Saturn’s Rings and the Roche Limit: The Tidal Forces Shaping Celestial Wonders

Above is a diagram that will help understand tidal forces. The acceleration vectors along the vertical line point in opposite directions to an observer standing at the centre of the bulged sphere. (Think of it this way. The side of the bulged sphere closer to the red dot – the object causing the tidal bulge – is being pulled more strongly than the observer, who is in turn pulled more strongly than the side away. This makes it appear to the observer that the two ends want to go in opposite directions.) Closer to the host planet, the moon experiences a steeper gravitational gradient.

Fair enough! You and I are standing on the surface of the Earth. Certainly, we are well inside our Roche limit with the Earth. Yet, we don’t seem to disintegrate!

This is where the true story hides. The Roche limit (also called Roche radius) is the distance from a celestial body within which a second celestial body, held together only by its force of gravity, will disintegrate because the first body's tidal forces exceed the second body's self-gravitation. Picture a planet-moon system. Let’s say you stand on the surface of the moon. Next to you, is a lump of rock that stays on the ground because the moon’s self-gravity is the dominant force here (Newtonian mechanics!), the other forces being the tidal force and the normal reaction (internal pressure) of the ground, both of which point upwards, thus keeping the rock in equilibrium. Imagine, now, that the moon you are standing on is gradually moving towards the planet. As you get closer to the planet, the self-gravity of the moon remains unchanged, but the tidal force gets stronger. (Remember, the smaller the distance to the planet, the steeper the gravitational gradient.) At one point, as you may have imagined, the tidal force alone balances the gravitational pull, and beyond that point becomes the dominant force on the rock. The rock, not being glued to the surface, will rise upwards. (Real levitation!) A moon could be approximated as a lump of rocks held together by self-gravity. Although molecular bonds exist, gravity is the primary binding force in a large object, so our approximation is reasonable! In this scenario, the ‘levitating’ rock is a mere representative of lunar material at the surface, so the entire surface would begin to rise. Likewise, the particles would ascend on the opposite side, and the moon would, thus, begin to disintegrate. In the human body, though, as in most objects around us, the electromagnetic force is the dominant binding force, so you and I don’t disintegrate, fortunately! The same holds about the International Space Station, or a mango hanging by a tree. (There is a swarm of perilous space debris swarming around the Earth at high speeds. Had they clumped together due to gravitational forces (accretion), cleaning would have been much easier. This has nothing to do with the Roche limit though; planetary accretion requires several other conditions to be met.)1 Gravity is indeed a very weak force whose effects are felt only at large scales like that of a planet.

How did Saturn get its rings then? Although the exact origin remains a mystery, they likely formed when objects like comets, asteroids, and even moons got tidally dispersed into fragments by Saturn’s intense gravity. These fragments collided with each other forming smaller and more numerous pieces. Then, they would gradually spread to form Saturn’s rings. An alternate explanation is that Saturn’s largest moon, Titan, destabilized the orbit of a smaller moon 100-200 million years ago, causing it to graze the planet and consequently disintegrate. The key is that these objects are closer than the Roche limit of the larger structure (moon) they would form should they coalesce under self-gravity. Being close to the gas giant, these objects have unstable orbits and short lifetimes. Even a slight disturbance would cause them to lose kinetic energy, eventually causing them to spiral into the planet. The beginning of the disappearance of Saturn’s rings has already been observed. Saturn’s rings would probably last another 100 million years, giving the ring system a net life of 200-300 million years, which is short compared to the planet’s age of over 4 billion years. Depressing as it sounds, there is still plenty of time to study its complex ring system and be in awe of this majestic spectacle. Also, there is no reason why a new ring system could not form later.

Saturn's celestial ballet: A delicate symphony of ice and dust, woven into shimmering rings that dance eternally in the cosmic twilight.

