# Is the Moon not in hydrostatic equilibrium?

Given the recently-announced observations from VLT/SPHERE that 10 Hygiea may be sufficiently round to qualify as the second main-belt dwarf planet, I found myself perusing Wikipedia's Hydrostatic Equilibrium article, and came across the following passage, which currently has no linked references:

The smallest body confirmed to be in hydrostatic equilibrium is the dwarf planet Ceres, which is icy, at 945 km, whereas the largest body known to not be in hydrostatic equilibrium is the Moon, which is rocky, at 3,474 km.

I'd long assumed that the Moon was in hydrostatic equilibrium, given its spherical-to-the eye shape and ranking among the 20 largest solar system objects. If the quoted statement is true, why isn't it in hydrostatic equilibrium?

• That might be just an issue with wikipedia authors sometimes using non-standard notions, but this passage should have a [citation needed]. Not being in hydrostatic equilibrium would mean that there's a net acceleration inside the body, and I can't see any rocks flying off from the Moon. – AtmosphericPrisonEscape Nov 23 '19 at 16:55
• @AtmosphericPrisonEscape - While the Moon is not in hydrostatic equilibrium, the wikipedia article is nonetheless incorrect. There are several larger bodies in the solar system that are not in hydrostatic equilibrium, one of which is our own Earth. – David Hammen Nov 23 '19 at 18:55
• @David Is that related to the lunar mascons? – PM 2Ring Nov 23 '19 at 19:32
• @PM2Ring - That's part of it ("it" being that the Moon strictly speaking is not in hydrostatic equilibrium). Another aspect is the Moon's fossil tidal bulge mentioned in antispinwards' answer. – David Hammen Nov 23 '19 at 20:03
• When I use "hydrostatic equilibrium" in an answer, I almost always pre-qualify that phrase with "more or less". Hydrostatic equilibrium is a spherical cow. – David Hammen Nov 23 '19 at 20:06

## 1 Answer

The paragraph notes previously that Mimas is not in hydrostatic equilibrium for its current rotation. A quick search for the moon and hydrostatic equilibrium turned up M. Burša (1984) "Secular Love Numbers and Hydrostatic Equilibrium of Planets". According to this paper the Moon, Mercury and Venus are all far from hydrostatic equilibrium. The discrepancy is much smaller for the Earth. The paper goes on to note that the rotation periods required for the flattenings of these objects to be explained as hydrostatic are 3.7 days, 4.7 days and 17 days respectively, all substantially faster than the current rotation periods.

According to the abstract of C. Qin's presentation "Formation of the lunar fossil bulge and its implication for the dynamics of the early Earth and Moon" the usual hypothesis in the case of the Moon is that the shape is a "fossil bulge", a relic from when the Moon was spinning faster early in its history. Possibly this explanation may also apply to Mercury and Venus, which also have been spun down by tidal forces.

• The Earth also is known to not be in hydrostatic equilibrium. Hydrostatic equilibrium dictates a strict relation between the Earth's oblateness and it's dynamical form factor $J_2$. Both of these are well-observed, and the observed values disagree with the hydrostatic equilibrium relation. The reason is that the Earth is still recovering from the glaciation that ended 10000 years ago. – David Hammen Nov 23 '19 at 18:53
• Huh, fair enough. I'll see what i can read in those. Kind of makes me wonder how far out of HE a world has to fall before it fails Test #2 on the '06 IAU planet definition. – notovny Nov 25 '19 at 21:18