From what I gather, the early moon was 4 or so radii away from Earth after formation/the big impact (3 being minimum without tearing apart via gravity and 5 being the maximum the debris would have been spread).
Now it is 60 Radii, moving at about 1KM per second. I assume it would have been faster after the Earth/Thea impact. Any idea how much?
The main reason for the move was tidal friction from Earths ocean "pushing" forward which transferred momentum to the move and therefore out by about 3CM a year.
However, there was is also a theory that the Earth's tilt was up to 60 degrees and that also resulted in an early and quick movement outward by the moon early in its existence. (Matija Cuk)
The moon will keep moving out until that angular momentum is transferred to the point where Earth and the Moon are "tidally locked".
Presumably, the moon's orbit early in its existence was quicker due to this shorter orbit, though I'm not sure of projected actual speed.
Question:
If Earth didn't have this "tilt" early on that gravitational interaction with the moon largely corrected (at the expense of the moon making a big and fast leap out), would the "tidal locking" of the earth to the moon have already occurred?
If the moon was 15 times closer (I don't know the speed back then so I can't calculate the "month"), would it be possible that the Earth's day/month would have already been "tidally locked" at something closer to what we know as 24 hours? That the moon would orbit so closely that the month would be far closer to what we know as a day than, in the future, our "day" will be closer to what we think of as a month?
I know that the Earth rotated faster prior to the impact, maybe 6 hour rotations immediately after (and probably before, I assume).
If Earth rotated 24 hours (as we know it) PRIOR to the collision and the moon was much, much closer, and this "tilt" issue wasn't involved, how quickly could the Earth/moon Day/Month be determined.
I'm trying to figure out if, after the "Thea" collision, that Earth and the Moon might have found a much earlier, and short, "day/month" combo.
Am I missing some large factor?
Obviously, the tides would much, much higher/worse and the moon would be far bigger in the night sky.
I ran some middle school math. Assuming the moon was formed at 1/10th the current, average distance, this means 2 x 3.14 x 38,500 (actual is 385,000) KM is 241,780 KM.
At the current 1.022 KM per second (again, I'm guessing it would be faster back then as the Moon's speed is slower as it moves out), this would mean 65.7154 hour long month?
Double the speed and you get pretty close to 33 hour month.
If the Earth had been rotating slower back then and the impact maybe slowed it a bit more, would the moon have remained in place at 6 radii?