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Discovery of the Moon's Mysterious Mascons
It was urgent that NASA identify what was throwing lunar spacecraft off course before sending the first astronauts to the Moon.
It was urgent that NASA identify what was throwing lunar spacecraft off course before sending the first astronauts to the Moon. cr. NASA

In 1968, moviegoers marveled at a new film called 2001: A Space Odyssey, in which unusual magnetism at one of the Moon's largest craters leads scientists to uncover a mysterious object that had been buried beneath the crater floor by an extraterrestrial civilization. Audiences might have been even more impressed had they known that as they sat there watching the movie, NASA scientists were scrambling to solve a real-life mystery involving unusual forces on the Moon -- in fact, as it turned out, at some of the Moon's largest craters.

As the story is recalled by Paul Muller and William Sjogren, who ultimately worked out the solution, the massive effort to solve this problem culminated in a bet over a cheeseburger.

It was just over a year before the first astronauts were scheduled to land on the Moon, and NASA's top priority was to determine what was diverting its unmanned spacecraft as they flew low over the lunar surface. Apollo astronauts were training to land within 200 meters of the targeted location, but lunar spacecraft were going off course by as much as 2 kilometers. So instead of a landing zone of an eighth of a square kilometer, they could only be confident of landing within an area of more than 12 square kilometers. "There was no way the astronauts were going to be able to learn 100 times as much surface area of the Moon," Muller said, "so they would know where they are when they rotate the spacecraft and look out the window to land."

Muller had recently started work at JPL, and was admittedly a novice when it came to space flight. "It was quite an education for me to understand how spacecraft actually behave in space," he said, "and how tiny, tiny little errors like solar wind and outgassing from control jets on the spacecraft make major impacts on the trajectory." According to Sjogren, NASA scientists and the professors with whom they consulted proposed many such explanations during the year or so since the navigation problem first appeared. Each possibility required time-consuming studies before it could be ruled out.

By the time Muller arrived on the scene, Sjogren said, the experts had winnowed the possible culprits down to gravity. But the computers of that punch-card era weren't up to the task of isolating what specifically was pulling the spacecraft off course. And without knowing that, there was no way to correct for it.

Muller had a hunch the answer lay in the differences between the masses of features on the lunar surface. "I had recently read Baldwin's The Measure of the Moon, which was the big book about the topography and geology of the Moon," he said, "and it was obvious the Moon was a very rough place.

"Imagine a basin the size of California and Nevada, 3 km deep," he said, "or a mesa 3 km high the size of California plus Nevada. That would be the largest feature on planet Earth. And yet the Moon is tiny compared to the Earth." He reasoned that the large differences in mass, especially on such a small world, would produce large enough differences in gravity to throw spacecraft seriously off course.

The Cheeseburger Bet

But according to Muller, his colleagues were skeptical. He recalled that over lunch one day, the JPL team leader argued that he had calculated that for the gravity of a lunar feature to produce the observed effect on a spacecraft, it would have as much mass as a cube of lead seven kilometers on each side! And as Muller remembers it, his own boss agreed that this was very implausible.

NASA Computers in 1968
Computers were big in 1968, but their power was too little to resolve the Moon's gravity field enough to identify the cause of the navigation problem. cr. NASA

"I'll bet you a cheeseburger for lunch tomorrow," Muller challenged his boss, "that I will have a memorandum on your desk by one o'clock this afternoon that proves the Moon is much, much, rougher than that."

"All you need for success," Muller said in recounting that day, "is ignorance and confidence." At the time, he didn't know about isostatic compensation, a process by which a body like the Moon evens out the amount of mass all around its sphere in much the same way that a bucket of water adjusts to a block of wood dropped into it. (The wood sinks and the water rises until equilibrium is reached and the distribution of mass is the same all across the bucket.) So Muller didn't worry about whether the Moon would have compensated for the missing mass of craters or the extra burden of mountains.

He rushed to the library, checked out Measure of the Moon, calculated the mass differences for four large lunar features compared to the lunar plains, wrote up his memo and left it on his colleagues' desks.

He got a call later that afternoon from the team leader, who said "I made a mistake at lunch today."

"Oh," Muller replied, "did you read my memo?"

"No," his colleague said, "but the cube of lead is roughly 70 km on a side, not 7."

