Finding period of revolution of stars?

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SUMMARY

The discussion centers on calculating the period of revolution for a binary star system where each star has a mass of 7.5 times that of the Sun and is separated by a distance of 7.5 astronomical units (AU). The formula used is T² = (4π²/(GM))r³, where G is the gravitational constant (6.67E-11 N(m/kg)²) and M is the total mass of the system. The initial calculation yielded a period of 7.54 years, which was incorrect due to a misunderstanding of the orbital radius, which should be based on the center of mass rather than the distance between the stars.

PREREQUISITES
  • Understanding of gravitational physics, specifically Kepler's laws of planetary motion.
  • Familiarity with the gravitational constant (G) and its application in orbital mechanics.
  • Knowledge of binary star systems and the concept of center of mass.
  • Ability to perform unit conversions, particularly between seconds and years.
NEXT STEPS
  • Review Kepler's Third Law of Planetary Motion and its application to binary star systems.
  • Study the concept of center of mass in multi-body systems.
  • Learn about gravitational interactions and how they affect orbital periods.
  • Practice solving problems involving T² = (4π²/(GM))r³ with varying mass and distance values.
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in understanding the dynamics of binary star systems and orbital mechanics.

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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