# What are the periods of Saturn's rings?

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I don't mean necessarily a granular chart of all of the different rings at different distances, but is it days? Weeks?

Hours to days.

The orbital period is proportional to the 3/2 power of the orbital radius, and the orbital period of the moon Methone (and thus of the particles in its associated ring arc) is very close to 24 hours. Working from the orbital radii given in this table, I get:

• D ring: ~5 hours
• C ring: ~6-7 hours
• B ring: ~8-10 hours
• A ring: ~12-14 hours
• F ring: ~14.5 hours
• Janus/Epimetheus ring: ~16-17 hours
• G ring: ~19-20 hours
• Methone & Anthe arcs: ~24 hours
• Pallene ring: ~27 hours
• E ring: ~21 hours to ~90 hours
• Phoebe ring: 90-500 days

Starting from the vis-viva equation one of the few equations I can actually remember:

$$v^2 = GM left( frac{2}{r} - frac{1}{a} ight)$$

You can set $r=a$ for a circular orbit, giving $v=sqrt{GM/a}$ where the product of the gravitational constant times Saturn's mass $GM$ is called the standard gravitational parameter and is about 3.793E+07 km^3/s^2. (beware of meters vs kilometers).

The circumference is $C = 2 pi a$, so

$$T = frac{C}{v} = 2 pi a sqrt{a/GM} = frac{2 pi a^{3/2}}{sqrt{GM}}$$

which shows the 3/2 power scaling mentioned in @RB's answer.

For the Methone Ring with a distance of 194,230 km, this gives 24.3 hours, same as the other answer of course.

One caveat is that for more accurate calculations, it's important to remember that for strongly oblate planets, the radial variation of the gravity field does not vary strictly as $1/r^2$ but will deviate significantly at shorter distances, and so the period will not scale precisely as $a^{3/2}.$

For a spherically symmetric body, no matter what the radial profile you can put all of the mass at the center point instead of integrating throughout the sphere, as long as you are outside of it. This is called the Shell Theorem first proven by Sir Isaac Newton.

But the oblate figure is only cylindrically symmetric, not spherically symmetric, so you actually do have to integrate the force from every point within the planet. Most of this will already be captured in the $J_2$ term, and so I've just asked Equation for orbital period around oblate bodies, based on J2?

## How Powerful Does a Telescope Have to Be to See Rings of Saturn?

Certainly, Saturn is one of the most beautiful planets in our solar system. Its glorious rings and beautiful shimmering pinks, hues of gray and a hint of brown color make it a delight to behold. However, to see all the details of this impressive planet, you’ll need a powerful telescope to watch rings of Saturn.

Choosing the right watching time is also important. July 2020 was the last time we were able to see Saturn’s rings facing directly against our planet. So, you’ll have to wait a few months more to enjoy this wonderful spectacle once again. But most of the day (without rainy day), you can watch Saturn’s rings easily with a Telescope.

In the meantime, it’s a good idea to upgrade your astronomy equipment and purchase the best telescope to see Saturn rings. Today, we’ll give some tips to make the best buying decision of a Telescope.

## Our view of Saturn evolves

When Galileo first observed Saturn through his telescope in 1610, he was still basking in the fame of discovering the four moons of Jupiter. But Saturn perplexed him. Peering at the planet through his telescope, it first looked to him as a planet with two very large moons, then as a lone planet, and then again through his newer telescope, in 1616, as a planet with arms or handles.

Four decades later, Giovanni Cassini first suggested that Saturn was a ringed planet, and what Galileo had seen were different views of Saturn&rsquos rings. Because of the 27 degrees in the tilt of Saturn&rsquos rotation axis relative to the plane of its orbit, the rings appear to tilt toward and away from Earth with the 29-year cycle of Saturn&rsquos revolution about the Sun, giving humanity an ever-changing view of the rings.

But what were the rings made of? Were they solid disks as some suggested? Or were they made up of smaller particles? As more structure became apparent in the rings, as more gaps were found, and as the motion of the rings about Saturn was observed, astronomers realized that the rings were not solid, and were perhaps made up of a large number of moonlets, or small moons. At the same time, estimates for the thickness of the rings went from Sir William Herschel&rsquos 300 miles in 1789, to Audouin Dollfus&rsquo much more precise estimate of less than two miles in 1966.

