So, suppose that we point our telescopes towards some distant star. It is so bright, and any possible planets around it are so faint, that we can only detect the light of the star itself.

Rats.

But suppose that we split this starlight into a spectrum and record it -- not just once, but over and over again, night after night, week after week. Maybe, just maybe, we might see the spectrum of that starlight change ....

Q: Why should the starlight shift back and forth, back and forth, in a periodic fashion? A: Because the star is moving towards us and away from us, towards us and away from us, as it circles around the center of mass between it and a planet!

A little animation illustrating radial velocity curves

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

Look at the measurements of a star called "tau Bootes".
This star is roughly the same mass as the Sun, so let's
use **M _{s} = 1.99 x 10^{30} kg**.
Measurements of its spectrum show that
the star moves in a circle with a period of

- What is the circumference of the star's orbit? In other words, how far does the star travel as it makes one complete circle?
- What is the radius
**R**of the star's orbit around the center of mass?_{s} - What is the centipetal acceleration of the star?
- Substitute for the mass of the planet in the above equation for acceleration,
leaving an equation which has acceleration on the left hand side
and only one unknown,
**R**, on the right-hand side._{p}Because stars are much, much more massive than planets, we can assume that the distance of the planet from the center of mass is much, much larger than the distance of the star from the center of mass.

In other words,

- Write an equation which shows the acceleration of the star
on the left-hand side, and an approximated, simplified
expression with only one unknown on the right-hand side.
Excellent!

Now you can figure out the radius of its planet's orbit.

- What is the radius of the planet's orbit around the star?
- How does the planet's orbit compare in size of the orbit of the Earth around the Sun?
- What is the mass of the planet?
- How does the planet's mass compare to the mass of the Earth?
- Would you like to live on this planet?

Now,
the planet is circling the star with a much larger
orbital radius **R _{p}**, but
with exactly the same period

The acceleration is caused by the planet's gravitational force pulling on the star, so we could write

That leaves two unknown quantities, **R _{p}**
and

- 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.

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