Calculating mass of an orbiting body

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The discussion focuses on calculating the mass of an orbiting body based on the distance between a star and its companion, which was determined to be 1.11x10^10 m. The radius of the star's orbit was calculated as 1.4x10^8 m, while the companion's orbit radius was found to be 1.096x10^10 m. The user applied the formula r^2 = m1(m1) + m2 x d to isolate m2, resulting in a mass of 5.47x10^27 kg, which is suspected to be incorrect as it should be significantly less than the star's mass. The discussion also highlights that the observed oscillation in radial speed is twice the actual orbital speed due to the geometry of the observation. This insight emphasizes the importance of understanding orbital mechanics in mass calculations.
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Homework Statement


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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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