"You better dig down through your stack and find my paper," Muller told him, "because it says that the cube of lead would have to be about 70 km on a side."

Sjogren, with whom Muller shared an office, overheard the conversation. The following morning, he brought in the results of a computer analysis he had run during the night on one of NASA's Lunar Orbiter missions. "Look," he told Muller, "the spacecraft moves exactly the same way when it comes back around again" -- that is, when it begins a second orbit. He produced an analysis of another Lunar Orbiter that showed a similar result.

"I went back to my other work," Muller recalled, "and after half an hour I threw my pencil up in the air -- it actually stuck in the acoustic tile above my head -- and I whirled around in my chair and said, 'Bill, it's because it's flying over the same territory and it is the gravity that's wobbling the spacecraft." Sjogren said, "I'll be back in a couple of hours," and disappeared.

According to Muller, the lunar navigation problem had top priority on all computers at all times. "Any member of the team could walk into the main computing center and demand exclusive use of one of the IBMs," he said. "And that's what Bill did."

The Dancing Gravity Tape

He ran 80 consecutive orbits, plotted them out on a paper tape, and came running back into the office shouting "Put this on the spool!" The two men wound the paper tape from one spool to the other and watched the graph lines which represented the motion of the spacecraft as it flew over the lunar surface. "They danced like dancing waters in a fountain display," Muller said. "Bill had just made the first detailed gravimetric map of the front side of the Moon."

The dancing tape, which showed that spacecraft were diverted in just the same way each time they flew over the same lunar features, confirmed that gravity differences between those features were responsible for pulling the spacecraft off course. And when Muller matched the gravity spikes to the specific lunar features causing them, the scientists reached an astonishing conclusion.

The extra gravity was coming not from giant mountains as one might expect, but from giant craters! And it was true of all five of the giant, circular, ringed "maria" on the visible side of the Moon.

These so-called "seas" are actually enormous impact craters, stretching hundreds of kilometers across. Their dark color is commonly thought to come from lava that has partially refilled them, but they are still several kilometers deep. And these vast, empty depressions in the lunar surface were producing as much gravity as enormous mesas would be expected to provide. The only possible explanation was that something tremendously massive lay beneath their floors, defying the principles of isostatic compensation (and suggesting that the Moon froze before it could adjust itself to these masses).

The 5 large, red blobs in the image at right are gravitational hotspots called "mascons." Note how their locations correspond to the large, dark depressions known as "maria" in the image at left. (left image from Galileo mission, right image based on Lunar Prospector data)
The 5 large, red blobs in the image at right are gravitational hotspots called "mascons." Note how their locations correspond to the large, dark depressions known as "maria" in the image at left. (left image from Galileo mission, right image based on Lunar Prospector data)

The discovery ended NASA's quest to explain the strange behavior of its spacecraft. NASA awarded the two men the second-largest cash prize it had bestowed up to that time. The American Philosophical Society presented them with its gold medals for outstanding discoveries "relating to navigation, astronomy, or natural philosophy." And Muller collected his cheeseburger.

Muller and Sjogren reported their findings in the journal Science, coining "mascons" as a shorthand term for the giant mass concentrations they had discovered.

But the mystery is not yet over. While it's clear that the mascons exist and exert large gravitational pulls, their nature is not fully understood. "There is to this day no satisfactory explanation for the lunar mascons," Muller said.

NASA's GRAIL spacecraft, scheduled for launch in late 2011 and for operations in 2012, will map the Moon's gravity with the highest precision yet, enabling scientists to deduce underground structure all the way to the core. The mission may enable scientists finally to complete the picture of the mysterious mascons.

Unlike the crater with the buried monolith in the classic science fiction movie, chances are the mascon story doesn't involve extraterrestrial intelligence. But it certainly provides an impressive testament to intelligence of the human kind.


Through a series of errors, a number of books and articles in recent years took credit for the discovery of mascons away from Muller and Sjogren, saying that these features were discovered during the Soviet Luna 10 mission. In fact, while Luna 10's wobbling was suspected to be the result of gravitational phenomena, the existence of mascons remained unknown until their discovery by Muller and Sjogren. The Solar System Exploration website is pleased to have played a key role in correcting this mistake.

- Bob Silberg

Last Updated: 16 July 2013

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Last Updated: 16 Jul 2013