Calculating mass of an orbiting body

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SUMMARY

The discussion focuses on calculating the mass of an orbiting body using the distance and orbital radius derived from the star's motion. The user calculated the distance between the star and its companion as 1.11x1010 m and the radius of the star's orbit as 1.4x108 m. The radius of the companion's orbit was determined to be 1.096x1010 m. The user applied the formula r2 = m1(m1 + m2) x d to find the mass of the companion, resulting in an answer of 5.47x1027 kg, which is deemed incorrect as it exceeds the expected mass of the star.

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Homework Statement


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Homework Equations





The Attempt at a Solution



I found out the distance between the star and companion which I calculated as 1.11x1010m (Ignoring the mass of the companion).Then I calculated the radius of the stars orbit, using r = vt/2∏ since vt = circumference. It turned out as1.4x108m. Then I simply found the radius of the companions orbit which was 1.096x1010m. I then used r2 = m1(m1) + m2 x d and then manipulated it to make m2 the subject. But my answer came out as 5.47x1027kg. Which I assume is wrong since it's supposed to be much less than the mass of the star.
 
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Remember that, assuming that we're observing the star\planet system edge on, the observed magnitude of the oscillation in radial speed is going to be twice that of the actual orbital speed of the star. Why? Because it's the difference between the observed speed when it's directly heading away from and when it's directly heading toward the observer.
 

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