In the vast expanse of our Solar System, beauty reveals itself in myriad forms, each celestial body a testament to the wonders of the cosmos. While planets of every hue dance in their orbits, playing a symphony of celestial artistry, nothing captivates observers more than the grand Rings of Saturn. Stretching outwards from the planet’s equator like a shimmering veil of cosmic lace, Saturn’s rings form a celestial spectacle like none other. Made up of countless icy particles, ranging in size from tiny grains to imposing chunks, the rings create a stunning interplay of light and shadow as they catch the Sun’s rays at different angles. What if I told you that the same tidal forces that caused those bulges on Earth were the architects of this astronomical magnificence?

Let’s start by looking at our beloved Moon. Our moon goes around the Earth in an elliptical orbit at an average distance of 385,000 km from us. (That’s roughly 30 Earth diameters!) Do you wish the Moon was closer to us so that the night sky would look epic, and moon trips would be more likely? Unfortunately, though, there is a limit to how close a moon can revolve around a planet – the Roche limit (thanks to the French astronomer and mathematician, Edouard Roche). Why? Picture a planet-moon system. The moon experiences planetary tides causing it to bulge, one side pointing at the planet and the other pointing directly away. The planet’s gravity pulls the near side more strongly than the far side. This difference in gravitational pull is realized as a stretching force that tries to rip apart the moon. When this difference is large enough (below the Roche limit), the moon disintegrates (much like a sponge ball stretched too much) to form rings.

1* There is an alarming scenario where the density of objects in the Low Earth Orbit due to space pollution is high enough that collision between objects will create a cloud of debris increasing the likelihood of further collisions so much that a cascade of collisions could begin leading to an exponential growth of space debris. This could render all space activities at certain orbital ranges impossible for several generations.

2* In a ring system, particles of varying sizes and masses orbit Saturn at different velocities. As particles collide or interact gravitationally, they exchange momentum, causing them to scatter and move relative to each other. This differential motion results in regions where particles are more densely packed and regions where they are more dispersed.

3* The Jovian planets, also known as the gas giants, are the four outer planets of our solar system: Jupiter, Saturn, Uranus, and Neptune. Named after the Roman god Jupiter (Jove), these giant planets are predominantly composed of hydrogen and helium, with smaller amounts of other gases and elements.

Despite the ring system stretching over 300,000 km, its vertical height is only about 10 m on average. Interestingly, Saturn’s rings will temporarily vanish from Earth’s view in 2025. However, this is nothing to worry about as this is simply due to the relative alignment of Earth and Saturn. The Earth reaches this particular vantage point every 13 – 16 years. This extraordinary thinness of Saturn’s rings is mainly due to the rapid collision rate of the ring particles in the asymmetric gravitational field caused by the planet’s oblate shape. The ring could have started out as a stream of menacing swarming moon fragments with eccentric and mutually inclined orbits. The ringlets above or below the ring have tilted orbits and have more energy than those closer to the ring plane. Collisions between these fragments, which are inelastic, would cause them to dissipate energy while conserving angular momentum, subsequently causing them to move to low-energy orbits closer to the ring plane. Tides induced on the rings by Saturn may also lead to its flattening as the ring particles would gain angular momentum and get pushed farther. Variation in the ring particle masses would cause this expansion to be differential, contributing to the thinning of the ring. 2

Another striking feature of the Saturnian ring system is the gaps in the rings where the particle density drops sharply. These gaps are maintained by embedded moons, fascinating celestial objects found in the rings of certain Jovian planets 3. When ring particles are accelerated by the gravity of an embedded moon, they gain angular momentum and move to a farther orbit. Likewise, the deceleration of ring particles causes them to lose angular momentum and move to a nearer orbit. This way, embedded moons clear a region within the ring, creating gaps in the ring. One such moon is Daphnis, which orbits within Saturn’s Keeler gap 4. Despite its small size, it has a significant gravitational influence on its surroundings, causing wave-like features in the ring material near the gap horizontally and vertically, as seen in satellite images.

