You were probably thought in school that the planets in our Solar System orbit around our Sun. It turns out that is actually not completely true. Instead, all the objects in our Solar System orbit around the barycenter. That is the center of mass of our Solar System. That center is actually outside of the Sun. The Sun rotates around that barycenter itself.
When we look at other stars, a wobble of a star is a hint that it has things orbiting around it as well.
Determining the orbital period of such wobble allows to determine the mass of the planet orbiting the star. Here's how.
Because most stars are so far away, it would be very difficult to detect a wobble of that star. So a Doppler Technique is used to determine the wobble of the star instead.
A Doppler Effect is produced when an object producing sound or light waves is approaching the observer. We all have experienced the Doppler Effect when listening to a police car zooming by. As the police car gets closer to us, the distance between us and the car shortens, so the sound waves coming from the car get compressed. This results in a rising pitch of the siren. As the car drives away, the waves are stretched, resulting in lowering of the pitch of the sound.
Same thing happens with light waves. As a light object approaches closer to us, its light waves get compressed. But instead of pitch, light waves change intensity of the light. Red is more intense energy-wise than blue. So when the light coming from the object is getting closer to red than blue, that means the object is moving away from us. When it gets to the blue side of the spectrum, the object is approaching us. Recording the amount of such shift, allows to determine how much the distance the object has traveled. Watching the object over time, allows us to determine the radius of its wobble.
We call that wobble the radial velocity, the motion a star makes toward us and than away from us.
Using a formula we can determine the mass of the wobbling object from it's rotation period.
M = (P/12)^1/3 * A/13
where P is the period in years, and A is the amplitude of the radial velocity in m/s.
M will be given as the number of Jupiter masses.
This formula only applies to stars that are like our Sun, and when the planet orbiting the star is perfectly edge on from our point-of-view. For systems that have a slight inclination from our plane of view, we can only determine the minimum mass.
Using Kepler's Law, and knowing the period of rotation of the planet around the star, we can determine the distance between the star and the planet.
P^2 = a^3
a would be given in Astronomical Units, or Earth-Sun distances.
West, Matthew. "Radial Velocity Method." Alien Worlds: The Science of Exoplanet Discovery and Characterization. Boston University. 19 Nov. 2014. Lecture.
Image Credit: European Southern Observatory