Radial Velocity (Super-Fast) Lab(!)

In this post I'll be doing the Radial Velocity (Super-Fast) Lab handed out in class earlier this week. We're supposed to determine the period, mass, and semi-major axis of an exoplanet, given its host star's radial velocity curve. Here are the graphs (assuming a star's mass that is 1.5 times that of the sun):

The period is easy to determine by inspection. For the first graph, the period seems to be about 1 year. We can use Kepler's Third Law to determine the semi-major axis:

So:

To determine the mass of the planet, we can use the following equation:

where K, the amplitude of radial velocity, is expressed in fractional units using a constant (29.8 m/s), the mass of the sun, a period of a year, and the mass of Jupiter. For the first graph, we have an amplitude of about 100m/s. So, our mass is:

, where M_J is the mass of Jupiter.

What about the second graph? We can see that the radial velocity amplitude K is about 50m/s, and the period is roughly 3.3 years. The semi-major axis, therefore, is:

The mass of the planet is: