Well... here are some back of the napkin calculations for you.
Nomenclature:
- M = larger body's mass
- m = smaller body's mass
- R = larger body's radius
- r = smaller body's radius
- d = distance between the center of the two bodies
- Theta = apparent angular size of the moon/planet in the sky
From scratching at a piece of paper, the apparent size of a moon in the sky is:
Theta = 2*tan^-1(r/(d-R))
From WikipaediaWikipedia the Roche limit for a rigid body (this is the extreme, but the math is a little easier):
d = 1.26r(M/m)^1/3
I pulled some numbers from this table and plugged them in to solve for Theta.
- Earth/Moon = 58.4 deg
- Earth/Earth = 150.9 deg
- Jupiter/Earth = 110.6 deg
- Sun/Earth = 103.4 deg
For the last two, I swapped the r and R in the Theta equation since it's the larger body's Roche limit we care about but the observer is still standing on the Earth.
Well those are fun answers. For reference the Moon is about half a degree or 30' (60 arc minutes in a deg). The take away would be that the biggest thing you can put in the sky is going to be a binary planet of equal mass. If you decide to have the Earth as the smaller body you get diminishing returns. These are closest pass numbers, most orbits aren't perfect circles so the moon doesn't have to look this huge all the time. Finally the real Roche limit is going to be somewhere between the rigid and fluid satellite numbers, I just did the rigid above and that lets the moon come a lot closer. So some in between distance isn't going to look nearly as impressive in terms of moon's apparent size. I'll look at the fluid stuff later and add it as an edit.