Astronomers understanding of the rings changed dramatically with the Pioneer 11 and twin Voyager missions to Saturn. Voyager&rsquos now famous photograph of the rings, backlit by the Sun, showed for the first time that what appeared as the vast A, B and C rings in fact comprised millions of smaller ringlets.

###### Voyager 2 false color image of Saturn&rsquos B and C rings showing many ringlets. NASA

The Cassini mission to Saturn, having spent over a decade orbiting the ringed giant, gave planetary scientists even more spectacular and surprising views. The magnificent ring system of Saturn is between 10 meters and one kilometer thick. The combined mass of its particles, which are 99.8% ice and most of which are less than one meter in size, is about 16 quadrillion tons, less than 0.02% the mass of Earth&rsquos Moon, and less than half the mass of Saturn&rsquos moon Mimas. This has led some scientists to speculate whether the rings are a result of the breakup of one of Saturn&rsquos moons or the capture and breakup of a stray comet.

## Cosmic quiver: Saturn's vibrations create spirals in rings

The researchers found the density waves propagate inward and appear to be generated from within Saturn rather than from any moon. Credit: NASA/JPL-Caltech/Space Science Institute

(Phys.org) —Astronomers know that gravity from Saturn's various moons tug at the planet's rings and make spirals in them. But the catalyst for certain spiral patterns has been difficult to pin down. Now, two Cornell astronomers have determined the source: Saturn itself.

The entire planet can vibrate like a bell within periods of a few hours, and these oscillations cause gravitational tugs that, in turn, create the spiral patterns in the rings. The cause of the vibrations remains unknown.

"The locations and properties of these ring disturbances tell us how and with what periods the planet oscillates," said senior research associate Matthew Hedman, whose new research was published June 11 in The Astronomical Journal. He also presented the research May 9 at the meeting of the American Astronomical Society's Division for Dynamical Astronomy in Paraty, Brazil. "Just like earthquakes can be used to study the Earth's interior, and solar oscillations can be used to study the interior of the sun, these vibrations in Saturn can help scientists figure out the internal structure of the giant planets."

Saturn's rings act as a seismograph that records these large-scale oscillations, possibly emanating from deep within the planet. The study of these records provides a completely new way to probe structure and rotation of Saturn's interior, and the astronomers have come up with a name for it: kronoseismology.

Saturn's oscillations are similar to what are called "whole earth oscillations" in terrestrial seismology. On Earth, these are generated by very large earthquakes, which make the Earth ring for several days.

The researchers focused on a handful of unexplained waves in Saturn's C ring that did not appear to be linked to well-understood gravitational interactions with anything within or outside of the rings. They used data from NASA's Cassini mission, which has repeatedly profiled Saturn's rings using "stellar occultations" via the spacecraft's Visual and Infrared Mapping Spectrometer instrument. The measurements record changes in light from a given star as the rings pass between the star and the spacecraft. Using numerous occultation measurements of the C ring, the researchers were able to piece together dossiers on these unexplained ring features.

The researchers found the density waves propagate inward and appear to be generated from within Saturn rather than from any moon the six waves also have the right pattern speeds and symmetry properties to be produced by oscillations within Saturn.

The paper, "Kronoseismology: Using Density Waves in Saturn's C Ring to Probe the Planet's Interior," was co-authored by Philip Nicholson, Cornell professor of astronomy.

## Our view of Saturn evolves

When Galileo first observed Saturn through his telescope in 1610, he was still basking in the fame of discovering the four moons of Jupiter. But Saturn perplexed him. Peering at the planet through his telescope, it first looked to him as a planet with two very large moons, then as a lone planet, and then again through his newer telescope, in 1616, as a planet with arms or handles.

