Calculating mass of an orbiting body

[MegaDeth]

Homework Statement

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.

 

[gneill]

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.