Saturn's moon Telesto is seen here in a 2005 image captured by the Cassini spacecraft. Telesto is one of four Saturnian moons in the unique Trojan configuration. Image credit: NASA/JPL-Caltech/Space Science Institute

Sep 1, 2015 Moons control moons at Saturn

Sen—I’ve often said that visiting Saturn is like having an entire universe to explore right here in our own Solar System. Want to know how tides can transfer energy? Enceladus and its ocean of liquid water are a fascinating example. Wondering how the gravity between particles can lead to large-scale clumping? The tumultuous F ring is among the most dynamic systems ever studied. Are extrasolar planets more up your alley? Titan could prove an excellent model for terrestrial worlds across the galaxy.

So it shouldn’t have surprised me as much as it did to learn that Saturn is home to a another curious kind of object: Trojans. In fact, at Saturn we’ve found not one or two, but four objects in this remarkable configuration.

Our journey to understand the Trojans will take us through the history of a field known as celestial mechanics, the prediction of the motions of the heavenly bodies. And, like a remarkable number of stories in science and mathematics, we’ll pick this one up with Isaac Newton.

Before Newton, a field known today as astrometry was the principal focus of astronomers. Astrometry is the charting of the positions and motions of celestial objects and it may well be the oldest area of scientific inquiry. For thousands of years, cultures all over the world have known the motions of the stars well enough to recognize that five of the thousands of pinpricks of light visible to the unaided eye were different from the rest. Today we know them as the planets Mercury, Venus, Mars, Jupiter, and Saturn.

All the planets moved with a similar shape, deduced by Johannes Kepler to be the squashed-circle-like ellipse, but until Newton we didn’t know why this was so. His theory of gravity provided the foundation on top of which generations of astronomers have built an understanding of the Universe.

Gravity as Newton described it is as simple as it is far reaching. The attraction felt between two objects is proportional to their masses and inversely proportional to the square of their distance from one another. Double the mass of an object and it pulls twice as hard; move it double the distance and its tug is just a quarter as strong.

Armed with this handy formula, mathematicians and physicists set forth to predict the motions of all sorts of objects in the Solar System. Quickly, though, they encountered a frustrating situation: while perfectly predicting the movement of one object due to the gravity of another was easy, predicting an object’s trajectory under the influence of two other bodies was nigh impossible.

In fact, it wasn’t nigh impossible, it was simply impossible. The so-called three-body problem is one of the great unsolvable mysteries of physics. Undeterred, mathematicians began to look for a way around this roadblock. Eventually two kinds of solutions were uncovered. Both abandoned the quest for an (unattainable) exact answer in favor of one that was good enough.

In a method employed today with the assistance of computers, the equations governing the motion of a particle can be solved step by step numerically to whatever precision was necessary. At each turn, the position and speed of each object is be approximated and plugged back in to find out what happens next. This technique has enabled the precise navigation employed by every interplanetary mission. The other approach is to make one grand approximation at the start and then return to the comforting (at least if you’re a mathematician!) world of equations.

It was in this latter method that a home for the Trojans was discovered. Known today as the restricted three-body problem, this method assumes that the third object in your collection has a mass that is insignificant compared to those of the other two. In such a case, the tiny particle experiences the pull of both other objects, but doesn’t meaningfully pull on them. This allows for simple equations predicting the motion of each to be discovered.

In the mid-1700s, mathematicians noted something unusual. These equations, they found, suggested that there were orbits that small objects could take which would cause them to circle the Sun in exactly the same amount of time it takes the Earth to complete the same journey. Thus, unlike all the other bodies in the Solar System, the positions of these objects would remain fixed relative to the Earth.

Leonhard Euler discovered three such locations corresponding to the three relative positions on the Earth-Sun line: one behind the Earth, one behind the Sun, and one partway between the two. A few years later, Joseph-Louis Lagrange would find two more. Today, we refer to all five of these locations as “Lagrange points.”


This diagram, not to scale, shows the locations of the five Lagrange points in the Earth-Sun system. Image credit: Xander89

All five points are not the same, however. The three discovered by Euler are what physicists call unstable: the tiniest deviation from the optimal path would cause an object to spiral out of control. Only the two deduced by Lagrange could provide a safe haven for interplanetary objects. The so-called L4 and L5 points exist at the third corners of the equilateral triangles defined by the other two bodies—a fact that would have tremendously pleased the geometry-obsessed ancient Greek astronomers.

When a tiny deviation tries to drive an object away from L4 or L5, something remarkable happens. The Coriolis force—the same mechanism that spurs the creation of hurricanes here on Earth—kicks in and curves the wayward trajectory back towards the Lagrange point. Objects actually end up orbiting around that point as if it had some invisible mass. Dark Matter need not apply!

To the mathematicians of the 18th century, all this seemed too perfect to actually exist in the real, physical world. And, for a while, evidence (or lack thereof) would seem to be on their side. It would take more than a hundred years for the first Lagrange-bound object to be discovered: asteroid 588 Achilles. Achilles orbits ahead of Jupiter near the planet’s L4 point. The first Trojan had been uncovered.

Soon, a torrent of similar objects were found near the L4 and L5 points. Astronomers, always on the lookout for the chance to name new things, developed perhaps the most unique naming scheme in all of planetary science for these new worlds. Noting that they formed two clusters on opposite sides of Jupiter, scientists began to name them after participants in the Trojan War of the Iliad—two “camps” of heroes kept at arm’s length by the Roman king of the gods.

