulting from tidal friction. The
nal torque. deceleration not accounted for in this way can be used
Since the Earth’s mass remains constant, any deter- to provide an estimate of the Devonian moment of
mination of the ancient moment of inertia of the Earth inertia of the Earth, which is found to be 99.4–99.9% of
would allow a calculation of its ancient radius and so its present value. Given the uncertainties in the calcula-
demonstrate if any expansion had occurred. tion, the moment of inertia does not seem to have

The theory behind any such determination is com- altered significantly. The expansion of the Earth required
plicated by the fact that momentum is conserved within to cause continental drift implies that the Devonian
a system comprising the Earth and the Moon. Through- moment of inertia would have to have been only 94%
out geologic time the angular momentum inherited of its present value. Consequently, such rapid expansion
from the fragments that accreted to form the Earth and can be ruled out.