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# Greeks, Trojans, and a Temporary Companion for Uranus

The views expressed are those of the author and are not necessarily those of Scientific American.

A tiny body (circled) orbits just ahead of Uranus...for now (Image: Mike Alexandarsen)

A telescopic survey looking for trans-Neptunian objects has chanced across a 37 mile wide chunk of rock and ice that instead moves around the sun in the same orbit as Uranus, just further ahead of the planet. This discovery is notable because such objects cannot stay in place for long – unlike planets such as Jupiter or Neptune where co-orbital pieces can stay for billions of years, for both Saturn and Uranus these must be temporary homes.

Stable co-orbits are funny things, and this particular type exists due to the combination of gravitational pulls from the Sun and a planet (as long as the planet is less than about 1/25th the mass of the Sun) and the movement of objects.

Although it’s often stated that they’re the result of ‘gravitational forces balancing out’ (which is true), the properties of these special orbital locations are not quite so simple. The great mathematician Joseph-Louis Lagrange figured this out in 1772 (Euler also solved some of the problem a little earlier). You can think of it as really the combination of gravitational forces from two larger bodies and the centripetal force acting on a third, smaller, orbiting mass.

The equi-potential contours surrounding a star and planet in orbit.

We can map out these forces in the form of a plot of ‘effective potential’, with contour lines that represent a fixed size of force on the body. The closer the contours, the greater the gradient in forces, and the stronger the pull if you stray into these zones.

Lagrange found that there are 5  points of equilibrium in this map, places we now, not surprisingly, call Lagrange points. Put the third, small, object at these places and it’ll orbit in-sync with the planet. Except that points L1, L2, and L3 are not stable – move a little off the sweet spot and you’ll soon get pulled away.

The L4 and L5 points are different, they’re at the center of great gentle mounds in the effective potential – those kidney-shaped zones. So objects at L4 or L5 tend to just meander around these points, even if they stray a bit, they’ll usually come back.

Map of major asteroids - showing the Greeks and Trojans co-orbiting with Jupiter (Public Domain, Wikipedia, Mdf)

It’s for this reason that Jupiter, and Neptune, have large populations of asteroidal-type material around their L4 and L5 Lagrange points. Historically the populations of stuff co-orbiting ahead (L4) and behind (L5) Jupiter have been called ‘Greeks’ and ‘Trojans’ respectively.

Over time we’ve gotten sloppy, and tend to refer to all L4 and L5 material in any circumstance as ‘Trojans’, and to just ‘trojan points’ in an orbit.

Studies of the long-term stability of Trojans in our solar system indicate that the subtle, but persistent, mix of forces at play causes objects co-orbiting with Saturn or Uranus to have a relatively short lifespan – in other words, the L4 and L5 points are not perfectly stable over millions of years.

So what of Uranus’s new companion, now named 2011 QF99? Its place around the L4 point is almost certainly temporary. Simulations suggest that it has probably not been there for more than about 10 million years, and is likely a captured Centaur – a class of asteroid or comet that follows somewhat perilous orbits through the terrain of the giant planets.

It is also unlikely to stay in this relatively safe haven for more than a million years from now, before drifting off again. But, by spotting it astronomers now have an extra piece of statistical leverage to evaluate just how many bodies like this get snared by trojan points amongst the outer worlds. And there are no great surprises, it agrees with the pre-existing estimate that some 2-3% of Centaurs are at any one time co-orbiting a giant planet.

About the Author: Caleb Scharf is the director of Columbia University's multidisciplinary Astrobiology Center. He has worked in the fields of observational cosmology, X-ray astronomy, and more recently exoplanetary science. His books include Gravity's Engines (2012) and The Copernicus Complex (2014) (both from Scientific American / Farrar, Straus and Giroux.) Follow on Twitter @caleb_scharf.

The views expressed are those of the author and are not necessarily those of Scientific American.

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1. 1. ladyofshallot18 6:16 pm 10/4/2013

This is very interesting! I always wondered what made certain things go in and out of orbits of planets and other celestial objects. Considering that Q99′s home with Uranus is only temporary, doesn’t that mean that Uranus’ mass fluctuates, or at least veers away from the 1/25 ratio? I had to dig deep for information on this planet, but it seems like we are discovering more and more about it as the future progresses. I even saw an article on a new moon being spotted orbiting it! Hopefully someday we can figure out how to land on its surface so that we can explore.

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