(In an unfortunate twist of fate, two asteroids were named for members of the opposite side before this scheme was formalized. Asteroids 617 Patroclus and 624 Hektor are forever doomed to roam behind enemy lines!)

Today we know of more than six thousand Jupiter Trojans. That’s likely just the tip of the iceberg: astronomers believe there are hundreds of thousands, perhaps even a million, of large Trojans. That’s a population similar in number to the main asteroid belt!


The two groups of Trojan asteroids ("Trojans" and "Greeks") are seen here in green relative to the main belt asteroids, depicted in white. Image credit: Mdf

Jupiter doesn’t have a monopoly on the Trojans. Earth, Mars, Uranus, and Neptune each have at least one known Trojan. An untold number probably exist, especially around the outer planets. Asteroids are relatively-small, dark objects, making their detection at distances as far as Saturn, Uranus, and Neptune a real challenge.

There’s nothing about Trojans that is specific to planets and asteroids, though. Lagrange points exist for objects of any type, a fact that was driven home by a surprising discovery in 1980.

Astronomers making ground-based observations of Saturn discovered a number of never-before-seen moons, including three Trojans. But these objects weren’t trapped in the triangle formed by the Sun and Saturn like Jovian Trojans are. Instead, they were stuck in the Lagrange points of larger Saturnian moons! A fourth such object was discovered by NASA’s Cassini spacecraft upon its 2004 arrival at Saturn.

The planet’s moon Tethys hosts Trojan moons Telesto and Calypso, while Dione retains Helene—named for Helen of Troy, the woman whose beauty mythically launched the Trojan War—and Polydeuces. The relative size between these moons isn’t nearly as vast as for the Jupiter Trojans, but it’s still enough for the restricted three-body approximation to hold true. Tethys, for example, weighs just 86,000 times as much as Telesto, while Jupiter is more than a billion times more massive than even the largest Trojan asteroids.

Until Cassini arrived on the scene, we had no idea what these Trojan moons would look like. With its powerful Imaging Science Subsystem, the spacecraft gave us our first up-close views of these strange worlds. What images and other observations have revealed are that the Trojan moons resemble not asteroids but other small moons of Saturn.


The largest of the Trojan moons is Helene, named for Helen of Troy and seen here in black and white against the backdrop of Saturn's cloudtops. Image credit: NASA/JPL-Caltech/Space Science Institute 

So how did these four moons end up trapped in Lagrange points?

We don’t yet have a complete picture of how the moons of Saturn came to be, but some recent research has painted a plausible picture. One of the most striking facts about the Saturn system is that the rings and many of the moons seem to be composed nearly entirely of ice. Had they formed alongside Saturn during the early days of the Solar System, we would expect them to include a mix of rock and metal, just like the planet itself.

A theory advanced by Robin Canup, among others, suggests that the rings may have formed out of the breakup of a giant, Titan-like moon. As the doomed world spiraled in towards Saturn, its icy exterior was stripped off to become a more massive version of today’s rings, while its rocky interior plunged deep into the planet.

If indeed the early rings were far more massive than they are today, Aurélien Crida and Sébastien Charnoz think they have an idea of how many of Saturn’s moons came to be. Today we observe that in the F ring the gravity between particles can bring them together to form a clump of material. Because the rings are presently so close to Saturn, the planet’s immense gravity rips these clumps apart before they grow too large. But in the distant past, a much-larger ring system would’ve extended farther from the planet and more massive objects could have developed.

Under the right conditions, these clumps could attain the size of Saturn’s moons. As they grew, they would migrate outwards until they squirted out from the rings. They could continue to move outwards through empty space by tugging on the rings, much in the same way our Moon is slowly receding from the Earth. Eventually they could blunder into the Lagrange points of larger worlds like Dione and Tethys, becoming trapped in their new Trojan lives.

But becoming a Trojan object doesn’t have to be an accident. We’ve stashed a bevy of spacecraft at Earth’s Lagrange points with the Sun because they provide an ideal perch for certain kinds of observations. The unstable L2 point is a particular favorite because, although it requires the use of fuel to keep in the proper place, the Earth, Moon, and Sun are all clustered in one part of the sky. This gives telescopes an unblemished view of the Universe.

When it launches in 2018, NASA’s James Webb Space Telescope will follow in the footsteps of famous telescopes like WMAP, Herschel, and Planck in setting up shop at L2. Of course, unlike Hubble, this places JWST out of the reach of repair or upgrade missions.

Our interest in the Trojans doesn’t stop there. In the 2013 Decadal Survey, a list of science priorities for the coming decade assembled by the planetary science community, a mission to the Jupiter Trojans is listed as one of five high-priority medium-class missions. In combination with the Dawn spacecraft currently in orbit about the main-belt asteroid Ceres, a Trojan explorer could help us understand the difference between asteroids in the main belt and ones trapped near Jupiter. Such information could be a key detail in helping to untangle the history of the Solar System.

Until that time, however, our closest encounter with any Trojan object will remain the four small moons of Saturn observed from afar by Cassini. They hint at the Solar System’s far more dynamic past and remind us once more that studying Saturn is like having a whole universe of discovery just down the block.