The Rings of Saturn

Sonny Vo
December 16, 2007

(Submitted as coursework for Physics 210, Stanford University, Spring 2007)

Fig. 1: The rings of Saturn. An image both ethereal and impressive to the senses. (Courtesy of JPL)

A Brief History

The rings of Saturn present a view that is both breathtaking and ethereal. The rings consists of a collection of thousands of ringlets made up of billions of ice pieces. The size of the ice chunks range from a piece of grain to many meters in diameter.

The storybook to the rings of Saturn first opened when Galileo, in 1610, pointed his primitive 20x telescope towards Saturn. He saw strange appendages which he thought to be moons. His understanding improved two years after, in 1612, when he was able to discern the disk-like structure of the rings. Galileo hypothesized these structures to be a solid ring. Subsequent to Galileo's observation, the rings of Saturn became one of the great mysteries in astronomy and captured the interests of many great scientists.

Many theories have emerged to explain the observation of Saturn's rings. For example, it was thought that the rings consisted of multiple moons. This explanation was readily modified for observable discrepancies by proposing that some of the moons were situated on the dark side of Saturn and thus no silhouette of the moons were seen. Christann Huygens, in 1655, regarded them as solid disks. This proposal inspired numerous attempts to understand the rings in the ensuing centuries. Laplace, in the late 1700s, was one of the first to propose a convincing theory against the solid-disk hypothesis. He found that if the rings were indeed a disk, the centripedal, gravitational and centrifugal forces would act on the center of the disk resulting in instabilities. As such, the small thickness of the disk versus the length of the disk would cause the edges to tear apart due to mechanical stress. However, Laplace retained the spirit of the disk model by stipulating that the rings were made up of numerous concentric ringlets.

It was James Clerk Maxwell, in the mid-1800s, who put forth a many-body model of the rings which came to be known as the "meteorite" model. He showed that the rings could only be stable if the average distance of separation between any two objects is greater than the objects themselves. Maxwell also considered the case of rings made out of liquid but the requirement would be an extremely low density in order for it to be stable. Furthermore, observations did not show specular reflection of the planet Saturn as would be expected should the rings be composed of liquid.

Some Properties of the Rings

The major boundaries and gaps of the rings labeled inward to outward: D, C B, A, F, G and E are named in the order of their discovery. The A, B and C rings form the major sections of the ring and have widths of 14,600 km, 25,500 km, and 17,500 km, respectively. There are numerous gaps amongst the rings, many of which are still inexplicable. The major gaps are named after famous scientists such as the Maxwell gap (1.45 Saturn radii), or the Huygens gap (1.95 Saturn radii). Gap formations can be attributed generally to orbital resonances which occurs when two bodies such as a moon and dusk or rocks from a region in the rings exert a mutual gravitational interaction. This interaction causes an angular momentum transfer which results in the dusk or rocks to spiral out of the resonant region, thus, leaving behind a gap.


The physical thickness of the rings have been estimated from measuring the brightness of the ring upon the passage of the Earth at zero elevation angle. This event occurred in 1966. The thickness of the rings can be found by measuring the flux of the intensity, using the relation

I/Lbc= bez/bc

where I is the total light emanating from the ring, L is the radial extent of the rings, bc is brightness at the center of Saturn’s disk. The fraction is related to the brightness of the edge of the rings, be, times the thickness, z. By making the assumption that be is equal to the average brightness of ring B, bB, which is a known value, z can be determined. However, the precise measurement of the flux is position sensitive and may suffer from errors due to light emanating from the face of the rings. Several independent estimates have yielded values between 2.8 to 1.6 km with a large error bar of around 1.5 km. Theoretical calculations taking into account estimated volume density, particle size and optical thickness yielded a value of 0.1 km. The precise value of the thickness of the rings, or even ringlets, is still a topic of debate and continual refinement. The present thickness of the rings can range from 10-30 meters for the A rings to about a 1 km as observed from Earth. Voyager spacecraft observations give the upper bounds to be about 100 to 200 m. [2]

Chemical Composition and Temperature

Recent study of the major Saturnian rings via reflectance spectroscopy have found the main chemical composition to be of crystalline water ice (A and B rings studied at 0.3 to 1.0 µm range) and amorphous ice and C-H (C ring studied at 3.1, 1.73 and 3.4 μm). Table 1 summarizes the size and chemical composition of the major rings. Furthermore, no evidence of spectral peaks for CH4, CO , N2, CH3OH, NH3OH, or CO2 were found. More compelling and interesting data came from the recent Cassini mission to Saturn. Cassini carried with it a Cosmic Dust Analyzer. The in situ measurement unambiguously revealed water-ice in the E and G rings, also known as the ‘dusty’ rings. In addition to water-ice, trace amounts of ammonia, acetylene, hydrogen cyanide, and propane were detected. This result is interesting since the dusty rings have a low optical depths and so standard spectroscopic techniques cannot clearly distinguish the chemical spectral peaks. Furthermore, the data can be used to better understand the properties of Enceladus, one of the major moons of Saturn. The motivation for this is the high density of the E ring near the orbit of Enceladus, which may be due to emissions from volcanic activities on Enceladus. [4]

Table 1: Composition of major rings compared to particle size. [3]
Major Ring Abundance (Vol %) Grain Size (μm) Component
A 57.0 10 water ice
29.7 130.0 water ice
11.0 1300.0 water ice
2.3 10.0 amorphous carbon
B 46.0 13.0 water ice
31.0 130.0 water ice
15.0 1400.0 water ice
8.0 10.0 amorphous carbon
C 57.0 1100.0 water ice
15.0 7500.0 water ice
28.0 30.0 water ice

The temperature of the rings of Saturn were measured in the 1970s to be of the order of 90 K. These early measurements were made by taking fluxes from different ring tilts. The Cassini infrared spectrometers gathered the optical depth spectra from the major rings.The data were collected in spring of 2004 with several hours integration at the major rings on the morning or afternoon ansa. The temperature is found through fitting a blackbody function to the average spectrum. It was found that the optically thick portions of the ring can be 20 K to 40 K cooler than the optically thin regions. The range of temperature from rings C, B and A was shown to be as large at 65 K to 125 K. [5]

The Origin of the Rings

The Saturnian ring system played a crucial role in the early theory of the origin of the solar system. The planets and suns are a product of the mass of early nebular gravitating together. The same explanation has been used to explain the origin of moons. Saturn is a scene whereby the mass and dust remain scattered and did not cohere into moons or planets.

