Finding period of revolution of stars?

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Homework Help Overview

The discussion revolves around calculating the period of revolution of two stars in a binary-star system, each with a mass 7.5 times that of the Sun, and separated by a distance that is 7.5 times the distance between the Earth and the Sun. The original poster attempts to apply Kepler's third law but encounters an incorrect result.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the implications of the stars revolving around their center of mass and question the correct interpretation of the orbital radius in relation to the separation distance. There is also a focus on whether additional information, such as the radius of the stars, is necessary for the calculations.

Discussion Status

The discussion is ongoing, with participants providing insights and questioning the assumptions made by the original poster. Some guidance has been offered regarding the need to consider the center of mass in the calculations, but no consensus has been reached on the correct approach or resolution of the problem.

Contextual Notes

There is a mention of the need for clarity on the definition of orbital radius and the relationship between the stars' masses and their separation. The original poster's calculations and assumptions are being scrutinized, indicating potential gaps in understanding the problem setup.

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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