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Overview

Neptune has 13 known moons. They are composed of rock and ice. Triton has a retrograde orbit. Nereid has a highly elliptical orbit. Voyager 2 discovered 6 of the moons not observable from Earth. Very recently, three more moons, S/2002 N1-3, were discovered from a ground-based telescope in 2002

Description
The first four moons of Neptune, Naiad, Thalassa, Despina, and Galatea, are so close to Neptune that they orbit within its ring system. Little is known about them.
The next one out, Larissa, was actually discovered in 1981, when it blocked a star. This was attributed to the ring arcs, but later was found to be the moon, being re-discovered by Voyager 2 in 1989.
Proteus is the second-largest moon in orbit around Neptune. It is so close to the planet that Earth-bound telescopes cannot see it.
Triton is next , and is one of the strangest moons in the solar system. First, it is one of only three moons in the solar system that has an atmosphere (Jupiter's Io and Saturn's Titan are the other two). It is thicker than Io's, yet much thinner than Titan's. Its pressure is 1/100,000 of Earth's.
Second, Triton has a retrograde orbit, which means that it orbits the opposite way the planet spins. This is a very strong indication that Triton was captured. This in itself is not strange; both of Mars' moons were captured. What is strange is that Triton is two-thirds the size of our moon. When two bodies have a close encounter, one does not automatically capture the other, especially if it is so big. One theory is that Triton must have actually hit Neptune, bounced off the atmosphere, and gone into orbit because it lost all of its momentum. Another way this could have happened is that Triton collided with one of Neptune's moons, smashed it to bits (possibly creating the rings), and lost so much momentum that it couldn't escape Neptune's gravity.
Third, it is only 38 °C (100 °F) above absolute zero (the temperature at which all matter comes to rest). In such frigid a climate scientists did not expect to find active geysers. But, they did. They spew out a gaseous form of nitrogen, which is what creates its atmosphere.
The eighth moon, Nereid, has a highly elliptical orbit that causes it to swing around Neptune at various distances. When closest, it is 1,342,530 km (834,210 miles) from the planet. At the farthest distance, it is 9,667,120 km (6,006,870 miles) from Neptune.
The last five moons were discovered in the first few weeks of and throughout 2003. They have not yet been given official names by the International Astronomical Union. Very little is yet known about them.
https://filer.case.edu/sjr16/neptune_moons.html