Friday, April 8, 2016

Was the Earth Ever Phase-Locked to the Moon?

Recall that one of the principal theories for the origin of the moon was that of a planetoid, nicknamed Theia, which impacted the proto-Earth. The collision spewed much matter into diverse orbits, but one large chunk of mass didn't get enough energy to completely separate from the majority of the mass, that which stayed behind, and go into a planetary orbit. Instead it went into a satellite orbit, and has hung around the Earth for all the following billions of years.

This collision was a pretty lucky one. There are at least two principal variables: the difference in speed, relative to the center of motion of course, and the projected closest point of approach. The second one is simply a way of describing how far from a heads-on collision it was. A heads-on collision would not have produced any moon, just broke the proto-Earth apart, provided the velocity difference was high enough. If the projected closest point of approach was just less than the radius of the proto-Earth, it would have been a glancing impact, with the two bodies, largely intact, proceeding on orbits close to what they originally had. Instead, the projected closest point of approach was enough to tear the proto-Earth apart slightly, as the Theia object accreted some mass from the proto-Earth, much like a bullet being shot through jelly picks up some jelly on its way through.

From a momentum point of view, the relative momentum that Theia had before the impact had to be shared with both its original mass and the accreted mass, meaning for the same momentum, less velocity. Less velocity can mean a velocity less than the escape velocity from the remaining mass of Earth, so Theia-plus was in a satellite orbit. Most likely, it was nothing like a circular orbit, rather an eccentric one, but the important point is that it was a bound orbit. Thus, after the impact, the moon was in an elliptical orbit, looping back to have a close pass at the Earth, over and over again.

Nothing was alive on Earth at that time, as it was a cauldron of molten rock, but if there had been, it would have been a spectacular sight, to watch the moon rise and fill a large part of the sky, and then soon set again. The perigee cannot have been very far above the Earth's surface, as the orbit originated in an impact, at roughly the radius of the Earth.

Tides would immediately begin to circularize the moon's orbit, and here we mean solid tides, not liquid ones. The orbital period of a circular orbit near the Earth is about an hour and a half, but the orbital period of a elliptical orbit is governed by its semi-major axis, not the perigee distance, so it would be longer. It may well have been that the orbital period was less than Earth's day, whatever that was at this time. That means that the tides would lengthen the semi-major axis of the moon's orbit, shortening its orbital period, while the diurnal rotation of the Earth would slow down, and the day lengthen. This is a recipe for tidal locking, as the two approached each other.

Right now the moon is phase-locked to the Earth, with its day and orbital period being the same. What may have happened back then, in the very early days of Earth, is that Earth may also have been phase-locked to the moon. If it did happen, it was only temporary, as eventually the moon's orbit drifted out further, and the day did not lengthen enough to continue to match the orbital period.

Skip forward from the early days of the Earth moon combination, shortly after the impact that formed them, to the possible period when the moon was still fairly close to the Earth, but the Earth was phase-locked. This is similar to what astronomers think many planets of red dwarfs would be doing, and there has been a little thinking about what the conditions might be on such a planet. A planet which is phase-locked to its satellite, albeit a large satellite by mass-ratio, is completely different. Only the locking process is the same.

There would be one face of Earth which always faced the moon. With the moon still in something of an elliptical orbit, this does not mean that the moon would be sitting constantly overhead at the same point. What it does mean is that the apparent orbit of the moon would be in the visible part of the sky, to someone sitting at the right point on Earth, right under the perigee. The moon would be coming closer and closer, moving one direction and then the opposite, and then going out further and further. If the rotational axis of the Earth were aligned with the axis of the moon's orbit, sitting on the equator under the perigee would be the best viewpoint.

As the moon gets closer and closer, what happens? Gravity happens. The crust endures this very large force of gravity, or rather variation of gravity, over and over again in rapid succession. The crust would crack and split, leaving volcanic activity at an unimaginable level. As time progressed through this window of phase-locked motion, the moon would circularize and move out, so the gravitational effects would diminish with time, but still the crust would be torn frequently.

In other words, there is a tremendous source of energy here, generating chemicals of all sorts, and making sure any oceans that formed would be full of a wild mixture of various elements and molecules, many of which would be energy-rich. Back when this blog was discussing the early origination of life in an organic ocean layer, there might have been questions about whether or not there would be abundant energy around. With this scenario, certainly yes. Note that the rate of evolution, both the early chemical type and the later biological type, is affected by the amount of available energy. With lots of energy around, life can evolve faster. Unlikely processes can come to fruition earlier. Things just seem to fit together.

The crust of the Earth is all one big connected shell, but someone might guess that there would be more cracking and erupting on the perigee side of the Earth, and the back side, where the moon was never visible, might be a bit calmer. Still, with the circulation of oceans, energy would be available, but disruptive geological events might be a bit more rare. Perhaps some parts of the crust on the rear side of the Earth could stay intact for a long period. This might be the home for early life.

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