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Question 10.9: Sirius A and B A typical example of a binary is Sirius in th...

Sirius A and B

A typical example of a binary is Sirius in the constellation Canis Major, the brightest star in the night sky. The large bright component is called Sirius A and its small dim companion Sirius B. The period of their mutual orbital motion is 50 years and the value of a is 20 AU. (This is about the distance from the Sun to the planet Uranus.) Find the sum of the masses of the two components of Sirius.

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In terms of astronomical units, in which G = 4π², formula (10.26) gives

\tau^{2}=\frac{4 \pi^{2} a^{3}}{G\left(m_{1}+m_{2}\right)}                     (10.26)

M_{A}+M_{B}=\frac{20^{3}}{50^{2}}=3.2 M_{\odot}

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