Three identical stars of mass M = 8.9 x 1030 kg form an equilateral triangle that rotates around the triangle's center as the stars move in a common circle about that center. The triangle has edge length L = 2.8 x 1010 m. What is the speed of the stars?
Kepler's 3rd Law: T^2=(4*π^2/GM)*R^3
The Attempt at a Solution
I used L to find an expression for R, namely R=L/sqrt(3), since its a equilateral triangle and L one of the sides (this is probably where I went wrong). I then used the two equations above to calculate the speed.
Now I know that the correct solution to this question is v=(GM/L)^0.5=1.456*10^5,
can someone pls explain to me why it is so?