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How Long Is a Day on Saturn, and How Can Anyone Measure It on a Planet With No Ground?

Category: Space & Astronomy

To time Earth's spin, you can watch a mountain move across the sky. Saturn has no mountains or coastlines, and no solid surface you could watch or stand on. It is a huge ball of hydrogen and helium, and the clouds you see are carried around by winds that blow at different speeds in different places.

So what counts as one Saturn day? The short answer: the best current estimate is about 10 hours 33 minutes. For decades, textbooks gave a figure of about 10 hours 39 minutes instead. This article follows one question: why was the first clock about six minutes off, and how did scientists build better ones?

1. Saturn's First Clock Was a Radio Signal, and It Gave 10 Hours 39 Minutes

Jupiter has a handy trick. Its magnetic field is tilted compared with its spin axis, so as the planet turns, its radio signal rises and falls in a steady beat, like a lighthouse. That beat works as a clock for the planet's deep interior. Saturn's magnetic field makes this trick hard to use: its magnetic axis lines up almost exactly with its spin axis, so there is no wobble to count. This does not mean Saturn has no magnetic field, only that the field gives no clear tick[1].

Scientists still wanted a number, so they used a stand-in. Radio waves from near Saturn's poles, called Saturn kilometric radiation, seemed to repeat about every 10 hours 39 minutes, and the Voyager spacecraft in the early 1980s settled on 10 hours 39 minutes 22.4 seconds. The assumption was that the radio beat follows the planet's interior[1]. For a long time, that assumption sat quietly in the reference tables, and it is still the number you will find in many of them.

2. The Radio Clock Drifted, So It Could Not Be Following the Planet's Interior

Then the Cassini spacecraft arrived at Saturn in 2004 and measured the radio signal for years. One of its values was 10 hours 47 minutes 6 seconds, about seven and a half minutes longer than Voyager's. Worse, the number kept changing from one measurement to the next[1].

A European team that studied several years of Cassini radio data found that the radio clock wanders by 1 to 2 percent over weeks to months. They concluded that changes in the speed of the solar wind, the stream of charged particles flowing out from the Sun, are probably responsible for the poor stability[2]. Another study found that the signal comes in two periods, linked to the north and south halves of the planet, which drift apart and sometimes lock together again[3].

A planet this heavy cannot plausibly speed up and slow down by a percent every few weeks. The radio beat was more like a clock hanging in a breeze than a clock bolted to the planet. By 2015 researchers were saying plainly that the radio period could not be used to find the planet's bulk rotation period[1].

3. A Spinning Planet Bulges at the Equator, and Gravity and Shape Gave 10 Hours 32 Minutes 45 Seconds

If radio is out, the planet's own shape can serve as a clock. A spinning ball of gas bulges at the equator, and the faster it spins, the bigger the bulge. A simple way to picture it is pizza dough: spin it faster and it flattens and widens. Spacecraft can measure Saturn's gravity from how they are pulled as they pass, and telescopes and probes measure how squashed the planet looks[1].

In 2015, Ravit Helled, Eli Galanti, and Yohai Kaspi combined those measurements with limits on how the planet's interior could be arranged. Their result was 10 hours 32 minutes 45 seconds, plus or minus 46 seconds, about six and a half minutes shorter than the radio value. As a check, they ran the same method on Jupiter, where the true answer is well known, and it gave the right period[1]. One caution: the method still has to assume what ranges of shape and density are possible inside Saturn, so it is not a measurement made from nothing.

4. Saturn's Rings Pick Up Vibrations From the Planet's Inside, and They Gave 10 Hours 33 Minutes 38 Seconds

The third clock is the strangest one. Saturn's rings are made of countless orbiting particles, and they are sensitive to the planet's gravity. When the inside of Saturn vibrates, a bit like a bell ringing very slowly, its gravity pattern wobbles slightly, and ring particles respond by forming waves at particular places in the rings. Researchers describe this as the rings acting like a seismometer, the instrument that records earthquakes. The rings do not show the spin directly. The waves reflect the planet's vibration modes, which are affected by how fast the planet turns, so researchers use the pattern of the waves to estimate the interior rotation period.

A team led by Christopher Mankovich matched more than twenty waves in the C ring, detected in Cassini data, with the planet's fundamental vibration modes. From the waves' pattern speeds and shapes, they estimated an interior rotation period of 10 hours 33 minutes 38 seconds. The estimate is not exact: the likely range runs from about 1 minute 19 seconds shorter to 1 minute 52 seconds longer. They also reported that the result is significantly faster than the radio-based periods from Voyager and Cassini[4].

