# Question regarding potential moon sizes

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.