LOS ANGELES — At least one in every four stars like the sun have planets about the size of the Earth circling them in very close orbits, according to the first direct measurement of the incidence of such planets, researchers said Thursday.

That means that our galaxy alone, with its roughly 200 billion sun-like stars, has at least 46 billion Earth-size planets orbiting close to the stars, and perhaps billions more circling farther out in what astronomers call the habitable zone, said astronomer Andrew Howard of the University of California, Berkeley, a co-author of the paper.

Such planets “”are like grains of sand sprinkled on a beach — they are everywhere,”” Howard said.

The discovery of such a large number of small planets so close to stars, reported in the journal Science, is somewhat surprising because it appears to contradict the current theory of planetary formation.

Current models suggest that most planets are born in the outer solar system by the accretion of dust and other materials. That theory says larger planets are drawn into the inner solar system by gravity, but “”small ones are stuck on the outskirts,”” Howard said. Obviously, he added, the theory “”needs something to move them in closer to the host star.””

Astronomer David Charbonneau of Harvard University, who was not involved in the new research, noted that “”contradictions have become the norm”” in the study of extrasolar planets. “”We have come to expect surprises. … The planetary formation models haven’t been successful as predictive models. There is still a lot more work to do.””

Howard worked with Berkeley’s Geoffrey Marcy, who has been one of the leaders in discovering extrasolar planets. They used the 10-meter Keck telescope in Hawaii to study 166 G and K stars within 80 light-years of Earth for five years. G stars, like the sun, are yellow. K stars are slightly smaller, orange-red stars.

Howard, Marcy and their colleagues charted the precise movements of the stars to look for slight wobbles in their paths caused by the gravitational influence of planets circling them. That technique allowed them to detect planets ranging in size from three to 1,000 times Earth’s mass and orbiting as much as one-quarter of an astronomical unit from the host star. An astronomical unit, the distance of the Earth from the sun, is 93 million miles.

The team found that 1.6 percent of the stars had giant planets orbiting close in — those the size of Jupiter or larger. About 6.5 percent had planets of intermediate mass, about 10 to 30 times that of Earth, or similar to the size of Neptune or Uranus. And 11.8 percent had so-called super-Earths, with masses three to 10 times that of Earth.

Extrapolating, they concluded that 23 percent of the stars hosted even smaller planets, which could not be detected.

Of course, all these planets so close to their stars are exceedingly hot and are certainly not habitable. But “”it is not a huge stretch to speculate that nature probably makes a lot of these planets farther out in orbits that might be habitable,”” Howard said.