EARTH’S PAST FROM THE PERSPECTIVE OF THE HYPOTHESIS OF THE ACCRETION OF A SECOND SATELLITE TO EARTH

L. A. Pukhlyakov

(Presented by the interdepartmental scientific seminar of the departments of general geology, historical geology, and mineral resources)

For a long time, the question of the origin of the planets and their satellites was dominated by the hypothesis proposed by P. S. Laplace, the main idea of which was as follows. As a result of the rotation of the planets, a certain quantity of matter supposedly could separate from them, which first formed rings similar to the rings of Saturn, and then satellites supposedly could form from these rings. However, in 1848 E. A. Roche proved that the rings of Saturn were formed from a satellite that had approached the planet too closely and had been torn apart by its attraction.

Subsequently, by G. H. Darwin [3] and other followers of Laplace, his hypothesis was somewhat transformed. The detachment of satellites began to be assumed in the form of a single whole. A representative of this school, B. Pickering, asserted in 1907 that the Moon had formed as a result of detachment from Earth, and that at the place of its detachment, according to Pickering, the Pacific Ocean was formed [24]. The author of one variant of the continental-drift hypothesis, A. Wegener, also adhered to the positions of this hypothesis [1–6].

It should be noted, however, that Wegener and many other proponents of the hypothesis of the Moon’s detachment knew facts from which it follows that in the place of the Pacific Ocean, in the recent geological past—literally 150 million years ago—there existed the gigantic continent of Pacifica. This is, first, the character of the Upper Jurassic deposits in the Chilean Andes between 34 and 39° S latitude, established by K. Burckhardt. These deposits in the west, near the coast of the Pacific Ocean, are represented by conglomerate, which, as one moves eastward into the interior of the continent, passes into sandstone and then into clay shale. At the same time, their thickness decreases [20].

Deposits of this kind are usually called stratigraphic wedges, and everywhere, near the places where they occur, geologists assume the existence in the past of large land masses. With regard to the Chilean stratigraphic wedge, geologists hold a different opinion. They believe that in the future this fact will receive some other explanation [16, pp. 66–67]. The basis for such an assertion is the opinion about the detachment of the Moon from Earth. More than fifty years have passed since the cited statement, but the Chilean stratigraphic wedge has received no explanation other than K. Burckhardt’s explanation, and the thought involuntarily arises that the Pacific Ocean is not the most ancient and that there was no detachment of the Moon from Earth.

An interesting assessment of the hypothesis under consideration is given by representatives of the very science that deals with the problem of the origin of the planets and their satellites, in particular by the major physicist of our time, Nobel Prize laureate Professor Hannes Alfvén. He notes, in particular: “Although this hypothesis is widely disseminated in the works of irresponsible popularizers, it was refuted long ago, and professional astronomers simply do not take it seriously. We have long been completely certain that the Moon could in no way have been torn away from the Earth, since the separation of so large a mass would have required an extraordinarily large expenditure of energy” [1a, p. 56].

In 1877 the American astronomer Hall discovered two satellites of Mars: Phobos and Deimos, which were distinguished by their unusually small dimensions, and also by the fact that one of them, Phobos, completes one revolution around the planet in 7 h 39 min, whereas the planet itself completes one rotation in 24 h 37 min. For a long time this did not agree with the hypothesis of the tearing away of planets. Finally, it was assumed that after the separation of Phobos, Mars slowed its rotation under the action of tidal friction caused by the Sun.

The dimensions of Phobos brought even greater difficulties to the supporters of the separation hypothesis. In fact, to persons who ignore the principle of energy, separation seems natural if the dimensions of the satellite are comparable with the dimensions of the planet. But how can one speak of separation if the dimensions of the satellite are incommensurable with the dimensions of the planet? And so the hypothesis of I. S. Shklovsky appeared, according to which both satellites of Mars are artificial. This hypothesis existed until the given satellites were photographed and their dimensions were refined. It turned out that Deimos has dimensions in one direction of 12 km, and in the other—13.5 km. The dimensions of Phobos are approximately the same [2]. For separation from the planet this is too little; for an artificial satellite—too much. In the opinion of V. Gubarev [2], the satellites of Mars are stone blocks, either captured by the planet or formed together with it.

