# Finding period of revolution of stars?

1. Apr 17, 2013

### rockchalk1312

1. The problem statement, all variables and given/known data
In a certain binary-star system, each star has the same mass which is 7.5 times of that of the Sun, and they revolve about their center of mass. The distance between them is the 7.5 times the distance between Earth and the Sun. What is their period of revolution in years?

2. Relevant equations
T2=(4∏2/(GM))r3

3. The attempt at a solution

multiplied mass of sun by 7.5 to get M, multiplied 1 amu by 7.5 to get r

T2=(4∏2/(6.67E-11)(1.491E31))x(1.125E12)3
T=2.38E8 seconds

changed this to years and got 7.54 years but this was the wrong answer.

Can anyone point out what I'm doing wrong? Thank you!

2. Apr 17, 2013

### Staff: Mentor

..."and they revolve about their center of mass"...

3. Apr 17, 2013

### rockchalk1312

...I wish I knew what that implies...

4. Apr 17, 2013

### Staff: Mentor

The orbital radius is not the distance between the stars. They orbit about the center of mass.

5. Apr 17, 2013

### rockchalk1312

Doesn't that mean you have to know the radius of the stars themselves?

6. Apr 17, 2013

### Staff: Mentor

No. You need their masses and their separation...

7. Apr 17, 2013

### rockchalk1312

But I used their masses--7 x that of the earth--and their separation is 7x the distance between the sun and the earth (1 amu).

8. Apr 17, 2013

### Staff: Mentor

Draw a picture. What point do they mutually orbit?