Gravity by George Gamow

Author:George Gamow
Language: eng
Format: epub, pdf
Publisher: Dover Publications
Published: 2013-04-13T04:00:00+00:00

where M is the mass of the Earth. Thus:

From this, and the above expression for I, follows:

and:

and the reader can take the author’s word for it, if he is unable to reproduce the derivation. It follows from the above formulas: the increase of the angular momentum of the Moon in its motion around the Earth must result in the increase of its distance from the Earth and the decrease of its linear velocity.

From the observed slowing down of the Earth’s rotation one can calculate that the recession of the Moon amounts to one-third of an inch per rotation. Thus, each time you see a new moon it is that much farther away from you. One-third of an inch per month is a tiny change as astronomical distances go, but, on the other hand, the Earth-Moon system must have existed for billions of years. Putting these figures together, George Darwin found that between four and five billion years ago the Earth and the Moon must have been very close together, and he suggested that they may once have been a single body (Earthoon or Moorth). The breakup into two parts may have been caused by the tidal force of solar gravity or by some other catastrophic event lost in the long ago of the solar system. Darwin’s hypothesis is a source of violent disagreement among the scientists interested in the origin of the Moon. While some are ardent believers (if only because of its beauty), others are bitter enemies.

A few more words may be said about the future of the Moon as it can be calculated on the basis of celestial mechanics. As a result of gradual recession, the Moon eventually will get so far from the Earth that it will become rather useless as a substitute for lanterns at night. In the meantime solar tides gradually will slow down the rotation of the Earth (provided the oceans do not freeze up), and there will come the time when the length of a day will be greater than the length of a month. The friction of lunar tides then will tend to accelerate the rotation of the Earth, and, by the law of conservation of angular momentum, the Moon will begin to return to the Earth until at last it will come as close to the Earth as it was at birth. At this point the Earth’s gravity forces will probably tear up the Moon into a billion pieces, forming a ring similar to that of Saturn. But the dates of these events, as given by celestial mechanics, are so far off that the Sun probably will have run out of its nuclear fuel and the entire planetary system will be submerged in darkness.

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