Thus, scientists again came to the conclusion that the satellites of planets are formed not as a result of being torn away from them, but as a result of capture by them. The situation is analogous with the origin of the planets. In the opinion of O. Yu. Schmidt [18], B. Yu. Levin [4], V. S. Safronov [11, 12], and others, the planets were formed by the concentration and sticking together of cosmic dust once captured by the Sun. Accumulations of clouds of such dust are located in the central plane of the Galaxy, which is crossed by the Sun every 100 million years. The dimensions of these clouds exceed the average distances between stars [4, p. 15], and therefore the passage of the Sun through one of such clouds is quite probable.

However, to pass through a cloud of cosmic dust does not yet mean to capture some quantity of this dust. Its capture by the Sun is possible only if, simultaneously with it, another luminary passes through the cloud, which creates a gravitational depression in the Sun’s field of attraction.

Moving in the direction of the Sun in the zone of the gravitational depression, a particle will have to overcome the attraction of the luminary that has approached the Sun and will not be able to develop a sufficient velocity relative to the Sun. When the particle under consideration overtakes the Sun and returns to the place from which its motion began, the perturbing luminary will have moved a considerable distance away, and the gravitational depression will disappear. As a result, the particle will begin to revolve around the Sun in its own orbit.

Further, according to O. Yu. Schmidt [18], V. S. Safronov [12, 13], G. Urey [19], and other authors, individual particles of the captured Sun-

...particles of the protoplanetary cloud will begin to collide with one another, “stick together,” and form comparatively large bodies—the embryos of future planets.

As for satellites, they could have appeared around planets only after the planets themselves had acquired comparatively large sizes. But the question arises as to what processes could have led to the capture of satellites by planets. Most likely these were collisions of individual wandering particles with one another in the zones of influence of the planets, i.e., where the accelerations of gravity produced by the planets exceed the differences of the accelerations produced by the Sun, on the one hand at the center of the planet, and on the other at the given point. As an example, let us consider the zone of influence of the Earth.

As is known, the acceleration of gravity produced by the Earth at some distance \(r\) from it is determined by the relation

\[ j_1 = 9.82 \frac{6.371^2}{r^2}, \tag{1} \]

where 9.82 is the acceleration of gravity at the surface of the Earth without subtracting the centrifugal component, in \(m/sec^2\); 6.371 is the mean radius of the Earth in thousand km; \(r\) is the distance from the center of the Earth to the given point, in thousand km.

The acceleration of gravity produced by the Sun at the center of the Earth is expressed by the relation

\[ j_2 = 273.8 \frac{695.3^2}{149500^2}, \tag{2} \]

where 273.8 is the acceleration of gravity at the surface of the Sun in \(m/sec^2\); 695.3 is the radius of the Sun in thousand km, and 149500 is the distance between the centers of the Earth and the Sun in thousand km. Finally, the acceleration produced by the Sun at the given point is expressed by the relation

\[ j_3 = 273.8 \frac{695.3^2}{(149500 \pm r)^2}, \tag{3} \]

whence the quantity of interest to us may be expressed either by the relation

\[ 9.82 \frac{6.371^2}{r^2} = 273.8 \cdot 695.3^2 \left[ \frac{1}{149500^2} - \frac{1}{(149500+r)^2} \right], \tag{4} \]

or by the relation

\[ 9.82 \frac{6.371^2}{r^2} = 273.8 \cdot 695.3^2 \left[ \frac{1}{(149500-r)^2} - \frac{1}{149500^2} \right], \tag{5} \]

or, expressing the accelerations of gravity at the surfaces of the planets and the Sun through masses and other parameters, and expressing the distances between the Sun and the planets through \(s\), instead of relation (4) we obtain

\[ \frac{1}{r^2} = \frac{m_0}{m_{\mathrm{pl}}} \left[ \frac{1}{s^2} - \frac{1}{(s+r)^2} \right], \tag{6} \]

and instead of relation (5)

\[ \frac{1}{r^2} = \frac{m_0}{m_{\mathrm{pl}}} \left[ \frac{1}{(s-r)^2} - \frac{1}{s^2} \right], \tag{7} \]

where \(m_{\mathrm{pl}}\) is the mass of the planet, \(m_0\) is the mass of the Sun in the same units. The remaining parameters are described above.

