In my world, there are 3 astrological bodies of significance, the sun, the moon, and a 3rd, geostationary object, believed to be the home of the gods. I want all three of them to have roughly the same size perspective (angular diameter), such as we have on earth. This is to give an awesome looking eclipse which happens once every very long time, for plot reasons. The reason the sun and the moon appear to be the same size is that the sun is 400 times more massive than the moon, but is also 400 times further away. With a bit of calculations, and internet searches, I have the following data;
Sun distance - 149.6 Million Km Sun size (Radius) - 695510 Km Suns angular diameter - 31'27'' to 32'32'' arc.
Moon distance - 363,104 to 405,696 km Moon size - 1737.1 km Moon Angular Diameter - 29'20'' to 34'6'' arc.
Geostationary orbit distance - 35786 km,
using average moon dist/Geostationary dist - 384391 km / 35786 km gives me 10,74, and dividing moon size by this gives me a total radius of Geostationary object radius - 161,72 Km. then, Using the formula x= 2arctan(d/2D) where x is radians, d is diameter of object and D is the distance between observer and object. x=2arctan(323,44/71572) gives me a total Angular Diameter of - 31'07'' of arc.
SO What I want to find out, 1. Would this setup be stable in the long term, and if it is then 2. Would this object be large enough to achieve hydro-static equilibrium.
I have found that Saturns moon Mimas, at 397 km, appears to be, but is not in hydro-static equilibrium, while the largest non equilibrium object is the rocky asteroid Vesta at 525 km.
If needed, I would make the object a watery, icy object, but then I think I will run into problems with it melting, but thats for another time.
The earth, moon and sun are as is in reality, Earth weight is 5.972 × 10^24 kg, Moon weight is 7.35 x 1022 kg,