Three contending theories have been proposed to answer the question of the origin of the rings: 1. the "tidal" theory, 2. the "condensation" theory and 3. the "impact" theory. [1] The tidal theory stipulates that the present supply of dusk and large rocks making up the ring's constituents were the result of fragmentation from a larger body like a moon or meteoroid. If an orbiting body is within the Roche Limit (first analyzed by Roche in 1847) given by


where D is the critical distance from the primary (Saturn), R is the radius of Saturn equal to 60,278 km, ρP and ρS are the mean density of the primary and satellite, respectively, the particle will break up due to force imbalance. This is conceptually similar to what Laplace had hypothesized for the solid disk. Silicate has a mean density of 3 gm cm-3 giving its Roche limit of D/R=1.49. This equation assumes liquid satellites which would be perfectly elastic . Extension of the analysis to solid bodies in the 1970s let to a modified Roche limit given by


Inverting this equation and setting D=R, we can get the minimum size of a particle


where α is the satellite radius, G is the gravitational constant, and ƒ is the tensional strength which for silicates and water is about 108 and 107 dyn cm-2, respectively. The lower bound on α is estimated at about 70 km for water-ice and 40 km for silicate objects. Below this limit, the particle will be fragmented. This limit is far greater than the dusk and meter-sized objects that make up the Saturnian rings. Hence, the tidal theory suffers from this major drawback.

The condensation theory posits that the rings arose from the early primordial solar nebula. The dusk clumped together forming larger solid matter. Heat radiation from the dusk cooled matter over time and facilated gravitational accretion. Furthermore, mutual attraction amongst the matter enhanced accretion rate. Large satellites were prevented from forming by the tidal forces. By estimating particle settling time and taking various numerical estimates, many conclusions had been extracted. For example, it was found that Jupiter’s condensation temperature was too high for ice formation within the Roche limit and hence the gas had dissipated.

The impact theory claims that the rings are a product of a high rate of meteoroid collisions with pre-existing orbiting bodies around Saturn. The escape velocity from the Saturn system is about 30 km/s which would be much greater than the ejecta velocities. This theory requires that the orbiting bodies be large, constrained by the pointing-Robertson effect which considers the body as non-perfect absorbers scattering incident sunlight. The process of absorbing or scattering light produces a drag force causing the particle to spiral into Saturn. The minimum particle size possible as a result is 2 cm for silicate and 6 cm for water-ice. [1] Below this limit, particles would be leave the ring system and be lost. Continual impact from meteors and subsequent inter-collisions amongst the orbiting rings produce the current particle size and distribution of the Saturnian rings as seen today.

The Future

The study of the Saturnian ring system have yielded a plethora of data unveiling its many remarkable physical properties. The thickness of the rings, its chemical composition and temperature are discussed here as a mere primer. The richness of details and wonders of interconnected facts that have aggrandized across the centuries since the time of Galileo can easily span many tomes. Numerous directions and angles of physical and mathematical approaches have been used in order to glimpse at a greater understanding of the rings of Saturn. Such attempts range from using the ring’s emissivity as a second approach to derive the effective temperature to the incredible ingenuity and diversity of models and simulations that have arisen in the past several decades to understand even one ringlet or even one moon such as Titan, the second largest moon in the solar system, or Phoebe, which is the outermost satellite and suspected to be a captured asteroid; perturbations amongst the meter-sized rocks to magnetospheric effects are but some of the dynamics one can spend a human lifetime to investigate.

Indeed, the tale of the rings of Saturn is a storybook filled with constant revisions and improvements in the art of experimental and theoretical science. With all the musings of science and philosophy, when we look up into the night sky towards Saturn with a modern "primitive" telescope which Galileo would have regarded as a feat of technological ingenuity, our sense of the calm and solitude of this spectral wonder of the night sky can best be captured by Christiaan Huygens' description:

"Annulo cingitur tenui, plano, nusquam cohaerente, ad eclipticam inclinato." (It is surrounded by a thin flat ring, nowhere touching, and inclined to the ecliptic.) - CHRISTIAAN HUYGENS, 1656

©2007 Sonny Vo. The author grants permission to copy, distribute and display the work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] J. B. Pollack, "The Rings of Saturn," Space Sci. Rev. 18, 3 (1975).

[2] H. A. Zebker and G. L. Tylor, "Thickness of Saturn's Rings Inferred from Voyager 1: Observations of Microwave Scatter," Science 223, 396 (1984).

[3] F. Poulet and J. N. Cuzzi, "The Composition of Saturn's Rings A, B and C from High Resolution Near-Infrared Spectroscopic Observations.
A&A 412, 305-316 (2003) <>.

[4] J. Hunter Waite, Jr. et al., "Cassini Ion and Neutral Mass Spectrometer: Enceladus Plume Composition and Structure," Science 311, 1419 (2006).

[5] F. M. Flasar et al., "Temperatures, Winds, and Composition in the Saturnian System," Science 307, 1247 (2005).