Investigating planets around other stars

How can we find planets around other stars? Astronomers have tried five or six different methods....

• An overview of methods for finding planets around other stars

The most successful method to date involves very careful measurements of a star's spectrum.

• Breaking light into a spectrum

It turns out that if an object is moving towards you, or away from you, then the wavelength of light (or sound) emitted by that object will change slightly. We call this effect the Doppler shift .

• Example of the Doppler shift in the spectrum of a star

When we look very, very, very closely at certain stars over a period of time, we see something wierd happen (click on the image below to see):

I've exaggerated the actual shifts by a factor of about 1,000 (!) for clarity.

  
  Q:  Why are the wavelengths shifting back and forth?

The wavelengths shift because the star itself is moving towards us, then away, then towards, then away -- in other words, the star is moving in a little circle. It is moving around the center of mass between it and one of its planets.

If you could figure out the size of the star's orbit, R_s, and if you knew the size of the planet's orbit R_p -- which is always much, much, larger -- then you could figure out the ratio of orbital radii, and, thanks to center of mass, the ratio of masses.

Look at the measurements of a star called "tau Bootes". This star moves in a circle with a period of P = 3.312 days and a speed of about v = 466 m/s.

1. What is the circumference of the star's orbit? In other words, how far does the star travel as it makes one complete circle?
2. What is the radius R_s of the star's orbit around the center of mass?
3. The planet is circling the star with a much larger orbital radius R_p, but with exactly the same period P. Use Kepler's Third Law to figure out the radius of the planet's orbit. You can assume that
   • (R_p + R_s) is roughly (R_p)
   • the mass of the star is about the same as the mass of the Sun
4. How does the planet's orbit compare in size of the orbit of the Earth around the Sun?
5. Use the ratio of orbital radii to figure out the ratio of masses. Then estimate the mass of the planet.
6. How does the planet's mass compare to the mass of the Earth?
7. Would you like to live on this planet?

For more information

• Different methods for finding extrasolar planets from an introductory astronomy course.
• A few thoughts on life on the known extra-solar planets, ditto
• The extrasolar planets encyclopedia has up-to-date information. The US mirror site may be faster.

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.