Calculating Center of Mass in Binary Systems

AI Thread Summary
The correct formula for calculating the center of mass in a binary system is R = (m1*r1 + m2*r2) / (m1 + m2). In this equation, r1 and r2 represent the positions of the first and second masses, respectively, measured along the line connecting the two masses. If written without vector arrows, R, r1, and r2 indicate scalar values on an imaginary ruler rather than vectors. The discussion clarifies the distinction between using scalar measurements and vector representations for these positions. Understanding this formula is essential for accurately determining the center of mass in binary systems.
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What is the correct formula for center of mass of a binary system? I had seen that it is

R=\frac{m_{1}r_{1}+m_{2}r_{2}}{m_{1}+m_{2}}
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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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.
 
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.
 
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