I am planning out ideas for a science-fiction world, and I want to make sure that what I include is reasonable and mathematically sound (outside of things like FTL as that is neccessary for the story to work I know it doesn't make sense).
Would it be possible for a planet to be massive enough for a sattelite to be of approximate Earth size. I am thinking between 0.7 and 1.3 g, with a similar density. So a density of approximately 5.51 g/cm3.
So, from what I found, it would mean a radius between 4456.5 km and 8276.33 km, and a mass bwteen 2.0427816158×10^24 kg and 1.3084393744×10^25 kg. (I used a formula that would find the required mass for a sphere of a certain radius, and then tested for the gravity of said planet, to find the desired range)
I ask because from what I read, planets of a high enough mass tend to not be able to properly hold large moons. Which raises the question of if a planet could potentially be less than this critical mass, and still be massive enough to hold a sattelite within the described range. At least at the lower 0.7 to 1 g end of the scale.
And if so, what would be the required mass of the planet it is orbiting? I hope I provided enough information for this to be able to be calculated. Is there a general formula for the largest moon a planet of a certain mass could reasonably hold in a stable orbit? I also do not care if the orbited planet is telluric or a gas giant, either is acceptable.
Your help is much appreciated.
Note: To clarify, I do not care about how unlikely it would be for such a moon to form, as I know it is unlikely for some large gas giants and such to capture moons, with most forming from the planetary disc. I can try to find an excuse for how it formed or was captured. I simply require answers on if a body of this size can act as a sattelite, and how massive the planet it orbits has to be for this to work. I just wanted to get this clarification out of the way so that nobody feels the need to bring it up.