Four decades later, Christiaan Huygens first suggested that Saturn was a ringed planet, and what Galileo had seen were different views of Saturn’s rings. Because of the 27 degrees in the tilt of Saturn’s rotation axis relative to the plane of its orbit, the rings appear to tilt toward and away from Earth with the 29-year cycle of Saturn’s revolution about the Sun, giving humanity an ever-changing view of the rings.

But what were the rings made of? Were they solid disks as some suggested? Or were they made up of smaller particles? As more structure became apparent in the rings, as more gaps were found, and as the motion of the rings about Saturn was observed, astronomers realized that the rings were not solid, and were perhaps made up of a large number of moonlets, or small moons. At the same time, estimates for the thickness of the rings went from Sir William Herschel’s 300 miles in 1789, to Audouin Dollfus’ much more precise estimate of less than two miles in 1966.

Astronomers understanding of the rings changed dramatically with the Pioneer 11 and twin Voyager missions to Saturn. Voyager’s now famous photograph of the rings, backlit by the Sun, showed for the first time that what appeared as the vast A, B and C rings in fact comprised millions of smaller ringlets.

Voyager 2 false color image of Saturn’s B and C rings showing many ringlets. NASA

The Cassini mission to Saturn, having spent over a decade orbiting the ringed giant, gave planetary scientists even more spectacular and surprising views. The magnificent ring system of Saturn is between 10 meters and one kilometer thick. The combined mass of its particles, which are 99.8% ice and most of which are less than one meter in size, is about 16 quadrillion tons, less than 0.02% the mass of Earth’s Moon, and less than half the mass of Saturn’s moon Mimas. This has led some scientists to speculate whether the rings are a result of the breakup of one of Saturn’s moons or the capture and breakup of a stray comet.

## Cosmic quiver: Saturn's vibrations create spirals in rings

Astronomers know that gravity from Saturn’s various moons tug at the planet’s rings and make spirals in them. But the catalyst for certain spiral patterns has been difficult to pin down. Now, two Cornell astronomers have determined the source: Saturn itself.

The entire planet can vibrate like a bell within periods of a few hours, and these oscillations cause gravitational tugs that, in turn, create the spiral patterns in the rings. The cause of the vibrations remains unknown.

“The locations and properties of these ring disturbances tell us how and with what periods the planet oscillates,” said senior research associate Matthew Hedman, whose new research was published June 11 in The Astronomical Journal. He also presented the research May 9 at the meeting of the American Astronomical Society’s Division for Dynamical Astronomy in Paraty, Brazil. “Just like earthquakes can be used to study the Earth’s interior, and solar oscillations can be used to study the interior of the sun, these vibrations in Saturn can help scientists figure out the internal structure of the giant planets.”

Saturn’s rings act as a seismograph that records these large-scale oscillations, possibly emanating from deep within the planet. The study of these records provides a completely new way to probe structure and rotation of Saturn’s interior, and the astronomers have come up with a name for it: kronoseismology.

Saturn’s oscillations are similar to what are called “whole earth oscillations” in terrestrial seismology. On Earth, these are generated by very large earthquakes, which make the Earth ring for several days.

The researchers focused on a handful of unexplained waves in Saturn’s C ring that did not appear to be linked to well-understood gravitational interactions with anything within or outside of the rings. They used data from NASA’s Cassini mission, which has repeatedly profiled Saturn’s rings using “stellar occultations” via the spacecraft’s Visual and Infrared Mapping Spectrometer instrument. The measurements record changes in light from a given star as the rings pass between the star and the spacecraft. Using numerous occultation measurements of the C ring, the researchers were able to piece together dossiers on these unexplained ring features.

The researchers found the density waves propagate inward and appear to be generated from within Saturn rather than from any moon the six waves also have the right pattern speeds and symmetry properties to be produced by oscillations within Saturn.

The paper, “Kronoseismology: Using Density Waves in Saturn’s C Ring to Probe the Planet’s Interior,” was co-authored by Philip Nicholson, Cornell professor of astronomy.

The Cassini-Huygens mission is a project of NASA, the European Space Agency and ASI, the Italian Space Agency.

