You cannot see most planets around other stars. A planet shines about a billion times fainter than the star it orbits, and the glare drowns it out. So astronomers do something sneakier: they stop looking for the planet and watch the star instead.
If a planet's orbit is lined up just right, then once per orbit it crosses the face of its star, as seen from Earth. For a few hours the star is a little dimmer, because a dark disc is covering part of it. Nothing has to be resolved. The telescope only needs to measure total brightness, again and again, and notice the dip.
How much does the star dim? The planet blocks a fraction of the star's disc equal to the ratio of their areas, which is the ratio of their radii squared. The Sun is about 109 times wider than Earth. So Earth crossing the Sun would block (1/109)², about 0.008% of the light, roughly 84 parts per million. Jupiter, about 11 times wider than Earth, blocks about 1%.
That is the whole trick, and also the whole difficulty. A 1% dip is easy for a good telescope. A 0.008% dip is a whisper, which is why finding Earth-sized worlds took telescopes in space, above the flicker of our atmosphere.
Below is a star seen from Earth, with a planet circling it. Drag up and down on the star to move the planet's path across it, or use the sliders to change the planet's size and how far from the star it orbits. The lower graph is the star's brightness during the crossing.
Drag up or down on the star to move the path.
Push the path to the edge of the star and the dip gets shorter and shallower. Push it past the edge and the dip vanishes, even though the planet is still there. Now slide the planet outwards and press Random tilt a few times. Far from its star, a planet almost never lines up.
Depth gives the planet's size, because depth is radius squared. The gap between dips gives the length of its year. Kepler's third law then turns the year into a distance from the star. The length of a single crossing says how fast the planet moves, which tells you something about its orbit too. Earth, crossing the middle of the Sun, would take about 13 hours, once a year.
A random orbit is tilted at a random angle, and only the ones that pass in front of the star count. The chance is roughly the star's radius divided by the planet's orbit distance. For an Earth-like orbit that is about 0.5%, one chance in 200. For a hot Jupiter hugging its star at 0.05 AU it is about one in ten. Every transiting planet we find therefore stands for many more, circling stars we saw edge-on to the wrong side.
That is why surveys stare at huge numbers of stars. NASA's Kepler telescope, launched in 2009, watched about 150,000 stars in one patch of sky, hoping that a small fraction would line up.
A dark starspot, or a faint companion star, can also dim a star. A planet gives itself away by repetition: the same depth, the same shape, the same gap, over and over. The first transit of a known planet was caught in 1999, when HD 209458 b was seen dimming its star by about 1.7% every 3.5 days. It had been found a few days earlier from the tiny wobble it causes in its star. Today NASA counts more than 6,000 confirmed planets beyond our solar system, and a large share of them were found by catching the shadow.