Astrometry And Radial Velocity
One of the more popular methods is using astrometry and radial velocity measurements. Astrometry is used to determine the proper motion of the star. If the star has a planet in orbit the gravitational force that the planet exerts on the star will cause it to move in small ovals that reflect the planet's orbital motion. Using other stars as a reference the star will be seen to move with a wobble as it travels the sky. A better way to see this is through its radial velocity. When viewing the spectrum of the star, the light will seem to shift towards the blue part of the spectrum when the star wobbles away from us and towards the red when it wobbles towards us, all relative to what the spectrum would be if there was no wobble and hence no planets. The problem with this is that the shift is a very small effect such that the change in wavelength is in the order of one part in ten million. This means there needs to be an error in the speed of less that 36 km/h. This is done by the absorption cell which consists of iodine vapour in a glass bottle near the focus of the telescope. The iodine absorbs certain wavelengths; thus the star is missing parts of its spectrum at these specific wavelengths and provides a reference for the shifting of the star's spectrum. The unchanging nature of these reference wavelengths is what enables the shifts to be measured with the accuracy needed. Doppler shifts of greater than 3m/s can measured from telescopes on the ground.
This is the method that the Space Interferometer Mission will employ to aid the search for extrasolar planets. SIM is an ambitious project consisting of a several telescopes linked to each other but unlike HST is not in Earth orbit, but in its own orbit around the sun. By combining the data from the telescopes, a much higher resolution can be achieved than by the use of a single scope.
The data from the shifts provides crucial insights to the nature of the planet. The size of the wobble is proportional to the ratio of the mass of the planet to the mass of the star. But as there is the uncertainty of whether or not the orbital plane is edge on to Earth, this is the minimum mass of the planet, as the shift would be diminished if the plane were not edge on. The frequency of the orbit can also be found as it relates to the periodic change from redshift to blueshift. The wobble itself can provide information on the orbit of the planet, as it is the orbit in miniature. A graph of shift over time provides an insight into the shape of the motion; if it is sinusoidal for example, then the orbit is circular.