Researchers are discovering strange facts about our very own satellite

The moon is slightly squashed, as if someone had held it at the poles between thumb and forefinger and squeezed, flattening it around its equatorial midsection. That is not surprising. The moon spins, and the outward centrifugal force should indeed have generated a bulge as the molten magma of a young moon cooled to solid rock eons ago.

But as far back as 1799, the mathematician Pierre-Simon Laplace noticed a back-and-forth wobbling because of the moon’s deformed shape. Although the flattening was slight — the moon’s width, 2,159 miles, is about 2.5 miles greater than its pole-to-pole height — it was still greater than would be expected for its current rotation period of 27 days 7 hours 43 minutes and 11.5 seconds.

“The puzzle had been the moon was too flat,” said Maria T. Zuber, a professor of geophysics and planetary sciences at the Massachusetts Institute of Technology.

Space probes of the 1960’s and 1970’s found a second deformity of the moon: it is slightly elongated along the moon-earth axis. That is, if the moon were sliced in half along its equator, the cross-section would not be a circle, but more like a football, with one of the narrow ends pointing toward earth.

But no one could come up with a completely convincing explanation for the moon’s current shape. That is not its only mystery. Another is why its near side, which always faces earth, is so different in material and appearance from the far side. The moon’s origin still holds some uncertainties, although many scientists believe that it formed out of the debris when a Mars-size object struck earth 4.5 billion years ago.

“Quite a lot of the darned thing is still quite mysterious,” said Kimmo Innanen, a professor of astronomy at York University in Toronto.

In the current issue of Science, Zuber, with Jack Wisdom and Ian Garrick-Bethell, say they have a possible answer to the problem of the moon’s shape. Actually, they say they have several.

What Laplace did not know is that the moon is moving away from earth and slowing down. Years of bouncing laser beams off mirrors left on the lunar surface by the Apollo astronauts show that each year the moon is another 1.5 inches farther from earth.

The moon now orbits in what astronomers call a 1:1 resonance with earth, its orbital period equal to its rotation time so that the same side of the moon always faces earth.

Thus, in the past, the moon was much closer and took less time to orbit. With the 1:1 resonance, the moon spun faster as well, possibly explaining the bulge. But those calculations did not come with the correct answer for observed distortion along the moon-earth axis. “They ought to be self-consistent,” Zuber said.

One suggestion has been that the moon by chance cooled into this somewhat odd configuration. Other solid planets like earth are not exactly in their predicted shape either.

The M.I.T. scientists, however, say the observed distortions are larger than would be expected for chance.

Instead, they suggest that in the moon’s early history, it travelled in an elliptical rather than a circular orbit and that it was in a 3:2 resonance, spinning three times for every two orbits.

It would have been in this resonance for only a few hundred million years at most, the scientists said, before tidal forces slowed its spin and it fell into the current 1:1 circular resonance. Their calculations show that such an orbit would provide the necessary forces to produce the moon’s shape. “There’s a 200-year-old problem, and we’ve got the first solution that works,” Zuber said.

They also found that orbits with higher resonances, like two spins for every orbit, could produce the same lunar shape.

“It’s a bunch of families of solutions,” Zuber said.