# Question on Kepler's Law

1. Apr 21, 2016

### i_hate_math

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
Kepler's 3rd Law: T^2=(4*π^2/GM)*R^3
v=2πR/T

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?

2. Apr 21, 2016

### Staff: Mentor

Start with the basics: centripetal force being provided by the net gravitational force on any given star in the system.

3. Apr 22, 2016

### i_hate_math

I had m*v^2/R = G*m*3M/R^2, this led me to
v=sqrt(3GM/R)
and L=sqrt(3)R, could u tell me where I went wrong?

4. Apr 22, 2016

### haruspex

That is the magnitude of the force exerted by (what exactly) in what direction?

5. Apr 22, 2016

### i_hate_math

I think this is the force exerted by the three suns and that is towards the centre of the circular orbit?

6. Apr 22, 2016

### haruspex

Each sun is only pulled by two others. But anyway, it looks to me like you calculated the force exerted by a single sun towards itself (GMm/L2).