Just a quick question regarding Neptune. Because Phobos is spiraling in towards Mars, Mars' rotation speeds up. Does the same thing happen with Neptune's rotation?
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$\begingroup$ I don't have enough information for an answer, but some things to keep in mind: Neptune has a lot more moons, and Neptune has differential rotation since it is a gas giant. $\endgroup$– called2voyage ♦Jan 3, 2019 at 16:19
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1$\begingroup$ The obvious answer is "yes, because Newton." What you need to consider is the magnitude of the effect, roughly by comparing the mass ratio of Triton/Neptune as compared with Phobos/Mars , to see if it is significant. [ the calculation is left as a homework problem :-) ] $\endgroup$– Carl WitthoftJan 3, 2019 at 16:33
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$\begingroup$ Let's just say it you have a moon and . planet, the moon orbits retrograde. Would it happen? $\endgroup$– StellarExileJan 3, 2019 at 20:07
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3$\begingroup$ This is an interesting question, and since Neptune is a gas giant rather than a rocky planet, there are some interesting differences. I think this question deserves a good answer that makes this difference clear. $\endgroup$– uhohJan 4, 2019 at 2:20
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1 Answer
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In short, the answer is yes -- because of the conservation of the angular momentum.
The orbital angular momentum scales as the square root of the semimajor axis. Therefore, if the satellite's orbit is shrinking, the orbital angular momentum is getting smaller.
Had Triton's orbit been prograde, I would have said that, to compensate for the said decrease in the orbital angular momentum, the rotational angular momentum of the planet must be increasing (i.e., the planet must be rotating faster).
However, Triton's orbit is retrograde. So the sign of the rotational orbital momentum is opposite to that of the planet's spin. (To simplify things, I am neglecting the inclination of the orbit on the equator.) In this situation, our conclusion will be opposite: to compensate for the decrease in the orbital angular momentum, the planet must be rotating slower.
