How Exoplanets Are Detected
Exoplanets—planets orbiting stars other than the Sun—are too faint and distant to be easily seen directly. Instead, astronomers detect them through indirect methods, nearly all of which rely on Kepler's laws.
Transit Method
When a planet crosses in front of its star as seen from Earth, the star's brightness dips slightly. By measuring the period between dips (the orbital period T), astronomers use Kepler's Third Law to calculate the planet's distance from its star. The Kepler Space Telescope used this method to discover thousands of planets.
Radial Velocity (Doppler) Method
A planet's gravity causes its star to wobble slightly. This wobble shifts the star's light toward red or blue as the star moves toward or away from us. The period of this wobble gives the orbital period, and again, Kepler's Third Law converts this into an orbital distance. Combined with the amplitude of the wobble, astronomers can also estimate the planet's mass (this connects to the principles described in How We Weigh Planets).
Direct Imaging
In rare cases, a planet is bright enough and far enough from its star to be photographed directly. This works best for young, massive planets orbiting far from their star. Once the orbit is observed, Kepler's laws apply just as they do in our solar system.
Gravitational Microlensing
When a star with a planet passes in front of a more distant star, its gravity bends the distant star's light. The planet creates an additional, brief brightening. This method is most sensitive to planets at moderate distances from their stars.
Astrometry
The most precise measurements of a star's position can reveal the tiny wobble caused by an orbiting planet. ESA's Gaia spacecraft is expected to detect thousands of planets this way.
External: NASA: Ways to Find a Planet