The gas planets (Jupiter, Saturn, Uranus, and Neptune) have no surface to speak of, so how was it determined how long a day is?
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An early attempt was to do some storm watching. Jupiter is constantly buffeted by atmospheric storms, so the theory was that you could locate the center of a storm and get some idea of the length of a day. The problem scientists encountered was that the storms on Jupiter are very fast moving, making them an inaccurate source of rotational information. Scientist were finally able to use radio emissions from Jupiter’s magnetic field to calculate the planet’s rotational period and speed. While other parts of the planet rotate at different speeds, the speed as measured by the magnetosphere is used as the official rotational speed and period.
However, Saturn is different. Its unique magnetic field is nearly perfectly aligned with its rotational axis. This is why the rings finding has been key to homing in on the length of day. During Cassini’s orbits of Saturn, instruments examined the icy, rocky rings in unprecedented detail and used the data to study wave patterns within the rings. Earlier findings had determined that the rings respond to vibrations within the planet itself, acting similarly to the seismometers used to measure movement caused by earthquakes. The interior of Saturn vibrates at frequencies that cause variations in its gravitational field. The rings, in turn, detect those movements in the field.
https://solarsystem.nasa.gov/news/814/scientists-finally-know-what-time-it-is-on-saturn/
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