Does it say how big Calpamos is in either the CMTM or WYR?
A large moon could be possible. I found this very interesting answer. It's possible someone who saw Prometheus and wanted a similar answer, asked it.
Is it possible for an earth sized planet to orbit as a moon around a gas giant?
On a Super-Jupiter or Brown Dwarf yes, (provided that your Planet is outside the radiation belt). Natural Moons of Gas Giants their mass should be less than 0.0001 of the mass of the gas Giant.
Jupiter's moons are pretty massive, but not as massive as Earth, so a Super-Jupiter would suffice. Saturn who's less massive, has less massive moons, Uranus even less.
There would be one problem, Gas Giants form out beyond the frost Zone (that we know of, we don't have gas giants closer in our Solar system for reference, but we see a lot of Hot-Jupiters though) so the moons of the Gas giants would be Water worlds if they're in the Habitable Zone of the parent star (the Gas giant can also generate heat for the moon).
A captured moon is completely plausible though. I wouldn't be surprised if Jupiter moved in and captured the rocky planets of our solar system. Fun fact: Triton is a moon caught by Neptune, so this even exists in our solar system. (Jupiter doesn't move in from perturbations of Saturn.)
How big does the (parent) gas giant have to be to be able to form a balanced orbit? Does "that massive" earth sized planet has to be "captured" to be its satellite, or can it form from debris of the original gas giant materials? Also, does the earth sized planet orbiting gas giants has to be tidally locked?The physics would work and it has been used a lot in Science Fiction. But as User says, moons are likely to be much smaller.
An inward-migrating giant might pick up a rocky planet as a new moon. That would probably mean a very eliptical orbit.
It's also possible that moon-formation in our solar system is not typical and that much bigger moons can form without a capture or the sort of collision that formed the Earth-Moon System.
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"There would be one problem, Gas Giants form out beyond the frost Zone (that we know of, we don't have gas giants closer in our Solar system for reference, but we see a lot of Hot-Jupiters though) so the moons of the Gas giants would be Water worlds if they're in the Habitable Zone of the parent star (the Gas giant can also generate heat for the moon)."
This is great for the movie, as I'm sure the gas giant Calpamos is far out of the habitable zone and most probably in the frost zone of it's host star, hence the cold moons. There are a lot of possibilities though in Astronomy, so it's hard to say, for example the gas giant could be providing heat to it's moon, etc. even if they are far out in the frost zone..I will check most of Jupiter's moons temp later.
What were the temperatures of LV-223 and LV-426 before terraforming?
PS> I hope there are 3 moons and that is not LV-426 in the picture with LV-223 circled. If LV-426 truly is 12.000km than that puts LV-223 at more than 25,000km...highly unlikely. They need to rethink this or better yet just add a name for the 3rd moon
and pretend that's the one pictured next to LV-223. LV-223 should be as big as LV-426, not bigger, for things to make sense.