Based on Kepler’s Laws, we know that not only do the planets in our Solar System orbit the Sun, but also that our Sun itself wobbles as a reaction to the orbiting planets. Strictly, we say that all the components of our Solar System orbit a common centre-of-mass, however since the vast majority of our Solar System's mass is in our Sun, the effect is quite small.
We can then apply this argument to extrasolar systems where the host star will wobble as a function of the mass, number and proximity of its planets. On occasion, the alignment of these systems will be such that the star is seen (by means of spectroscopy) to exhibit repeated blue-ward and red-ward Doppler shifts.
These shifts allow us to measure the relative velocity of the star towards (blue) and away (red) from us (see Figure 1). From these measurements, an orbital period can be measured for the exoplanet and further parameters, such as its mass and composition can be calculated.
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