# Why are the moons of Neptune sorted by diameter?

The five moons closest to Neptune are sorted by increasing size. Naiad < Thalassa < Despina < Galatea < Larissa. The trend continues with Proteus and Triton, only interrupted by Hippocamp, which is smaller than the closer moons.

Is this ordering due to pure chance? Is there a reason why moons closer to Neptune should be smaller? Is it possibly an observational bias?

• I have drawn the d-M graph for Neptune moons (one excluding Triton and one including Triton (Triton was well out of scale, hence I drew one without it)) in Excel sheet. It kinda looks like a cusp graph . So obviously, there is a kind of a pattern for Neptune moons. Nov 25 '20 at 5:12

b) Neptune exerts tides onto the moons. Typically no moons can exist within the Roche limit. How close a moon can exist depends on the rigidity of the body, though. Big moons (mass $$M_m$$) cannot exist as far inward (distance $$d$$ to Neptune) as a small moon (Neptune's radius $$R_N$$ and mass $$M_N$$): $$M_m = \left(\frac{R_N}{d}\right)^3\cdot2M_N$$ or easier expressed as ratio of the moon's radius $$r_{moon}$$ and the moon's distance to Neptune $$d$$ as well as its density $$\varrho_{moon}$$: $$\left(\frac{r_{moon}}{d}\right)^3\cdot\varrho_{moon} = constant$$ Thus the further out, the larger the moon can be without falling apart due to tidal forces. Wikipedia has a page on Neptune's moons and references which indicates that the inner moons are somewhere at the tidal limit for bodies which are of somewhat granular nature as is expected for at least the smaller moons or maybe even all with the exception of Triton.
• $\varrho_{moon}$ being the density of the moon I suppose? Nov 11 '20 at 14:02
• yes, $\varrho$ is as usal the density Nov 11 '20 at 14:14