Angular resolution question

[Bedlasky]

Hello!

 

I am working on my world-building project and I am making science-based world. I am trying to be realistic in my world-building. I have a binary star system with several planets, my "home" world orbits bigger star on S-type orbit. There are several planets with large moons in relatively close distance from my home world. I want to know if those planets and moons are distinguishable on the night sky by naked eye. I calculated planet-moon separations in angular diameter and apparent magnitudes. Here are my candidates for possibly observable moons (I didn't choose names for planets and stars yet, so for now I use just generic names):

 

δ - Planet-moon separation as angular diameter (in arcminutes)

m - apparent magnitude

 

AcI: δ = 27,81' ; m = -3,1

AeI: δ = 80,01' ; m = -2,95

AfI: δ = 35,84' ; m = -0,22

AhI: δ = 8,98' ; m = 5,78

AhII: δ = 11,77' ; m = 5,05

AhIII: δ = 18,68' ; m = 4,43

AhIV: δ = 29,66' ; m = 3,44

 

There are also three candidates which could be maybe observable on a clean moonless sky with very low light polution:

AhV: δ = 45,12 ; m = 6,79

AhVI: δ = 52,92 ; m = 6,97

AiIV: δ = 6,73 ; m = 7,92

 

Planet apparent magnitudes are:

Ac: m = -8,62

Ae: m = -6,08

Af: m = -5,75

Ah: m = -3,3

Ai = 0,97

 

I know that average angular resolution of human eye is 1 arcminute, all of these moons have high enough separation to be distinguishable (in theory). But big role also plays apparent magnitude of the planet. The planet could be so bright that it outshine them. I searched some relation between magnitude and angular resolution, but I didn't found anything. Moons AhI-IV have quite similar values to Galilean moons, which usually cannot be seen by naked eye (I know that Callisto and Ganymede can be seen by people with very good eyes on clear sky with low light pollution). So my question is, how can I tell that certain moon is visible by naked eye and that planet wouldn't outshine it? Is there some calculation or chart which would generalize this for any moon?

[vlaiv]

I think that after some separation there is not much influence from magnitude difference.

Most separations you listed are quite large separations. Only few of them are less than width of a full moon - and that is quite a large angular separation (half a degree).

Just to get the idea of separation - take next clear night, and although Ursa major is not well positioned - observe Alcor / Mizar pair they are very easy to tell apart and have about 11' of separation.

 

[Bedlasky]

Thanks!