The Origin of Moons

One of the interesting parts of the theory of the origin of life proposed in this blog involves the impact of a planetesimal into the proto-Earth to create some of the unique conditions that are required for the origination of life. This impact had to be mild enough to not destroy the proto-Earth, shattering it, and a relative velocity of the order of orbital velocities might be too much.

An output of the theory was that the origination of life would be rare if the impact of planetesimals onto planets was rare, and common if this class of impact was common. So, which is it, both common or both rare? Obviously, this affects how likely it is for aliens to find us and send something our way.

One example that comes to mind relating to things hitting Earth are the various impacts by asteroids. Nothing huge has hit that we know of, but some substantial asteroids, notably the Chicxulub one that cratered in the Yucutan, have had a major effect on existing life on Earth. The Chicxulub asteroid came in with orbital speed, but was only of the size of 10 kilometers. For reference, the diameter of the moon is 3500 kilometers. Anything with a size like that impacting with orbital speed has so much kinetic energy the planet would be disassembled.

This impact happened to the Earth early in its history. Somewhat before that time, there was a planetary disk, busy condensing into the sun and the planets. To review, there was a large gas cloud, rotating, that was supported in its volume by thermal motions. As it cooled and shrunk, gravity became more important and it condensed. Rotation kept increasing because of angular momentum, and centripetal force began to replace gas pressure as the supporting force. Regrettably, centripetal force only works in the direction perpendicular to the axis of rotation, so the gas cloud has to collapse down to an oblate spheroid and then into a planetary disk.

Disks are nice, but they are not stable completely. Once the disk gets thin enough, some axisymmetric instabilities form and bands of gas separated by fairly sparse bands form. There is shear motion between two adjacent bands, but with a space between them, no angular momentum is coupled, and the bands start to be somewhat independent. These gas bands also are unstable to gravitation, but in the non-axisymmetric sense: blobs start to form. These are the protoplanets.

What exactly happens during this gas blob to protoplanet phase? Gas moves around the band to become more dense at the blob, and the blob begins to have some condensation. The core of the planet is starting. The rest of the gas in the band doesn’t really care if there is condensation or not, as the gravitational force from an uncondensed blob and a condensed blob are about the same. Think about the Lagrangian points relative to the condensing gas blob. These are points where there is no gravitational force pulling them either one way in the band of gas or the other way. They are equilibrium points.

You may recall that three of the Lagrangian points are co-orbital with the gas blob that causes them. They form an equilateral triangle, with one point being exactly opposite the gas blob’s location in the orbit, and the other two closer by. These are three points where gas could collect to form, what else, but planetesimals. Things are about to get very interesting.

Thus, in one band of gas, we are likely to see a large blob condensing out into a planet, and three blobs condensing out to become small planetesimals. Other blobs in different gas bands are jostling these four objects gravitationally, so they don’t just sit there gathering more gas. Some planetesimals may scatter out of orbit and be lost, but one or more may migrate around the band and wind up at the big gas blob. If one does, it isn’t moving very fast relatively, certainly not with a relative speed anything like orbital velocity. It just moseys along, picking up a little extra relative velocity when it gets close enough to the gas blob to feel the gas blob’s pull. The gas blob may already be condensed into a planet, if the condensation process can speed up enough once it gets started compared to the time taken for the planetesimals to migrate to a closer location.

This scenario has exactly what is desired. A low relative velocity, large mass body is about to impact a proto-planet. It’s Theia and Earth, and here is a way in which it might happen, all courtesy of the Lagrangian points. The impact velocity would be of the order of the free-fall velocity, actually a bit larger because both bodies are large enough to provide gravitational acceleration to the other. For the moon to form from this impact, it is necessary that the impact trajectory be not dead-on, and not so far out as to be only a tangential touch, but some grazing angle. There doesn’t seem to be any reason to suspect that such a trajectory would not be possible from the approach of a co-orbiting planetesimal.

What does this imply? It implies that the existence of a planetesimal with minimal relative velocity is something that might emerge in the formation of any planet. As opposed to being a rare event, where something just happened to fly in from farther out the solar system, and just happened to have an elliptic orbit where the velocities at time of impact closely matched, we have an ordinary, run-of-the-mill event, where most planets have planetesimal neighbors sharing their orbit and likely to slide around to an impact scenario. Large moons are not rare, or at least, not so extremely rare as would be required by the asteroid impact scenario. Then the origin of life, by the early life hypothesis touted elsewhere in this blog, is not necessarily unusual, and we might have aliens in the galaxy not too far from us.

It does imply that the search for large moons might be bumped up in priority. We detect planets around other stars using the wobble method, and perhaps with another order of magnitude improvement in the digging out of a wobble signal from the noise of the star’s own instabilities, we could detect the presence of large satellites, with a mass ratio similar to that of the Earth-moon system. There is nothing else in our solar system with anything near that ratio. Similarly, for transiting planets, with one or two orders of magnitude improvement in finding signals in the stellar noise, we might see an Earth-moon analog around some other planet.

Doesn’t this remind you of the days when no one could see exo-planets, and the existence of aliens was, among other things, wholly dependent on speculations that there were lots of them? Now, if the early life hypothesis is correct and a moon is necessary, with impact included, the existence of aliens might be dependent on the existence of a large planet-moon system. Just when astronomers were so proud of themselves for finding all these exo-planets, we up the requirements for them.