These new worlds were discovered not by viewing them through a telescope but by their affect on their parent star. This page serves to explain the doppler detection method as clearly and concisely possible.
If we tried to observe these planets directly astronomers would need a telescope with a mirror at least 100 meters across. The reason for this is because these stars' out shine their respective planets like a "firefly next to a nuclear blast" (Marcy&Butler). This apparent difficulty and monumental engineering feat was circumvented through elementary physics. Every object pulls on every other object gravitationally equally and in the opposite direction.
Using this principle, Marcy & Butler determined that as a planet orbited its sun the resulting graviational attraction between the two bodies would result in the star's position to be perturbed or wobble (much like when as a child you would hold your friend's hand and play Ring Around the Rosey and the two of you would stagger around some common point in the school yard). By measuring this perturbation over several years, it was calcualted as to how big and how far away a planet would have to be to generate such a wobble.
The below animated GIF illustrates the planet's orbital affect on the position of its parent star.
(Note: affect is greatly exagerated and the green cross is the center of mass of the system)
This perturbation can be measured by measuring its parent star's spectrum. The light from a star can be broken down into its constituent colors and analyzed. This 'broken down' light or spectrum contains dark and light lines which are specific to the elements, ions and molecules which make up the star. This chemical fingerprint of the star can be accurately measured and using the Doppler Effect provide clues to the characteristics of the perturbing planets.
The Doppler Effect is the physical effect of waves created by a moving source that causes them to be compressed when approaching an observer and spread out when the wave has past the observer (like the change in the pitch of a train's whistle as it comes into and then leaves the station). This Doppler Shift applies to light also. Light that is captured when the star wobbles toward the earth looks more blue and redder when it is moves away from the earth. By measuring the movement of the spectral lines over a period of time the orbital period of the planet can be determined. The resulting size of the displacement then allows the mass of the planet to be calculated.
The below animated GIFs illustrate the Doppler Shift of starlight caused by a perturbing planet.
The grey lines are the hypothetical spectra from a stationary source.
The red lines are due to the star wobbling away from the earth.
The blue lines are due to the star wobbling toward the earth.
Unlike this animation actual star systems are not oriented at 90 and 180 degrees to our own system and do not afford us an optimal viewpoint to observe their mechanics. This observational fact lends itself to what is called the "sin i" problem where i represents the inclination of the observed system to our own and sin is a trigonometric function sine. Currently we do not know what inclination these new solar systems have to our own system so our calculations on the planets masses are only estimates down to a minimum value deliminated by sin i.
This indirect method has shown us that planets do exist outside our solar system and that these other worlds about distant suns are new destinations on the celestial map.
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