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pierce15

- 315

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I wasn't sure whether I should post this is the homework section since it's technically a textbook problem, but I figured I'd get better responses here. The problem is as follows:

Sirius is a visual binary with a period of 49.94 years. Its measured parallax is .37931"## \pm ##.00158", and the angular extent of the semimajor axis of the reduced mass is 7.61". The ratio of the distances of Sirius A and B to the center of mass is ## a_A / a_B = .466 ##. Find the masses of the two stars, assuming that the motion is in the plane of the sky.

First, you can use the ratio to get ## m_A / m_B = 1/.466 = 2.146##. I'm pretty sure I next have to use the 7.61", but I don't know how. After that, I would have all the unknowns in Kepler's third except the masses, so I could solve the system. So how do I get the semimajor axis of the smaller star?