If you pick up a textbook on astronomy, chances are that the origin of the Moon is ascribed to impact on the Earth by a large object, about the size of Mars. That is also the currently accepted view among non-specialists.

But the impact hypothesis was never worked out or published completely.  We simply don't know if the hypothesis leads to the current Earth-Moon properties.

On the other hand, starting with the present Moon and working backward in time guarantees success.  The only question is whether the initial conditions are reasonable.  We find that they are and are publishing that fact.

The backward calculation is time-honored.  It was used first by Sir George Darwin in 1870 and since then by Harold Urey and Hannes Alfven, two Nobel-Prize winners, and other distinguished scientists.

Darwin noted that the Moon raises tides on the Earth.  These tides, in turn, perturb the orbit of the Moon, causing it to move away from the Earth.  In other words, the orbital radius increases by about 1.5 inches per year; thus, the Moon gains "angular momentum" at the expense of the Earth (since total angular momentum of the Earth- Moon system has to be conserved and remain constant).  The Earth's angular momentum resides in its spin, which slows down about 2 milliseconds per year as days become slightly longer.  Astronomers know about this increase in the length of day, as they observe the position of fixed stars.

The recession of the Moon from the Earth has also been measured precisely by laser reflection from mirrors on the Moon's surface, mounted by astronaut and Moon-walker "Buzz" Aldrin.  It matches well the length of day and gives us an independent check of the tidal perturbation.

Calculating backward in time puts the Moon ever closer to the Earth and shortens the month (as the orbit shrinks) and lengthens shortens the day.  Eventually, the length of the month approaches an hour or so and becomes identical with the length of the day.  In other words, the Earth's spin becomes identical to the orbital period of the Moon.

At this point, I depart from previous work.  When Darwin did his original calculation, he stopped and simply assumed that the Moon was spun off from the Earth's mantle by centrifugal forces – the so-called "Earth-fission" hypothesis, since then proven to be untenable.

A German physicist bravely continued Darwin's calculation and found that the Moon was captured gravitationally as it passed close by the Earth.  However, an American geophysicist, Gordon MacDonald, found that this method of capture would result in a much larger spin of the Earth.  In fact, the Earth would rotate so fast that it would become unstable and fission.  In addition, the rotational spin energy would have to be dissipated within the Earth and would vaporize the Earth.

I amended MacDonald's work by correcting the tidal theory and found a technical way to keep both spin and rotational energy within reasonable bounds.  In fact, the energy dissipated would merely melt the Earth rather than vaporize it.

This is now my present position: capture of the Moon is not only possible, but in harmony with physics and geophysics.  The melting of the Earth's interior would create the central iron core (assuming that it had not existed previously) as the heavy iron flowed to the center – as well as melt the mantle.The geothermal energy is released very slowly in volcanoes and hot springs.