# Question on Kepler's Law

## Homework Statement

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?

## Homework Equations

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

## 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?

gneill
Mentor
Start with the basics: centripetal force being provided by the net gravitational force on any given star in the system. • i_hate_math
Start with the basics: centripetal force being provided by the net gravitational force on any given star in the system.
View attachment 99491
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?

haruspex
Homework Helper
Gold Member
G*m*3M/R^2
That is the magnitude of the force exerted by (what exactly) in what direction?

That is the magnitude of the force exerted by (what exactly) in what direction?
I think this is the force exerted by the three suns and that is towards the centre of the circular orbit?

haruspex