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According to the NASA overview about Triton, this, the largest satellite of Neptune is unique in that it has a retrograde orbit around Neptune. The page also suggests that Triton is a captured Kuiper Belt object.

What is the current accepted hypothesis as to what caused Triton's retrograde orbit? Also, is this orbit sustainable - meaning, is it degrading?

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According to this source from SOA/NASA Astrophysics Data System on Tidal evolution in the Neptune-Triton system (Chyba, C. F., Jankowski, D. G., & Nicholson, P. D.),

Tidal evolution in the Neptune-Triton system, Chyba, C. F., Jankowski, D. G., & Nicholson, P. D.

Transcript: Many investigators have speculated on the reason for Triton's retrograde orbit. Lyttleton (1936) suggested that both Pluto and Triton originated as prograde satellites of Neptune, only to experience a catastrophic gravitational interaction. McCord (1966) showed that tidal evolution could have brought Triton inward from a near-parabolic orbit, lending plausibility to a capture origin for the satellite. Jarrington and Van Flandern (1979) suggested Triton's peculiar orbit and Pluto's supposed "escape" were caused by ab encounter with a massive "rogue" body, a conclusion contested ny Farinella et al. (1980). Finally, McKinnon (1984) combined momentum and energy constraints with an improved knowledge of Pluto's mass to show that all Pluto-Triton interaction scenarios for the origin of Triton's retrograde orbit are untenable, leaving the capture hypothesis as the most likely possibility.

Now, that summarizes all the theories one might have about it, at least all I could find.

As far as evolution of the system is concerned, the same document follows up to it and demonstrates how tidal effects are responsible for the evolution of the system. "Degrading" is a strange term. Let us go with evolution.

One of the possiblities stated is that Triton will reach a perfectly retrograde state and stay in it for ever! For a detailed analysis, you may read up section 6 in the link provided, "The future of Triton"

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