"When we try to analyse the global shape of the moon using spherical harmonics, the craters are like gaps in the data. We did a lot of work to estimate the uncertainties in the analysis that result from those gaps," explained Ian Garrick-Bethell, an assistant professor of earth and planetary sciences at University of California-Santa Cruz.

The results indicate that variations in the thickness of the moon's crust caused by tidal heating during its formation can account for most of the moon's large-scale topography.

Tidal heating and tidal-rotational deformation had similar effects on the moon's overall shape, giving it a slight lemon shape with a bulge on the side facing the Earth and another bulge on the opposite side.

"The two processes left distinct signatures, however, in the moon's gravity field. Because the crust is lighter than the underlying mantle, gravity signals reveal variations in the thickness of the crust that were caused by tidal heating," Garrick-Bethell said.

As the moon cooled and solidified more than four billion years ago, the sculpting effects of tidal and rotational forces became frozen in place. The idea of a frozen tidal-rotational bulge, known as the fossil bulge hypothesis, was first described in 1898.

In the new study, researchers found that the moon's overall gravity field is no longer aligned with the topography, as it would have been when the tidal bulges were frozen into the moon's shape.

"The moon that faced us a long time ago has shifted, so we are no longer looking at the primordial face of the moon," Garrick-Bethell informed. Changes in the mass distribution shifted the orientation of the moon.

"The craters removed some mass, and there were also internal changes, probably related to when the moon became volcanically active," researchers concluded in the paper published in Nature.

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