This video animation shows planets believed to be detected in or near Gliese 581’s habitable zone. Researchers debunked the existence of two of the “Goldilocks” planets. The three planets shown in the 2014 frames of the animation are the only ones that the study found to be actual planets. (Mike Bostok)

The discovery four years ago of a rocky, not-too-distant planet was a thrilling development in the search for alien life — proof, it seemed, that our planet might not be the only one with just the right mix of life-sustaining conditions.

But two Penn State scientists say they have debunked the possibility of a “Goldilocks” planet once believed to revolve around Gliese 581, a faint dwarf star that is 20 light-years from Earth.

Using a technique they are developing to confirm the existence of small, hard-to-detect planets, the researchers say they have determined that physical changes within the star itself created the illusion of an orbiting Goldilocks planet. They say their method showed that a second planet — much larger but also potentially habitable — also does not exist.

Three other planets do exist in the Gliese 581 planetary system, they said, but none within the star’s “habitable zone” — an area just the right distance from the star to allow the presence of liquid water.

“It’s bittersweet,” said Suvrath Mahadevan, one of the researchers who conducted the study, published Thursday in the journal Science. “We are pleased the technique works, but on the other hand, we have disproved these two planets. It would have been nice if they had existed.”

One of the astronomers who first reported the existence of the Goldilocks planet, Steven S. Vogt of the Lick Observatory at the University of California at Santa Cruz, did not respond to e-mails seeking comment this week. Vogt’s co-researcher, R. Paul Butler of the Carnegie Institution in Washington, declined to comment for this article.

This is not the first time the planet’s existence has been questioned.

Vogt and Butler initially reported their discovery in the Astrophysical Journal in September 2010. They said they had found, for the first time, something long predicted by astronomers: a planet, orbiting a distant star, with the right balance of temperature and mass to host liquid water and an atmosphere, two conditions presumably necessary to support life as we know it.

The planet, Gliese 581G, was about three or four times the mass of Earth, they said. Unlike Earth, which rotates on its axis, Gliese 581G was fixed in relation to its sun, with one side perpetually bathed in light, they said. The most likely area for life, they said, was in a band around the planet where the dark side met the illuminated one.

“The logic now says there are lots of planets like this out there,” Vogt told The Washington Post at the time. In later interviews, he said he believed that the planet probably hosted alien life.

Since then, however, a number of astronomers have cast doubt on the existence of Gliese 581G. A Swiss team reported that it was unable to find evidence of the planet. Vogt and Butler published a follow-up paper defending their research.

“We stand by our data and results and are hard at work obtaining more of our own data on this system,” Vogt told in February 2011.

The background image is a composite photo of our Sun. The left side of the Sun is seen through a filter that allows the camera to see wavelengths of light only in the deep-blue range, while the right side is seen through a filter that blocks all wavelengths except those in the red range. While the blue region is traditionally used to detect a star’s activity, this study used the red region of the light spectrum. (Alan Friedman)

The Penn State researchers said they used a new technique to process existing data and were able to correct for activity on the star’s surface — a sun spot, for example — that could be misinterpreted as evidence of a planet. The new analysis strengthened evidence that the three true planets in the system exist, and the suspect planets disappeared, they said.

Paul Robertson, the lead researcher on the Penn State paper, said his intent was not to criticize Vogt and Butler’s methods but to provide a new tool for scientists who are hunting for planets.

“I think the astronomers did more than due diligence,” he said of Butler, Vogt and other researchers who have looked at this system. “I think their work is more than defensible. It’s perfectly good science, and all those groups continue to do good science. This is the scientific method. You have this happen all the time, where you have a result that looks to all the world correct, but if you introduce a new perspective or a new tool, those results can change.”

Since Butler and Vogt’s initial report, scientists have found 22 other potentially habitable planets outside Earth’s solar system, according to the Planetary Habitability Laboratory at the University of Puerto Rico at Arecibo, which keeps a catalogue of “exoplanets,” or planets outside Earth’s solar system. Dozens of others are awaiting confirmation that they exist and are habitable.

In astronomy circles, given the previous skepticism about the Goldilocks planet, the bigger news in Thursday’s report was the debunking of Gliese 581D, a massive “super-Earth” thought to have a dense, murky atmosphere.

Its purported discovery in 2007 by French scientists was a bombshell because 581D was so different from Earth and yet still seemed able to harbor life.

“It would be extremely disappointing if one of our favorite exoplanets . . . actually does not exist,” said Sara Seager, a professor of planetary science and physics at the Massachusetts Institute of Technology. It is “one of our favorite planets because it motivated people to seriously consider planets more massive than Earth as potentially habitable.”