Calculating Center of Mass in Binary Systems

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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 distances of the first and second masses from a reference point along the line connecting the two masses. It is crucial to note that if the variables are written without vector arrows, they denote scalar values rather than vectors, indicating positions along an imaginary ruler.

PREREQUISITES
  • Understanding of binary systems in physics
  • Familiarity with the concept of center of mass
  • Basic knowledge of mass and distance measurements
  • Ability to interpret scalar and vector notation
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  • Research advanced applications of the center of mass in astrophysics
  • Explore the implications of center of mass calculations in orbital mechanics
  • Learn about vector representation in physics
  • Study the effects of mass distribution on center of mass in complex 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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