Excluding gas giants, roughly what percentage of planets in the habitable zones of their stars would have large moons like Earth does, as opposed to Mars and its small moons/captured asteroids?
closed as primarily opinion-based by Carl Witthoft, Mike G, Sir Cumference, J. Chomel, Rob Jul 15 '18 at 23:29
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It's not quite the drake equation in terms of your inputs determining your estimate but it's not too far off. Our telescopes can't get a good look at existing or forming solar systems. They've spotted several thousand planets but only a tiny number of possible moons and I don't think any of them are confirmed. It's also not always possible to tell is some of the "earth-like" planets that have been observed are more like sub-neptunes or perhaps water worlds. Any kind of gaseous/water or ice world planet would have a hard time making an impact moon. Two rocky bodies colliding are best for that.
Young solar systems are full of collisions during their planet formation period so there are probably enough collisions with the approximate size/ratio of Theia-Earth. At least, it's probably not uncommon, but size isn't the only factor. The impact has to be at the right angle to generate sufficient angular momentum, because the main body ideally rotates faster than its Moon orbits. This faster rotation and the tidal force of the moon on the planet pushes the moon outward over time and stabilizes the Moon's orbit (provided the hill sphere is larger than the Moon's distance over time). If the main body rotates slower than the moon orbits, the moon is drawn towards the planet and would likely destabilize before long.
An impact too straight on is bad for moon formation and too glancing is also bad. The impact needs to be within a proper range in size, ratio between the two objects and angle of impact and without a surface with lots of ice and/or water. The requirements are pretty precise, so stable large collision moon formation should at least be somewhat rare because of all the necessary conditions. It's also not known with accuracy how many of the "habitable" planets started out rocky.
Migrating jupiters and other planets are another problem. It's fairly common for Jupiters to migrate which should destabilize a percentage of inner planets with stable collision moons.
The biggest issue is the size of the star. The habitable zone of red dwarf stars is very close to the star and moons wouldn't be stable around planets in those systems. Those planets would likely be tidally locked, which means they'd rotate slower than their moon orbits and that would likely lead to destabilizing the moons orbit and the moon crashing into the planet, that is, if the planet had a moon at all, it would need to form in a very tight orbit.
So there's a few estimates to make a guess at an input. I don't think an accurate estimate is possible but if I was to guess, I think large collision moons will be found. I don't think they're super rare, and I base that guess on a reasonable abundance of rocky material in solar system formation and a very large number of collisions, so even if the Earth-Theia collision was one in a million, there's enough collisions happening that other two body systems like ours probably create long term stable moons from time to time. So, rare but I think, not super-rare.
We probably won't have an answer for this until we get a better look with the James Webb Telescope.