Rotating binary star system & three star system

[bcjochim07]

Homework Statement

1) Astronomers discover a binary star system that has period of 90 days. The binary star system consists of two equal mass stars each with a mass twice the sun's. They rotate about the center of mass at the midpoint between them. How far apart are the two stars?

2) Three stars each with a mass of our sun, form an equilateral triangle with sides 1* 10^12 m long. The triangle has to rotate because otherwise the stars would collide. What is the period of rotation?

Homework Equations

The Attempt at a Solution

For #1,

There doesn't seem to me to be any clear pivot or mass around which the stars orbit, and that's what baffles me. I thought about pretending they were connected by a massless string and calculating the moment of inertia, and then using rotational kinetic energy, but I'm not sure how to start

#2 I think I'll have a better grasp on this after figuring out #1

 

[alphysicist]

Hi bcjochimo07,

Draw a force diagram for one of the stars. What is the only force that acts on it? The stars are moving in a circle, so you also know a formula for the acceleration.

Be careful when you assign distances--the distance that is used in the force formula is not the distance that is used in the acceleration formula.

 

[bcjochim07]

Thanks! I got the first problem right. Now for the second one... I would have to choose one of the stars and sum the force components. Next I would use trigonometry to find the radius & then I would solve for angular velocity & then the period.