Solar System -
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Neptune has 14 identified moons, as at September 2013, named for minor water deities in Greek mythology. Triton, the largest at more than 2,700 km in diameter, and the one first discovered soon after Neptune itself on October 10th 1846 by the English astronomer William Lassell, orbits in a Retrograde Orbit, in the opposite direction to most of the other moons. This leads astronomers to believe that it was captured long in the past, as virtually all natural satellites, formed along with their parent body, orbit in Prograde Orbits. It was once, possibly, a Kuiper Belt Object as it is very similar to Pluto. It is the only large moon in the Solar System that has a Retrograde Orbit. Triton is in a synchronous orbit around Neptune, meaning that, like our own Moon, the same side faces Neptune. Unfortunately, for Triton, its orbit is decaying, and in the relatively near future, perhaps several million years, it will disintegrate, and could form a new, more distinct ring system. Triton is so much larger than the other moons that it makes up about 99.7% of the total mass of all the moons.
Below, a table lists the known moons, with information about their orbits and diameters. Particularly for the five outer moons, some of this information is conjectural, and subject to change.
There is an excellent resource for more information about Neptune's Moons on the NASA website. Here is a table of Neptune's Moons with additional information.
Triton has a sparsely cratered surface with smooth volcanic plains, mounds and round pits formed by icy lava flows. The crust is frozen nitrogen over an icy mantle believed to cover a core of rock and metal. Credit: NASA/JPL/USGS
Despite its mass, Proteus is an irregularly shaped moon. It has many craters varying in diameter up to about 100 km (60 miles), though most are less than 50 km (30 miles). Generally, they are largely unchanged due to lack of geological activity. Pharos is the largest crater at around 160 to 230 km (100 to 140 miles) across. Credit: NASA/Voyager 2
Larissa appears to be a smaller version of Proteus, and similarly heavily cratered. Credit: NASA/JPL
List of Neptune's Moons