Solving equations (6) and (7) for the Earth, we find that the attraction produced by the Earth exceeds the difference of the accelerations produced by the attraction of the Sun within a zone bounded, on one side, by a value of 1723, and on the other (on the side of the Sun) by 1703 thousand km.

Obviously, the Earth cannot have satellites that would be more than 1723 thousand km distant from it. Consequently, if a collision of two wandering bodies occurs beyond this zone, then whatever

no matter how small their velocities after the collision, neither of them will be able to become a satellite of the Earth. But if the collision of the bodies under consideration occurs within this zone, and one of them thereby reduces its velocity to a value less than parabolic, it will become a satellite of the Earth.

Another outcome of the collision is also entirely probable: both of them become satellites of the Earth. In that case their collisions may recur, and in the end they may be able to form a single mass. When this mass collides with bodies free relative to the Earth, it may be fragmented; however, part of the kinetic energy of the colliding bodies will be converted into heat, and subsequent collisions will have less force. This, in turn, will lead to the fact that, sooner or later, their fragments will have to merge into a single mass capable of preserving its unity in collisions with new bodies free relative to the planet. Such a hypothesis was advanced in 1973 by L. A. Pukhlyakov [11-a], and in 1975 by E. L. Ruskol [11-b].

The capture by a planet of a satellite in the form of a large body similar to the present Moon is hardly possible. First, the probability of the passage of such a body through the zone of influence of one planet or another is too small, since the larger the celestial body, the less elongated its orbit is. Second—and this is the main point—the collision of such a body with a similar body within the zone of influence of one planet or another is still less probable. The situation is analogous with respect to the possibility that, at the appropriate moment, a gravitational depression may arise in the gravitational field of the planet.

There is yet another hypothesis for the origin of planetary satellites, proposed in 1967 by A. N. Sheiko [15]. It consists in the assumption that the Moon became a satellite of the Earth after colliding with the Proto-Moon—a body that exceeded the modern Moon by approximately a factor of three (about 3.7% of the present mass of the Earth). A similar hypothesis was proposed in 1955 by J. Demortier, who supposed a collision with the Earth of a gigantic bolide 7000–7600 km in diameter [21, p. 413], corresponding to a mass of 16–20% of the present mass of the Earth. True, J. Demortier did not speak of the possibility that the Earth acquired a satellite as a result of this, but that does not change the essence of the matter. The main shortcoming of this hypothesis is that the supposed impact should have led to the disintegration of our planet into a great multitude of the smallest particles and several large bodies, each of which would have begun moving in an independent orbit. And if one assumes that the mass of the colliding body did not reach 1% of the Earth’s mass, then such a massive satellite as the Moon is not obtained. Moreover, the Moon’s orbit is too circular compared with what follows from A. N. Sheiko’s hypothesis.

As for the passage, through the zone of influence of one planet or another, of celestial bodies of small size, and their collisions with one another within this zone, then in the past, when the formation of the planets had only just begun and the number of small bodies in the Solar System was much greater than now, such passages and collisions could have occurred very often.

From what has been said, it follows that any planet may have several satellites of the most varied sizes, including ones such as the Moon. The question arises: why does the Earth have only one such satellite? In several works devoted to the problem of the development of the Earth [7, 11], it was shown that in the past, besides the Moon, it had two more satellites: Perun and Lel, whose orbits lay inside the orbit of the Moon.

The nearest of these satellites, Lel, as early as the Docambrian, equalized the speed of its revolution with the speed of the Earth’s rotation; then, when the Earth slowed its rotation under the influence of tidal friction caused by Perun and the Moon, it began to overtake its surface. This led to the Earth, striving to turn one of its sides toward it, beginning to increase the speed of its rotation, while it lost energy and drew closer to the Earth. This was accompanied by an increase in the speed of its motion, a new loss of energy, and a new approach toward the Earth. Ultimately Lel approached the Earth so closely that it reached the Roche limit. A considerable part of its matter broke away from it; this matter rushed toward the Earth and scattered into many fragments, each of which began to move in an independent orbit.

The energy per unit mass of the undisintegrated part must thereby have increased somewhat; hence all of it must have moved somewhat away from the Earth and slowed the speed of its motion. Following this, the Earth too must have somewhat reduced the speed of its rotation, after which a new cycle of approach and breakup of Lel should have begun, accompanied by a new increase in the Earth’s rotational speed. This process must have continued until, after several cycles of approach and breakup, Lel was completely converted into fragments that formed the rings of the Earth, like the rings of Saturn.

