As an extrasolar planet and its host star orbit their common centre of mass, both will move. Imagine a sumo wrestler and a hamster balanced on a see-saw: the heavy star, like the sumo wrestler, must sit far closer to the pivot of the see-saw than the hamster, in order for the see-saw to balance. Then, if the see-saw is set spinning around the pivot, the sumo wrestler will move only slightly, following a tiny circle around the location of the pivot, while the hamster's own circle will be far wider, and it will move far fast. The situation with planets moving around distant stars (or our planets moving around the Sun) is just the same! The star with an exoplanet moves only slightly in response to the gravity of the much less massive planet, while the planet speeds around a large orbit, in a manner similar to the hamster on the see-saw.
Another way to visualise
this is to picture an athlete throwing the hammer. As the thrower spins
around, building speed to launch the hammer, the two "orbit" around
their mutual centre of gravity, as can be seen in the above clip
(courtesy of YouTube). See how the hammer thrower wobbles, as the
hammer itself follows a wide circle around him? When planets move
around their parent star, they move in wide circles (or ellipses),
while the star wobbles around the centre of mass. For a star like our
Sun, with 8 planets and other debris moving around it, the wobble is
actually fairly complicated, as the star responds to each object moving
around it, but the most massive planets, and those that are the
closest, have the largest effect on the star, and so can quite easily
be detected.
Astronomers detect this
subtle motion of stars as a "Doppler wobble". When the light reaching
us from a given star is split into its component colours (just as
sunlight passing through raindrops is split into a rainbow), the
rainbow spread of the star's light can be seen to be crossed by a
number of dark lines. These lines are characteristic of the various atoms
which make up the star - each type of atom (such as hydrogen) absorbs a
very specific colour of light, leaving that part of the rainbow blank.
The location of these lines is very precisely known, and they can be
measured fairly easily, particularly for nearby stars.
When a planet moves around a star, causing it to wobble, the colour
(or wavelength) of these characteristic spectral lines shifts very
slightly towards the red as the star moves away from us and
very slightly towards the blue as the star approaches us. This
phenomenon is the optical version of the Doppler effect – more commonly
experienced as the change in pitch heard from the siren of passing
police cars. Using current technology, the star’s velocity can be
measured with an accuracy of one metre per second, which is below
walking speed! The bigger the wobble, the further to the red and blue
the lines will move, allowing us to determine the speed with which the
star wobbles. Also, the lines wobble backwards and forwards once for
each complete wobble of the star - each complete orbit of the planet.
So we can easily work out how long the planet takes to move around the
star, just by watching the lines, as can be seen in the video below
(from YouTube). The video shows the case for two stars moving around
one another (a binary star). The situation is the same for a planet
orbiting a star, except that we would only observe one set of lines
moving, not too, since there is only one star involved!
The first planet orbiting
a star other than the Sun was found in 1995, when scientists observed
the wobble of the star as the planet moved around it. Since then, this
technique has enabled the discovery
of most of the nearly 300 extra-solar planets known today.
Doppler-wobble measurements tell us the length of the planet's year and
the shape of its orbit, but because the orientation of the orbit is
usually unknown, these only provide a lower limit to the mass of the
planet. If the star and planet are orbiting in our line of sight, then
the star will wobble backwards and forwards towards us, and we will be
able to measure the whole wobble. But, the further from our line of
sight the orbit is tilted, the smaller the fraction of the movement
that will be in our line of sight, and the smaller the observed wobble
will be. If the planet orbits the star at right angles to our line of
sight (the orbit being face on), then the star will not be seen to
wobble at all, and the planet could not be detected!
The above video tells the story of the discovery of the planet 51 Pegasi b,
in 1995. Video taken from the Open University/BBC series,
The Cosmos: a Beginner's Guide,
with permission.