At the time, nobody knew if any other stars besides the sun harbored planets. NASA turned down Mr. Borucki and Dr. Koch five times before the experiment was finally approved in 2001.

Kepler was launched into an orbit around the sun on March 6, 2009, with a simple mission: to stare at some 160,000 stars in a patch of sky in the constellation Cygnus. If any of those stars dimmed periodically, the size of the dip in light could tell you how big the planet passing in front of it was. The length of time between blinks would tell you how many days long its year was.

In the case of the Earth as seen from space, the amount of dimmed light would be about 0.008 percent of the sun’s light — about as much as a few fleas crossing a car headlight — once a year. Kepler can detect the equivalent of one flea in the headlight. Since the rules of engagement required three transits to verify a planet, that meant it would take that many years on average to discover an exact analog of our own home: Earth 2.0, it was sometimes called.

At the time Kepler was launched, more than 300 exoplanets, planets outside our solar system, had been found, mostly by examining stars one by one to see if they showed signs of being perturbed — “wobbled” — by the gravitational pull of a planet or planets.

Those on the Kepler team did not know what they were going to find. Dr. Batalha recalled that they had argued about how to construct their catalog of interesting objects — whether it would only be able to go to 1,000 or 10,000. In the end, they almost ran out of room on the list, Dr. Batalha recalled, which wound up running to 9,000.

In its first few months of observations, Kepler almost immediately doubled the number of known or suspected exoplanets. The tally kept climbing, to 1,200 by February 2011 and to more than 4,700 a year ago.