Finding period of revolution of stars?

AI Thread Summary
In a binary-star system where each star has a mass 7.5 times that of the Sun and is separated by a distance 7.5 times that between the Earth and the Sun, the period of revolution needs to be calculated. The formula T² = (4π²/(GM))r³ is applied, but the initial calculations yield an incorrect period of 7.54 years. The discussion highlights the importance of understanding that the stars revolve around their center of mass, which affects the orbital radius used in calculations. Clarification is provided that the separation distance is sufficient for determining the orbital period without needing the stars' radii. Accurate application of the formula with the correct parameters is essential for finding the correct period of revolution.
rockchalk1312
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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!
 
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..."and they revolve about their center of mass"...
 
...I wish I knew what that implies...
 
The orbital radius is not the distance between the stars. They orbit about the center of mass.
 
Doesn't that mean you have to know the radius of the stars themselves?
 
rockchalk1312 said:
Doesn't that mean you have to know the radius of the stars themselves?

No. You need their masses and their separation...
 
gneill said:
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).
 
Draw a picture. What point do they mutually orbit?
 
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