Orbital Period Calculation for Binary Star Systems

AI Thread Summary
The discussion focuses on calculating the orbital period of binary star systems, emphasizing that the distance of each star from the center of mass (c.o.m.) is not simply L/2. Instead, each star is L/2 away from its adjacent stars. The correct formula for orbital period is T^2 = (4π^2/GM)r^3, where M represents the mass of the attracting body, not the mass of each orbiting star. This distinction is crucial for accurate calculations in binary star dynamics. Proper application of these principles is essential for solving related astrophysical problems.
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Homework Statement

Homework Equations


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The Attempt at a Solution


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PAstudent said:

Homework Statement

Homework Equations


(In picture)[/B]

The Attempt at a Solution


(In picture)View attachment 91892 [/B]
The distance of each star from the c.o.m. of the system is not L/2. Each star in the group is located L/2 from the two stars immediately adjacent.
 
You start with the formula ##T^2=\Big( \frac{4 \pi^2}{GM} \Big)r^3## where ##M## is the mass of the attracting body.

But in your solution you use ##M## for the mass of each orbiting sun.
 
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