It was after midnight on Sept. 19 and Paul Chodas, the manager of the Center for Near Earth Object Studies at NASA’s Jet Propulsion Laboratory in Pasadena, Calif., was working late, studying an object called 2020 SO that other astronomers had spotted in the night skies just the day before. Something about its orbit was peculiar.

The computer program he was working with showed that 2020 SO followed a nearly circular path just slightly outside our planet’s orbit. And the plane of the object’s orbit was just barely tilted relative to Earth’s.

“I was suspicious immediately,” he said.

Out of curiosity, Dr. Chodas ran his simulation in reverse. With time dialing backward, he watched 2020 SO pass very near Earth in September 1966. “Close enough that it could have originated from the Earth,” he said.

At 1:12 a.m., Dr. Chodas acted on his hunch, and sent an email to fellow astronomers with a subject line of “2020 SO = Surveyor 2 Centaur r/b?” In the months that followed, amateur skywatchers and professional astronomers alike have been tracking this specter with their telescopes, following what many believe is a rocket booster that flew toward the moon more than 50 years ago during a failed NASA mission.

On Tuesday, the object, now temporarily orbiting Earth, will make its closest pass. And with more observations, scientists hope to find conclusive evidence that the dot on their monitors really is a ghost of the Cold War moon race.

Hopes were high when Surveyor 2 lifted off from Cape Canaveral, Fla. (then known as Cape Kennedy), on Sept. 20, 1966. NASA designed the roughly one-ton lunar lander to collect images of the moon in preparation for the Apollo missions. It was following close on the heels of its successful predecessor, Surveyor 1, launched just a few months earlier, which had landed on the moon and returned over 11,000 images.

Surveyor 1 performed flawlessly, said Mike Dinn, then the deputy station director of Australia’s Tidbinbilla Tracking Station, where giant radio antennas communicated with the spacecraft during its journey. “We fully expected Surveyor 2 to be a complete success.”

But it wasn’t — the spacecraft crashed into the moon. Its death knell came roughly 16 hours after launch, when one of the three small engines attached to the spacecraft’s legs failed to fire. The imbalanced thrust sent Surveyor 2 into a spin, and after 38 unsuccessful attempts to revive the engine it became clear that the mission could not be salvaged. Mr. Dinn and his colleagues at Tidbinbilla were the last people to communicate with the spacecraft.

(Five more Surveyor missions followed, and four were successful before NASA switched its focus to human exploration of the moon.)

The orbit of 2020 SO is also ever so slightly anomalous, deviating from what is expected based on gravity alone, said Davide Farnocchia, an asteroid dynamicist at NASA’s Jet Propulsion Laboratory. That may shed light on its identity.

The cause of that irregularity is most likely the pressure exerted by solar radiation. Particles of sunlight — photons — have energy, and they exert a force when they collide with something, Dr. Farnocchia said. “They cause a gentle push away from the sun.”

The fact that 2020 SO is being shoved around by sunlight suggests that it’s something relatively large and low mass, like an empty rocket booster, as opposed to something small and massive, like a rocky asteroid.

Dr. Farnocchia compared the phenomenon with the wind.

“If you have an empty soda can, you’re going to move it much farther,” he said. “If you have a solid rock, it’s much harder to push it away.”

In the last few weeks, scientists have been gearing up for a much closer look at 2020 SO. It was captured by Earth’s gravity in early November, and it will make its closest approach to our planet on Tuesday. At that point, 2020 SO will be about 27,400 miles away, or roughly one-tenth of the distance to the moon.

The visit is temporary, however — 2020 SO will escape Earth’s gravity by March 2021 and once again start to orbit the sun. But we’ll have another chance to observe this object, whatever it is, up close in the future, Dr. Chodas said.

“In 2036, it’s coming back.”

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