The icy gas planet Neptune, like all the planets, rotates along its axis. However, calculating the exact rotational speed is very difficult because the planet is mostly atmosphere, which doesn't rotate uniformly like a rocky planet's surface does. Because of this, calculating the rotational speed and rotational period of Neptune, or the other gas planets for that matter, is very complicated because all we can observe are the motions of the clouds in the atmosphere, and we must work out what the overall spin is from those complicated weather systems in the atmosphere of the planet. In the case of the planet Jupiter, this isn't necessary, because the planet emits radio signals from its core every rotational period, and because the waves are detectable from Earth, it is easy to calculate the spin of Jupiter based on this. However, for the other planets, it is harder because their radio waves do not reach Earth, so they are only detectable from Spacecrafts.
But even using Spacecrafts sent to these far away planets does not guarantee a consistent result for the spin of the planets, as results from space voyages to the outer planets showed. Therefore, a better way to calculate the spin and rotation of Neptune would be to look at many, many photographs of the atmosphere of Neptune and chart how many storm systems there were, and how they moved over time on Neptune. This resulted in a more accurate measurement of its rotational period, accurate possibly down to the very seconds. And although it is based on measuring the cloud cover of Neptune, it has given a quite good estimate of the rotational rate of the entire planet, including the rate of the rocky core, which is, naturally, where the entire rotation of the planet originates. Also, this method of analyzing many, many old pictures of Neptune from the past, was a great use of available data that didn't require any new data, like what would be required from a Spacecraft expedition which attempted to measure the rate of spin using only what it observed right there and then.
Now Neptune is the only outer planet aside from Jupiter that has had a accurate measurement made of its spin. However, the other two planets, Saturn and Uranus, are more complicated and have not yet been fully analyzed. When the Voyager probes passed by Saturn, they measured its spin rate by measuring its radio signals from the core, which was similar to how Jupiter's spin rate had been determined previously by using radio wave emissions. However, when the Cassini probe did the same measurement later, it found a different result. This suggests that the radio waves alone were not enough to provide accurate measurements of the remaining outer planets, and it also suggests that the interplay between the core and the atmospheric layers, as well as the liquid and metallic hydrogen layers of these planets, is much more complicated than previously thought, if the results from Voyagers and from Cassini were different. There is still much to learn about exactly what goes on in the interiors of these gaseous planets, and the complicated weather patterns and storm systems that emerge on the surface as a direct, or indirect, result of all this.
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