Equilibrium between different masses

[cm_student]

1. Homework Statement

I am trying to find the easiest and simplest way of calculating the distance that two celestial bodies would need to be apart, in order for those celestial bodies to never get closer or further away from each other. I have the values of the mass, density, radius, volume and gravity of the two celestial bodies, is it possible to use the values I have to work out how far apart they would need to be to remain in a state of equilibrium?


2. Homework Equations

There are no relevant equations I know of, sorry. But if it helps, I am happy to also know how to work out the gravitational force exerted between two objects that would keep those two objects at a constant distance from each other.



3. The Attempt at a Solution

This one has me stumped. Thanks for any and all help. Please keep answers as simple as possible :D

 

[ehild]

They have to orbit around their common centre of mass so as their distance stay unchanged.

ehild

 

[cm_student]

Thanks for the reply, what equation would I use to work out their common center of mass?

Keep in mind that the only values I have are mass, volume, density, gravity and radius.

 

[cm_student]

oops, A VERY IMPORTANT DETAIL that I forgot to mention is that the celestial body with the small mass is orbiting around the celestial body with the larger mass.

does this help?

 

[ehild]

Well, it is better now, although both bodies orbit around the CM really. Saying that the body with the smaller mass orbits around the other is a good approximation if the larger mass is very much larger than the smaller one. Assume that it is the case, one body with the large mass is fixed, the other orbits around it along a circle. In this case, there is a relation between the speed of the smaller mass and the radius of the orbit. You know that the force of gravity acts between the bodies. You know that bodies of spherical shape and uniform mass distribution act each other as if all their mass were compressed in their centres. You know that a circular orbit requires a centripetal force, mv^2/R. Find out the relation between the speed and radius.

ehild

 

[cm_student]

I appreciate your help, ehild.

I know you are trying to get me to work it out for myself, but I don't think you appreciate my situation. I have been awake for 36 hours and I need answers not more questions. I'm a visual artist, I'm not a scientist, and I've spent all day trying to figure this out. So please, can you let just let me know if you can help me with this or else point me to some other place that I can get help.

 

[ehild]

I know only this place for Physics homework help. Could you please send the original formulation of the problem? One thing - either the speed or the time period is missing from your question. ehild