Finding period of revolution of stars?

[rockchalk1312]

Homework Statement

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?

Homework Equations

T²=(4∏²/(GM))r³

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!

 

[gneill]

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

 

[rockchalk1312]

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

 

[gneill]

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

 

[rockchalk1312]

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

 

[gneill]

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

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

 

[rockchalk1312]

You need their masses and their separation.

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).

 

[gneill]

Draw a picture. What point do they mutually orbit?