How Do We Calculate the Mass of Binary Stars Like Centauri A and B?

AI Thread Summary
To calculate the mass of binary stars Centauri A and B, the equation (m1 + m2) P^2 = (d1 + d2)^3 is applied, assuming both stars have equal mass. The separation of the stars is 3.45x10^12 meters and the orbital period is 2.52x10^9 seconds. An initial calculation was attempted, but it was noted that the conversion of the period squared was incorrectly handled. The correct approach requires careful attention to unit conversions and proper application of the formula. Accurate calculations are essential for determining the mass of binary star systems.
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Homework Statement



Centauri A and Centauri B are binary stars with a separation of 3.45x10^12m
and a period of 2.52x10^9s

Assuming the two stars are equally massive (which is approximately the case), determine their mass.

Homework Equations



( m1 + m2 ) P^2 = ( d1 + d2 )^3 = R^3
I used this and it doesn't work :x

The Attempt at a Solution



M1=M2
D1=D2

M(2.52x10^18)=3.45x10^36

M=3.45x10^36/2.52x10^18

= wrong :X
 
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<br /> {(2.52 \times 10^9)}^2 \neq 2.52 \times 10^{18}<br />
 
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