What follows is an original, mathematical analysis of the genesis of the moon, inspired by certain parts of the African Dogon astronomy and mythological system.
The Triple Saros eclipse cycle.
The most famous of all the eclipse periods is the 6,585.32-day cycle, named the saros (which means "repitition"). It is a period of 223 synodic months. According to Anthony Aveni, in his book, Skywatchers of Ancient Mexico (the University of Texas Press, 1980), it was discovered by the ancient Chaldeans. The saros interval is a whole number, 242, of draconic months. A draconic month is 27.21222 days, the interval between successive passages of the moon by a given node. It is named after the dragon who, the ancient Chinese believed, devoured the sun or moon during an eclipse.
Not all solar eclipses in a saros will be visible from the same place on earth. If a series of solar eclipses begins at the extreme eastern end of the ecliptic limit, most of the early ones will be partial and visible only in the south polar regions. At the middle of the seies more total and annular eclipses visible in the middle latitudes will occur. At the end of the series, when the moon and sun meet at the western ecliptic limit, the eclipse tracks experience a latitude shift to the north polar regions.
In a saros eclipse cycle, longitude shifts,also, will occur among successive eclipses. Suppose that the first solar eclipse in a series is visible in the central United States. One saros later the first eclipse will strike the earth's surfac 1/3 of a rotation, or 120 degrees west of its original position. The eclipse will be visible off the coast of Japan. The initial eclipse of the third saros cycle will be visible 240 degrees west of the original or somewhere in western Europe. But the first eclipse in the fourth cycle, occurring fifty-four years and one month later, will return to the same longitude as the first of the first cycle. Thus, eclipses separated by a "triple saros" interval will recur at about the same place on earth.
The saros is also an integral multiple of the interval between successive perigee passages (i.e., close approaches of the moon to the earth.) This interval is called the anomalistic month. It has 27.55455 days and fits exactly 239 times into the saros. (This means that corresponding eclipses in successive saroses will be of the same type: "annular" if the moon is distant from the earth and "total" if the moon is near.)
All of the above observations were mentioned by A. Aveni in Skywatchers of Ancient Mexico, but there is another coincidence about the "triple saros" interval, I've never seen mentioned by anyone before. The "triple saros" interval of 19,755.96 days or 54.04 years is almost exactly equal to the product of the periods of Venus and Mercury 224.7 days and 87.99 days, respectively.
For a long time, I groped to visualize the meaning of this last observation. It seemed to correlate with the following idea: The Triple Saros interval was similar to the period or interval between the times when Venus and Mercury came in conjuction or simultaneous opposition with each other on a fixed ray from the sun. The "triple saros" was virtually a "divisor" of that particular interval of time. This would be obviously true if both planets had orbital periods, which were integers, because then, the product of their periods would be integrals multiples of each of their periods, respectively--times when both planets would return to their previous positions, in opposition, on the fixed ray.
This implied to me that Venus and Mercury might have some influence on the moon.
Assume that at the start of a Triple Saros cycle, we have Mercury lined up with Venus and Earth on a fixed or "pre-determined" ray emanating from the sun. Then at each of the, say, nine or intervals of the cycle, Venus remains on the fixed ray since the period of Mercury is virtually integral. And Mercury revolves, say, clockwise around the sun, at increments of -.3 (or .7) parts of an orbit subdivided into 10 arclengths, before returning, in conjunction with Venus, on the fixed ray.
During theTtriple Saros cycle, we know that the moon is always on the synodic ray between the earth and the sun. On the other hand, during the cycle, the same side of Venus always faces Earth. Therefore, we can visualize that, as the earth revolves around the sun during the Triple Saros cycle, Venus revolves (effectively) on its axis at exactly the same rate. If the sun were displaced to the center of Venus, Venus would be like the axis of a wheel, on the rim of which Earth is attached and, what is more, the moon would always lie on the same spoke of the wheel emanating from Earth to Venus. This gives some evidence that the moon was once part of Venus.