Calculating Center of Mass in Binary Systems

In summary, the correct formula for the center of mass of a binary system is R=(m1r1+m2r2)/(m1+m2). The variables r1 and r2 represent the numbers read on an imaginary ruler for the center of mass and the masses respectively. Alternatively, they can also represent the location vectors of these points.
  • #1
Stratosphere
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0
What is the correct formula for center of mass of a binary system? I had seen that it is

[tex]R=\frac{m_{1}r_{1}+m_{2}r_{2}}{m_{1}+m_{2}}[/tex]
If that is the right equations what exactly does r one and two stand for? I had also seen a much more complicated formula.





Side note: This is not homework
 
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  • #2
If you write it like this without vector arrows above, than this means the capital R and r1 and r2 are the numbers that you would read on an imaginary ruler (for the center of mass, and the first and second mass respectively), that lies on the line connecting the two masses.
Otherwise these are the location vectors of the center of mass and the masses.
 
  • #3
0xDEADBEEF said:
If you write it like this without vector arrows above, than this means the capital R and r1 and r2 are the numbers that you would read on an imaginary ruler (for the center of mass, and the first and second mass respectively), that lies on the line connecting the two masses.
Otherwise these are the location vectors of the center of mass and the masses.

Thanks.
 

What is the center of mass in a binary system?

The center of mass in a binary system is the point at which the two objects in the system have equal mass and are balanced. It is the point around which the two objects orbit.

How is the center of mass calculated in a binary system?

The center of mass in a binary system can be calculated by using the masses and distances of the two objects in the system. The formula for calculating the center of mass is:
Center of Mass = (m1 x r1 + m2 x r2) / (m1 + m2)
Where m1 and m2 are the masses of the objects and r1 and r2 are the distances of the objects from the center of mass.

Is the center of mass always located between the two objects in a binary system?

No, the center of mass can be located anywhere between the two objects, depending on their masses and distances from each other. If one object is significantly larger than the other, the center of mass may be closer to the larger object.

What is the significance of calculating the center of mass in a binary system?

Calculating the center of mass in a binary system is important because it helps us understand the motion and behavior of the objects in the system. It also allows us to predict the orbits of the objects and determine their gravitational interactions.

Can the center of mass change in a binary system?

Yes, the center of mass can change in a binary system if the masses or distances of the objects change. For example, if one object moves closer to the other, the center of mass will shift towards that object.

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