Setting up a daily schedule for Saturn is not as easy as you might think.

Measurements that were made using a NASA Cassini spacecraft showed that a ringed planet has a longer day than previously thought. The first calculations of the duration of the day on Saturn were carried out more than 20 years ago using the Voyager 2 apparatus. To more accurately measure the speed of rotation of Saturn, a group of scientists used a mathematical approach based on measurements of the gravitational field of the planet.

“Although an inaccuracy of 15 minutes may seem small compared to about 10, 5 hours, during which Saturn makes a turn around its axis, it’s important to know its speed,” said Ravit Helled, a leading expert at Tel Aviv University in Israel. "To know the rotation period is important in order to better understand the dynamics of the atmosphere and the internal structure of the planet."

## Mysteries of appeal

When Voyager 2 visited Saturn in 1981, its measurements showed that the planet makes one revolution in 1 hour 39 minutes. But when Cassini first flew up to Saturn in the early 2000s, it turned out that the orbital period was 10 hours and 47 minutes, and this value changed with each new measurement.

Gas giants such as Saturn do not have a hard surface, so scientists need to look for other approaches. Voyager and Cassini used the method of measuring radio emission, but due to the fact that the readings were constantly changing, he was declared untenable.

Radio emission is not the only method to measure the rotation of gas planets. For planets whose magnetic pole does not coincide with the axis of rotation, measurements of the magnetic field can help to find out how fast the planet rotates. However, Saturn's magnetic field coincides with the axis of rotation, so this method cannot be applied to it. The third way is to measure how quickly a cloud in the atmosphere of Saturn turns around the planet. However, the speed of the cloud will not necessarily coincide with the speed of rotation of the planet, which makes this method controversial.

Helled and her team decided to use a more mathematical approach to measuring the speed of rotation of Saturn. The team calculated the rotation period using coefficients representing the inner part of the planet, then searched for a rotation period value that suits most calculations.

"We did not want the computed period to be fully associated with the internal structure, so we took into account many of the possibilities in their physical range," Helled said. "There are many meanings of conversion speed, but we found that they all tend to about the same value."

The theoretical value of the orbital period was 10 hours and 33 minutes, which correlated well with previous measurement results.

## Theory Test

The new calculations were based on the precisely measured magnetic field of the planet. When Cassini flew around Saturn, he measured the impact of the planet on a spacecraft, determining the increase or decrease in gravity. Although changes in gravity are based on changes in the internal structure, the team’s mathematical approach took into account differences in the internal structure that affect information about the gravitational field.

“The advantage of our method is that it takes into account the specific internal structure of Saturn, does not rely on the wind-dependent cloud trajectory, and allows us to take into account a wide range of values within the measured physical properties of the planet and their uncertainties,” said Helled. To clarify the calculations, the team also used measurements of the flatness of the planet. Flattening arises from the fact that rotating bodies are almost never ideal spheres; the faster they rotate, the more they stretch along the equator. Helled, however, stressed that the winds also affect the flatness - strong winds at the equator increase it.

After theoretical calculations of the rate of Saturn's circulation, the team switched to Jupiter, whose velocity of circulation is well known. Using the same mathematical approach, the researchers obtained a theoretical value of the velocity of circulation, which coincides with the real one. This result confirmed their method. Helled calls the results of their work on Jupiter "very inspiring."

New, accurate determination of the rate of circulation of Saturn will help scientists determine the external and internal structure of the planet. It will help to know the structure of the protoplanetary disk from which the planets were formed, as well as to understand the process of formation of gas giants. It can also help in the study of atmospheric dynamics.

"This value of the speed of Saturn confirms that the structure of the latitudinal winds is more symmetrical and contains both eastern and western hurricanes, such as we see on Jupiter," said Helled.