5. Three Different Methods Now Agree on About 10 Hours 33 Minutes, but the Answer Is Not Final

Here is the satisfying part. The gravity method, the ring waves, and later analyses of Cassini's final close orbits, the Grand Finale, were built on different ideas, yet they landed within a minute or two of each other. A 2023 review of Saturn's interior says that at depth, a variety of different investigations now point to a rotation period of 10 hours 33 minutes[5].

The same review adds a catch. The winds seen in Saturn's atmosphere appear to reach down at least 10,000 kilometers, about a sixth of the way to the center, so the planet may not turn like a single solid ball. Because of that, "the" rotation period depends partly on how you define it and what depth you measure[5]. The ring-wave paper reports that its global fit showed no clear sign of strong differential rotation, meaning different layers turning at different speeds, in the outer envelope[4]. Scientists are still working on how to combine both views.

That is why reference tables still show 10 hours 39 minutes. It is a real measurement, but of a radio signal that was influenced by things outside the planet, not of the deep interior. If a book gives a different number than this article does, it may simply have been written before the newer methods existed.

6. How to Feel Why One Measurement of a Spin Can Be Off

  • Time a paper plate's spin. Stick a small sticker on the rim of a paper plate. Spin it slowly with the palm of your hand, and time one full turn with a stopwatch or a clock with a second hand. Do this five times. Then time five turns in a row and divide by five. Which set of numbers is more steady? Hold the plate flat and keep your fingers away from the edge. This is not Saturn, but it shows why scientists prefer measurements that average over many turns.
  • Find Saturn in the sky. When Saturn is above the horizon at night, it is often easy to spot, and a small telescope, such as one at a science museum or an astronomy club night, shows the rings. Think about how those rings caught the planet's shaking.
  • Read the abstract. The sources below link to short summaries of the original papers on arXiv, a free site where scientists post research. The abstracts are only a few lines. Try finding the minutes and seconds in them.

Sources

This article is a personal summary based on the public sources listed below.

  1. R. Helled, E. Galanti, Y. Kaspi, "Saturn's fast spin determined from its gravitational field and oblateness," Nature (2015); preprint arXiv:1504.02561. https://arxiv.org/abs/1504.02561 (Abstract page read; the full paper was not read. It supplies the aligned magnetic and spin axes, the Voyager radio period of 10 h 39 m 22.4 s, the Cassini value of 10 h 47 m 6 s that changed between measurements, the result of 10 h 32 m 45 s plus or minus 46 s, and the Jupiter check. The claim that the radio period cannot give the bulk rotation period is the paper's own summary. The comparison with Jupiter's tilted field is standard background that this abstract does not spell out.)
  2. European Space Agency, "Saturn's radio rotation" (image caption, December 2007). https://www.esa.int/ESA_Multimedia/Images/2007/12/Saturn_s_radio_rotation (Full caption read; it is short. It supplies the 1 to 2 percent fluctuation over weeks to months and the statement that solar wind speed is "probably responsible." This is a probable cause, not a proven one.)
  3. Annales Geophysicae 32, 1463 (2014), on changes in the periods of Saturn kilometric radiation and the 2011 Great White Spot storm. https://angeo.copernicus.org/articles/32/1463/2014/angeo-32-1463-2014.xml (Only the abstract and opening of the paper were read. It supplies the northern and southern radio periods that separate and sometimes lock together. Its authors argue for a link to a giant storm, which this article does not rely on.)
  4. C. Mankovich, M. Marley, J. Fortney, N. Movshovitz, "Cassini Ring Seismology as a Probe of Saturn's Interior I: Rigid Rotation," Astrophysical Journal (2019); preprint arXiv:1805.10286. https://arxiv.org/abs/1805.10286 (Abstract page read; the full paper was not read. It supplies the more than twenty C-ring waves, the period of 10 h 33 m 38 s with the 5 and 95 percent range, the comparison with radio periods, and the finding of no clear strong differential rotation in the outer envelope. The seismometer wording is a common way to describe ring seismology; the abstract itself does not use that word.)
  5. J. Fortney and colleagues, "Saturn's Interior After the Cassini Grand Finale" (review, 2023); preprint arXiv:2304.09215. https://arxiv.org/abs/2304.09215 (Abstract page read; the full review was not read. It supplies the deep rotation rate of 10 hours 33 minutes from a variety of investigations, and differential rotation reaching down to at least 10,000 km, about one sixth of the planet's radius. The individual values from the Grand Finale analyses are not given in the abstract, so this article does not quote them.)

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