After this there came a period of decreasing the speed of the Earth’s rotation, which continued until it came into resonance with the speed of revolution of Perun. Soon after this, Perun began to approach the Earth, gradually giving up the energy of its motion to it. But the fate of this satellite developed somewhat differently, since on its path toward the Earth there were no rings remaining from Lel. The angular speed of their motion exceeded the speed of Perun’s motion, and therefore, falling onto Perun’s surface, they imparted to it a certain proper rotation and a certain additional velocity of its center of gravity. This led, first, to the fact that Perun’s approach to the Earth was temporarily halted and ultimately stretched out over several cycles, and second, to the fact that, having gathered onto itself all the fragments of Lel, Perun acquired significant retrograde rotation. This allowed it to remain a single whole within the Roche zone until it came into contact with the Earth.

Coming into contact with the Earth, Perun lost its retrograde rotation and began to scatter into separate fragments, each of which immediately joined the Earth. At the same time the speed of its center of gravity began to slow, which accelerated the process of its accretion to the Earth.

Initially Perun’s fragments were situated on the Earth in the form of a gigantic pile-up, with an average height of up to 600 km above the geoid surface. Subsequently, however, this pile-up subsided in accordance with the principle of isostasy, and in its place a depression formed—the future Pacific Ocean. This occurred at the end of the Upper Cretaceous.

With respect to the Pacific Ocean the word “future” is used here. This is because the amount of free water on the Earth at the moment of Perun’s accretion was approximately 20 times smaller than at present. At that time, the greater part of the modern free water was in a bound state within sedimentary rocks. After being covered by Perun’s fragments, a significant part of these rocks warmed up and underwent metamorphism. As a result, the bound water contained in them passed into a free state and was released onto the Earth’s surface. The same occurred with those rocks that ended up in

deep zones of the Earth as a result of fold-forming processes. But this occurred somewhat later.

In its original version, the meteoritic hypothesis of the origin of the planets and their satellites assumed only a gradual increase in the masses of the planets through the fall onto their surfaces of particles of the protoplanetary cloud. The acquisition of satellites by planets in this version was spoken of only in general terms, and the hypothesis practically did not concern the evolution of satellites. For geology it provided an explanation only for explosion craters, which arose when large meteorites fell to Earth. However, such formations on the surface of our planet are generally rare, and therefore among geologists this hypothesis is not popular.

The proposed version of the meteoritic hypothesis, which amounts to the idea that the satellites of planets are first formed in the zones of influence of the planets from the same material as the planets themselves, and are then accreted to the planets in the form of large masses, explains many geological phenomena.

First of all, by assuming repeated increases in the rate of the Earth’s rotation, we can explain the appearance of gigantic fractures in the Earth’s crust, including such fractures as the Atlantic and Indian oceans. Allowing for repeated decreases in the rate of the Earth’s rotation, we gain the possibility of explaining the appearance of numerous folds that mantle its surface. And this is not merely some comparatively short interval of time, but any moment in the history of the Earth. Indeed, the accretion to the Earth of one of its satellites could have occurred at any time.

Further, in the new version the meteoritic hypothesis explains the relatively recent origin on its surface of the Pacific Ocean, which, according to the latest data [5, 22, 23], has a very young age of about 70 million years, whereas the age of the oldest rocks on Earth exceeds 3 billion years.

One more very acute question is resolved by the meteoritic hypothesis in its new version—the question of changes in the quantity of free water on Earth. In fact, if one rejects the hypothesis of the accretion to Earth of a second satellite, then one can speak only of a decrease in the amount of free water on the Earth’s surface owing to its transition into a bound state in the process of weathering. Meanwhile, from the data of G. Menard [16, 17] and other scientists [14] it follows that it increased sharply. Proceeding from the hypothesis of the accretion of Perun to Earth, this fact was explained above.

There are a number of other factors that are easily explained from the standpoint of the version considered here of the meteoritic hypothesis of the origin of the planets and their satellites. However, these explanations have already been discussed in the literature [6, 7, 8, 9, 10, 11], and there is no need to repeat them here.

REFERENCES

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