What Is the Orbit Radius of Two Equal-Mass Particles?

[FissionMan1]

1. Two particles of equal mass are orbiting each other in circular orbits. What is the radius at which they orbit?


Energy = T + U = 0 (for circular orbits)

T = 1/2 m v^2

U = -(Gm*m)/r + [L^2] / [2(mu)r^2]

period=[2 pi r] / vt

vt is tangential velocity
L is angular momentum
mu is a constant
G is the gravitational constant
r is the radius from one particle to the center of their rotation

I have attempted to solve for R by plugging those equations in and simplifying, but I do not believe my answer is correct (it would require a lot of skill to represent it with mere type here). I must calculate the radius in order to find the time it takes for the two to collide if they were stopped in their orbits and fell towards each other. So any help calculating the velocity?

 

[FissionMan1]

Similar to this problem, be forewarned that this other thread didn't get anywhere.

https://www.physicsforums.com/showthread.php?t=192000

 

[FissionMan1]

I actually figured out that r = (mu tau^2 / 4pi^2)^1/3

The problem I have now is figuring out how long it takes until they collide.

 

[FissionMan1]

scratch that, i have no idea. back to square one.

 

[Dick]

Let's go back to the first question, ok? Do you know v? Otherwise there's no answer, they could orbit at any r with appropriate v.

 

[Meir Achuz]

Use the centripetal force equation to get r=mG/(4v^2).
You have to know v or some other parameter to find r.