If the diurnal period had been increasing even by such a small quantity as sec/year, (or even sec/year) but over a very long period, such as approximately 3 —4 billion years, the rotational velocity of the Earth would have decreased to a value at which the stresses in its shell would exceed its strength by many times, resulting in a rearrangement of the Earth's configuration so as to re-establish the disturbed equilibrium. There would have been considerably less flattening of the poles and the figure of the Earth would have more closely approximated a sphere. As will be seen below, a decrease in the polar flattening of the Earth would be closely related to deformations in the outer portion of its shell. The shell's outer portion would undergo compressive deformations (such as folding or overthrusts) in the equatorial regions, and tensile deformations (such as domed swells, troughs, or faults) in the polar regions.
According to the universally accepted tidal theory originated by G. H. Darwin (1923) and subsequently modified by H. Jeffreys (1960 and earlier works), approximately four billion years ago the Earth and the Moon were separated by only a very short distance of about 15,000 km. At that time the velocity of revolution of the Moon and the rotational velocity of the Earth were considerably higher than they are now, about 3.90-4.36 Tidal friction has decreased the angular velocity of the Earth's rotation to its present value of 0.7292 It will be appreciated that such a considerable decrease in the rotational velocity of the Earth (by a factor of 5.3-6) must have inevitably trans formed the Earth's figure causing conjugated crustal deformations on a tremendous scale.
Recently E. A. Ruskol advanced a hypothesis on the origin and evolution of the Moon based on the principles of O. Yu. Shmidt's theory of the origin of the solar system. According to Ruskol's hypothesis (presented at the Moscow Astronomic-Geodetic Society on 10 February 1961), the Moon was formed from particles of the protoplanetary cloud soon after the formation of the Earth, at a distance of about 5-10 terrestrial radii from the latter. At that time the velocities of the revolution of the Moon about the Earth and of the Earth's rotation were considerably higher than they are now. Subsequently both velocities decreased continuously because of tidal friction, down to their present-day values. The majority of scientists engaged in determining the Earth's age date the Earth's formation as 4.5-5 billion years ago; if this is correct the Moon could not have been formed more than four billion years ago.
According to the Darwin—Jeffreys tidal theory, the angular velocity of the Earth's rotation must have been higher than the angular velocity of the Moon's revolution about the Earth in order that the tidal friction could decelerate the Earth's rotation and accelerate the Moon's revolution about the Earth (so that the Moon must increase its distance from the Earth, the velocity of its revolution eventually decreasing again). Shternfeld
(1958) calculated that if the distance between the Earth and its satellite is equal to five terrestrial radii (about 31,850 km), the satellite must have a tangential velocity of revolution of 3.538 km/sec; if the distance is equal to ten terrestrial radii (about 63,700 km), the velocity must be 2.502 km/sec. Consequently, assuming that the Moon was formed at a distance of 63,700 km from the Earth, we must also assume that the angular velocity of the Moon's revolution about the Earth must have been approximately 0.4 in the initial stages. If it is assumed that the Moon was formed at a distance of 32,000 km from the Earth, the initial angular velocity of the Moon's revolution must have been approximately 1.111 According to the first assumption, the mean variation in the Moon's angular velocity over a period of 4 years would have been about 0.093 per year, which is only half of the present rate of decrease of approximately 0.19 per year. However, this is inconsistent with the tidal theory, since the intensity of tidal friction is inversely proportional to the sixth power of the distance between the mutually attracted bodies and is almost directly proportional to the squared velocity of the propagation of the tidal wave. Consequently, the initial velocity of the Moon's revolution around the Earth shortly after the Moon's formation must have been considerably higher than 0.4 and its distance from the Earth must have been considerably less than 10 terrestrial radii. On the second assumption the mean decrement of the Moon's revolu tion velocity over a period of four billion years would be 0.27 per year, i. e., slightly larger (by a factor of 1.4) than the present-day decrement.
Thus, Ruskol's hypothesis was found to be the most probable one. According to this hypothesis the Moon was formed at a distance of almost five terrestrial radii from the Earth, i.e., about 31,800 km, while the angular velocity of the Moon's revolution was approximately 1.2 In addition to the friction generated by lunar tides, the Earth is affected by the friction resulting from solar tides. It is the consensus among astronomers that the friction of the solar tides has decreased the angular velocity of the Earth's rotation, the decrement in the past being essentially the same as that prevailing at the present time, since there has been very little change in the distance between the Sun and the Earth. According to computations performed by G.H. Darwin (1923), the ratio between the present rotational deceleration of the Earth due to the friction of the solar tides and its total deceleration due to both lunar and solar tides is approximately 1 : 3.2, the total deceleration having been approximately 0.28 per year on the average over the last 2000 years. Con sequently the present-day deceleration of the angular velocity of the Earth's rotation due to solar tides amounts to about 0.875 per year, totalling 0.35 over the period of four billion years.