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I would like to propose a possible different scenario. I think the core of Phobos could be a captured comet.
This is not an original idea at all. This is still a valid and old idea. Phobos and Deimos are either a Mars ejecta, a broken up moon, or captured asteroids. The problem with a captured asteroid scenario is that the physics of orbits + timing do not work out. You literally have to play solar system collision billiards for them to get captured like that. Not saying it didn't happen, but that was one heck of luck. Remember, asteroids do not have second stage orbit insertion engine burns
I agree that the Marsian ejecta theory is not that original and seems more of a cop out, but at least it plausably explains the current orbits and Mars does have craters large enough to produce such ejecta.
Note that I said captured COMET, not asteroid. There is a big difference. I'm aware the the asteroid theory is a no go. An asteroid would have to be a collision billiards problem. However, comets enter and exit the inner planetary orbits on their own on a regular basis. One hit Jupiter recently.
Posit that a comet had a VERY near miss with Mars, where there was atmospheric braking from the encounter, and the comet was outward bound from a loop where it had been slowed both by a bad gravitational set of alignments, and/or a jetting of ejecta, and a capture is highly plausible. Once captured, over time, the orbit would move from elliptical to more or less circular.
That it is Mars that captured Phobos, rather than Jupiter or Saturn, is probably luck of the draw, but I think we still aren't sure about some of the Saturn moonlets, so maybe Saturn has a few imprisoned comets within the rings.
The more I consider the problem, the more I think comet capture is the most likely scenario.