## Our View of Saturn Evolves

When Galileo first observed Saturn through his telescope in 1610, he was still basking in the fame of discovering the four moons of Jupiter. But Saturn perplexed him. Peering at the planet through his telescope, it first looked to him as a planet with two very large moons, then as a lone planet, and then again through his newer telescope, in 1616, as a planet with arms or handles.

Four decades later, Christiaan Huygens first suggested that Saturn was a ringed planet, and what Galileo had seen were different views of Saturn’s rings. Because of the 27 degrees in the tilt of Saturn’s rotation axis relative to the plane of its orbit, the rings appear to tilt toward and away from Earth with the 29-year cycle of Saturn’s revolution about the sun, giving humanity an ever-changing view of the rings.

But what were the rings made of? Were they solid disks as some suggested? Or were they made up of smaller particles? As more structure became apparent in the rings, as more gaps were found, and as the motion of the rings about Saturn was observed, astronomers realized that the rings were not solid, and were perhaps made up of a large number of moonlets, or small moons. At the same time, estimates for the thickness of the rings went from Sir William Herschel’s 300 miles in 1789, to Audouin Dollfus’ much more precise estimate of less than two miles in 1966.

Astronomers understanding of the rings changed dramatically with the Pioneer 11 and twin Voyager missions to Saturn. Voyager’s now famous photograph of the rings, backlit by the sun, showed for the first time that what appeared as the vast A, B, and C rings in fact comprised millions of smaller ringlets.

The Cassini mission to Saturn, having spent over a decade orbiting the ringed giant, gave planetary scientists even more spectacular and surprising views. The magnificent ring system of Saturn is between 10 meters and one kilometer thick. The combined mass of its particles, which are 99.8% ice and most of which are less than one meter in size, is about 16 quadrillion tons, less than 0.02% the mass of Earth’s moon, and less than half the mass of Saturn’s moon Mimas. This has led some scientists to speculate whether the rings are a result of the breakup of one of Saturn’s moons or the capture and breakup of a stray comet.

## Current Spacecraft Exploration

Cassini – Computer generated image of the spacecraft. Credit: NASA

There is currently a satellite in orbit around Saturn called the Cassini Satellite, which is presently on its second extended mission known as the Cassini Solstice Mission. The satellite’s first extended assignment was called the Cassini Equinox mission. The Cassini Solstice mission will continue until September 2017. The satellite arrived at Saturn just after the planet’s northern winter solstice so it will be in space for a complete seasonal period. Saturn’s orbital period (the length of time it takes to complete one full orbit of the sun) is 29 years. During this mission, the Cassini Satellite will study the moons Titan and Enceladus. Close to the end of the mission it will more closely explore Saturn and its ring structures. 10

The spacecraft was launched with two main elements: The Cassini orbiter and the Huygens probe. The probe was designed to explore the surface of Saturn’s largest moon, Titan. When the probe landed on Titan, it allowed scientists to study the complex organic chemistry of the moon’s atmosphere for the first time. The orbiter of the spacecraft remains in orbit and takes readings and measurements from a distance. Between the two parts of the satellite, the spacecraft was equipped with the necessary instruments to gather data on 27 diverse scientific investigations. 11 A few examples of the types of instruments used are: 11

• Optical Remote Sensing –
Mounted on the remote sensing pallet, these instruments study Saturn and its rings and moons in the electromagnetic spectrum.
• Fields, Particles and Waves –
These instruments study the dust, plasma and magnetic fields around Saturn. While most don’t produce actual “pictures,” the information they collect is critical to scientists’ understanding of this rich environment.
• Microwave Remote Sensing –
Using radio waves, these instruments map atmospheres, determine the mass of moons, collect data on ring particle size, and unveil the surface of Titan.

The video below gives a brief overview of the Cassini missions and the information it has gathered over its fifteen years of exploration.

## References

2 Spahn, F. et al. (2006). “Cassini Dust Measurements at Enceladus and Implications for the Origin of the E Ring”. Science 311 (5766), pp. 1416–1418.

3 P. Goldreich and S.Tremaine. “The formation of the Cassini division in Saturn’s rings.” Icarus 34, no. 2 (1978), pp. 240-253.

