Three Traditional Theories (and why they were wrong)
Prior to the Apollo trips to the Moon, there were three commonly discussed theories of the Moon's origin:
(1) Either the Moon formed as part of the Earth, and broke off it,
or it didn't. If it didn't,
(2) Either it formed in orbit around the Earth,
or it didn't. If it didn't,
(3) It must have formed elsewhere, and been captured.
Although this "logical" way of expressing things would seem to include all possibilities, there was a particular assumption involved in these theories that meant that they could all be wrong. That assumption was that the Moon might once have been much closer to the Earth than now.
At the end of the 1800's it was discovered that the Earth's rotation is not uniform, but is gradually slowing (by about 1/1000 of a second each century), so that the Earth's rotation cannot be used as an absolutely uniform clock. The cause of this slowing is believed to be friction (within the oceans, and within the body of the Earth) between the Eastward-rotating Earth and the tides raised in the Earth by the Sun and Moon, which are more or less aligned with the Moon. Historical and geological evidence indicates that this slowing has been going on for at least hundreds of millions of years, and probably throughout the Earth's existence, so that the Earth must once have rotated considerably faster than it now does.
Because the tidal bulge is only approximately lined up with the Moon's position, as the rotational motion lost by the Earth is transferred through the tidal forces to the Moon's orbital motion, its orbit gradually becomes larger (currently at about 1 inch per year). This means that the Moon must have been closer to us in the past, and its tidal influence on us would therefore have been larger, which would have made the tides larger, which would have made tidal slowing larger, which would have made it move away from us faster, and so on. As a result, a simple calculation indicates that the Moon would have been right next to the Earth, and the Earth would have been spinning at "breakup" velocity, only about 2 or 3 billion years ago. Since the Earth is 4.5 billion years old, this opens the possibility that the Moon might have been broken off of the Earth, or captured by it, in the "recent" past. Of course, if this tidal calculation were to be proven wrong, then the Moon could have been in orbit around the Earth since they were first formed.
Problems With the Basic Theories
These are some of the problems with the various "simple" theories:
(1) The Moon broke off the Earth (the "Fission" theory). It would require an inconceivably large force, either internal or external, to blast something as large as the Moon out of the Earth. It hardly seems possible that much, if anything, on Earth could survive such a catastrophe. In fact, most of the material blasted out would either escape the Earth's gravity, or fall back onto the surface, so the mass involved would have to have been much larger even than the present mass of the Moon.
(2) The Moon formed in orbit around the Earth (the "Sister" theory). Current theories of the origin of the Solar System suggest that the physical structures and compositions of the planets depend on their distance from the Sun. Mercury, which is closer to the Sun than we are, is considerably richer in dense materials, while Mars, which is further from the Sun, is considerably richer in less dense materials. The Moon has a density like that of Mars, and considerably lower than that of the Earth. It would be much easier to understand this low density if the Moon were formed near the orbit of Mars, and then captured by the Earth, or if it consisted mostly of materials broken off the mantle of the Earth, as suggested by the Fission theory.
(3) The Moon is captured from somewhere else (the "Capture" theory). When an object comes by a planet, it should either run into it, or pass by it in a hyperbolic orbit, which carries it off into space. Even if, though missing the planet, it passes so close to it that it is torn into pieces (as in the case of Jupiter and Comet Shoemaker-Levy 9), those pieces will usually either run into the planet or escape into interplanetary space.
Results of the Apollo Missions, and the Big Crunch Theory
When the Apollo Moon-landings succeeded in bringing several hundred pounds of Moon rocks back to Earth, it became obvious that, for all practical purposes, the Moon must have been in orbit around the Earth since its origin. All of the rocks gave radioactive-age-dates in excess of 3 billion years, and the highland rocks gave ages between 4.3 and 4.4 billion years. All theories of the origin of the Moon from rocks blasted out of the Earth or captured from interplanetary space predict that the radioactive age of current Moon rocks should be the same as or less than the date when that event occurred. Since the older Moon rocks have an age which is almost the same as the age of the Solar System, the Moon must have been in orbit around the Earth essentially since their formation, as predicted by the "Sister" theory.
This of course means that the theory of tidal slowing must have incorrectly predicted that the Moon was right next to the Earth in the "recent" past. As it turns out, it has been possible to "reasonably" modify that theory so that it gives results in which the Moon has never been less than 2/3 of its present distance, and the Earth never rotated faster than once every 16 hours or so, so it looks like that particular problem has been taken care of.
However, we still have the problem of the puzzlingly low density of the Moon, and the Moon rock studies even added two new problems!
(1) If a rock is melted, and the elements within the rock are mixed together, when the rock cools and re-solidifies, the mineral grains have certain chemical characteristics which show that they were once part of a single mixed object. Rocks from the Moon have some chemical characteristics that are so similar to rocks from the Earth that, if we didn't know their origin, we would think they must have originated on the Earth. Of course, if the Moon had once been part of the Earth, and blasted out of it, then we could explain this result,, but we've eliminated that idea, haven't we?
(2) Certain elements, such as sulfur and oxygen, which are volatile, or easily turned into gases, and cannot be held onto by small, hot bodies, are very deficient on the Moon, especially in comparison to the Earth, which is odd, given the similarities just discussed.
We try to solve all these problems by essentially combining all three of the original theories, but with some changes. As discussed in the textbook, we now embrace a Big Crunch, or Big Collision, theory in which an object about the size of Mars runs into the Earth, knocking off a part of its mantle. The pieces blasted out into space orbit the Earth, and form into the Moon.
This theory is attractive because it solves all the problems listed above. The low density of the Moon is explained by its being made up mostly of mantle material. The similarity with Earth rocks is explained by the Moon having been part of the Earth. The low abundance of volatile materials is explained by having them escape into space when the pieces of the Earth which are to become the Moon are blasted out of the Earth.
For this theory to work, however, we must place certain restrictions on events:
The impacting object must be much smaller than the Earth, or the Earth would break apart. But it must also be much larger than the Moon, because most of the material broken off the Earth will fall back to the Earth or escape into interplanetary space. For this reason, in the original version of this theory, it was proposed that the impacting object was about the size of Mars, which is ten times smaller than the Earth, and ten times bigger than the Moon, so that it is sort of in-between in size.
The impact must be a glancing blow, and must occur after the Earth has started to melt and differentiate, so that mostly lower-density mantle rocks are thrown into space. Otherwise, we won't be able to explain the Moon's low density.
The impact must occur long enough ago so that the Moon's rocks can be blasted into space, form into the Moon, melt and differentiate, and then resolidify, all before the 4.4 billion year age of highland rocks.
We believe that the planets started to form 4.5 billion years ago. Based on current theory, they melted primarily from the heat of short-lived radioactive materials which would have decayed and dissipated their energy within 30 to 50 million years. So we need to melt the Earth, blast out the Moon, reform the Moon, and melt it within this time period. Once that is accomplished, we have another 50 to 70 million years to resolidify the lunar surface rocks. With this time scale, for all practical purposes, the Moon has always been in orbit around the Earth, or at least for 4.47 or so of the 4.5 billion years since the Earth started to form.