# Are there tidally locked bodies where the "far side" is denser?

It makes sense that tidal forces lead to tidal locking. Celestial bodies have varying densities and shapes, so some orientations have a lower gravitational potential, and eventually the tendency will be for the body to settle into the orientation of lowest potential, similar to how dice with imperfections, when buoyant in water, will roll until the denser side faces down.

For the Earth and the Moon, it seems like the story is that the denser side faces earth:

The mass of the Moon is not evenly distributed; mass concentrations, called Mascons, lie beneath many of the lunar basins, and the center of mass of the Moon is displaced several kilometers towards the Earth.

However, unlike the die floating in water, in a system of two orbiting celestial bodies (like the Earth and Moon) each body has two gravitational wells. These two areas of lower gravitational potential cause, for instance, the two high tides on earth. The explanation straightforward: Bodies oribiting around their mutual barycenter experience a centripetal acceleration which is equal to the gravitational force only at the center of mass. There is a net inward force on the near side of each body (where the acceleration is less than the gravitational force), and a net outward force on the outside (where the acceleration is greater than the gravitational force).

Since there are two areas of locally lower gravitational potential, it seems equally likely (or at least quite possible) that the mass concentrations of the Moon would end up on the far side of the Earth. Is this reasoning correct? Are there examples of such systems?

• Follow-up: The causality also partially goes in the reverse direction, where the tidal locking caused a shift that promoted more volcanic activity on the near side [0] "As the Moon became tidally locked to the much bigger Earth, the entire core of the Moon shifted slightly closer to the Earth, and consequently closer to the near side’s crust." My above question predates this effect, but it raises a natural follow-up: If tidal forces go in both directions, why would the moon's core move toward earth and not away? Was that also chance? [0]: futurism.com/the-moons-fixed-face May 20 at 13:23
• I don't think it's equally likely for mascons to end up on the far side. If you look at my diagram of the combined gravitational and centrifugal pseudo-potential in the co-rotating frame here: space.stackexchange.com/a/57679/38535 you can see that the pseudo-potential is slightly lower on the L1 (near) side than on the L2 (far) side. May 20 at 13:44
• BTW, you can easily hack that script to print potentials. Eg, insert for u in (0.9, 1.1): print(-func(x=u, y=0)) anywhere after func is defined. May 20 at 14:06
• I suspect the case of "dense side farther away" is one of unstable equilibrium. Any tiny perturbation will lead to rotation & rocking until the dense side is near. May 23 at 12:33
• @CarlWitthoft I don't think that's true. It would be for dice in water but for bodies in free fall, having the densest part maximally far from earth should be the locally lowest potential configuration. pm2ring points out that the potential on the near side is actually globally lower, but both should be local minima. May 23 at 12:41