Similar to embedded moons are shepherd moons. Saturn’s shepherd moons give the rings an organized and discernible appearance. Imagine two shepherd moons, one orbiting just outside and the other just inside a ring. The outer moon will push some of the ring particles inwards, while the inner moon, and the centrifugal force, will push some of these ring particles outwards. This way, the ring particles are shepherded into a ring, like a shepherd herding sheep. An example is the pair of Pandora and Prometheus, two shepherding moons believed to keep Saturn’s F-ring in place.

You might wonder how shepherd moons and embedded moons exist inside the Roche limit. The key is the small size of these objects. Every object has some degree of cohesion keeping it intact. Only when the body is large is its self-gravity the primary reason for its intactness.

The Roche limit plays a critical role in celestial dynamics. Saturn may lose its rings one day, but did you know Mars could get one? The Martian moon Phobos 5 is migrating towards its parent body and is expected to reach the planet’s Roche limit in a few million years. The weakest material will then tidally disperse, giving birth to a new ring system that could last up to a hundred million years. Neptune’s largest moon Triton 6 is expected to meet a similar fate in a few billion years.

4* The Keeler Gap is prominent in Saturn's rings, located within the A Ring, the outermost of the planet's large, bright rings. It is named after American astronomer James E. Keeler, who discovered the gap in 1888. The Keeler Gap is notable for being one of the narrowest gaps in Saturn's ring system, with a width of approximately 42 kilometres (26 miles).

One of the most fascinating features of the Keeler Gap is the presence of a small moonlet, named Daphnis, which orbits within the gap. Daphnis is only about 8 kilometres (5 miles) in diameter and creates gravitational disturbances in the surrounding ring material as it orbits Saturn. These disturbances manifest as waves and ripples in the edges of the gap, known as ‘wavemaker’ features, which were first observed in images taken by the Cassini spacecraft.

All four Jovian planets have rings systems - Saturn's is the largest and brightest of them all.

Courtesy: slideserve.com

Phobos is the larger and innermost of Mars’ two moons, orbiting the planet at a distance of only 9,378 kilometers—closer than any other moon in the solar system to its host planet. It is an irregularly shaped, heavily cratered body, measuring about 22 kilometers across at its widest point. Phobos is slowly spiraling inward due to tidal forces, and within 30 to 50 million years, it is expected to either crash into Mars or be torn apart, forming a ring around the planet. Its proximity and slow inward migration make it unique but ultimately doomed in the long term.

Courtesy: Pinterest

Saturn’s ring system is divided into several main sections, labeled alphabetically in the order of their discovery: A, B, C, D, E, F, and G rings. The most prominent and brightest rings are the A, B, and C rings.

• A Ring: The outermost of the large rings, it is separated from the B ring by the Cassini Division, a 4,800 km gap caused by the gravitational influence of Saturn's moon Mimas.

• B Ring: The brightest and most massive, located closer to the planet, containing dense and tightly packed particles.

• C Ring: Lying inside the B ring, it is fainter and contains less material.

• D Ring: A very faint and innermost ring, lying closest to Saturn.

• F Ring: A narrow, complex ring outside the A ring, shaped by shepherd moons Pandora and Prometheus.

• E and G Rings: Faint, diffuse rings made primarily of icy particles, with the E ring formed by material from the moon Enceladus.

Tell Me More

5* Phobos orbits Mars at a distance of approximately 9,378 kilometres (5,827 miles) above the Martian surface, making it one of the closest moons to its parent planet in the solar system. Unlike our Moon, it was likely captured from the Asteroid belt, not formed in orbit around Mars.

6* Triton is the largest Neptunian moon and the 7th largest in the Solar System. It has a thin atmosphere composed mainly of nitrogen. Its retrograde orbit suggests that Neptune's gravity may have captured it after originally forming elsewhere in the solar system. The capture hypothesis proposes that Triton may have been a dwarf planet or Kuiper Belt object that was gravitationally captured by Neptune.

Courtesy: SciTech Daily

A Cassini image of Saturn's embedded moon Daphnis (right) maintains the Keeler gap. Notice the gravitational ripples on the lower ring.

Test your understanding with a short quiz!