5 Malhotra, R. “Orbital Resonanec and Chaos in the Solar System.” Solar system Formation and Evolution ASP Conference Series, (1998). 149.

6 Murdin, P., Cassini, Gian Domenico [Giovanni Domenico Jean Dominique known as Cassini I] (1625-1712) from Encyclopedia of Astronomy and Astrophysics, (2000). 1, pp. 3523.

## Planetary History Written in Saturn’s Rings

By: AAS Nova September 9, 2019 0

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Saturn may appear calm and motionless from afar, but the immense planet is subtly pulsing and oscillating — and those oscillations impose a pattern on the planet’s rings that could tell us about Saturn’s history.

This natural-color image from the Cassini spacecraft reveals Saturn's famous rings in detail.
NASA / JPL-Caltech / Space Science Institute

### A Planet in Motion

This extreme close-up of Saturn’s rings from Cassini shows the alternating dark and light bands of spiral density waves.
NASA / JPL-Caltech / Space Science Institute

As the Cassini spacecraft orbited Saturn, it watched light trickle through the planet’s icy rings as they passed in front of distant stars. The flickering starlight revealed density waves — alternating stripes of compacted and loose material. Those density waves tell us much more than just what’s going on in the rings — they also tell us about the motions of Saturn’s surface.

Yanqin Wu (University of Toronto, Canada) and Yoram Lithwick (Northwestern University) combined observations and theory to study Saturn’s surface oscillations. They found that impacts from small objects were the most likely cause of the oscillations, with convection and atmospheric storms playing a minor role. Each of those impacts caused Saturn to “ring” like a bell, and the volume of the “sound” that we hear now depends on how hard it was struck, how many times, how long ago, and how quickly it fades.

### Ringing Like a Bell

Energies associated with different oscillation modes as derived from Cassini observations (black squares) and theory (colored circles and grey dashed line). While the impact theory matches the observations well for high l-values, it’s several orders of magnitude too low at low l-values. Alternative explanations, shown in the right-hand plot, match the data more closely at those low l-values. Click to enlarge.
Wu & Lithwick 2019

Saturn’s oscillations diminish as energy is carried away by the density waves in its rings, a process that can take up to 20 million years. By considering the expected frequency and size of impacts over that time period, the authors find that collisions in the distant past could have imparted enough energy to set Saturn ringing in the way we see today — with the exception of a few oscillation modes.

The authors explored several possibilities to explain the mismatch. Saturn could have experienced a once-in-a-million-year impact within the past 40,000 years — a so-called “lucky” strike. It’s also possible that some oscillation modes fade away more quickly than others or that energy is transferred between modes.

Another intriguing possibility is that those missing modes are excited not by impacts but by something more exotic: rock storms. These massive storms might begin deep within Saturn, where the atmospheric pressure is roughly ten thousand times higher than the pressure at Earth’s surface. Since it’s still not clear whether these massive storms actually exist, the authors acknowledge that the theory can’t yet be proved or disproved.

Simulations of two potentially observable signatures of the impact of a 150-km object: gravitational moments (left) and radial velocity (right).
Wu & Lithwick 2019

Simulations of two potentially observable signatures of the impact of a 150-km object: gravitational moments (left) and radial velocity (right). [Wu & Lithwick 2019]

### From One Gas Giant to Another

Could oscillations be used to learn about the impact history of other planets? Since Jupiter lacks an extensive ring system to act as a dampener, any impact-induced oscillations would last far longer — potentially as long as billions of years — and we may be able to spot them.

To show this, Wu and Lithwick estimated how Jupiter would respond to a collision with a 150-km body a billion years ago. They found that the resulting changes in Jupiter’s gravitational field and surface velocity should be detectable by Juno and ground-based spectroscopy, respectively. With further study, we may be able to read the oscillations of Saturn and Jupiter to look back in time.

Citation
“Memoirs of a Giant Planet,” Yanqin Wu and Yoram Lithwick 2019 ApJ 881 142. doi:10.3847/1538-4357/ab2892

This post originally appeared on AAS Nova, which features research highlights from the journals of the American Astronomical Society.