Astrophile: The Most Cruel Death of Cupid and Belinda

Objects: Cupid and Belinda, doomed moons of Uranus
Orbits: A lamentable collision course

A pair of star-cross'd lovers orbits Uranus, and when they rush to meet their fate, the duo could leave the cosmic stage littered with more bodies than the final scene of Hamlet.

But the deaths of the moons Cupid and Belinda might not bring down the curtain on Uranus's satellites. Instead they could mark the beginning of a cycle between moons and rings that has been the central drama of the Uranian system for hundreds of thousands of years.

Named mostly after characters in Shakespeare plays, Uranus's inner moons are a tight and mysterious group. They orbit closer to the planet and each other than any other set of satellites in the solar system, packing 13 moons into the space of 10,000 kilometres.

Earlier work from 1997 suggested the inner moons would bump into each other, and often. Since then, three new inner moons ? Perdita, Cupid and Mab ? have been discovered in archival data from Voyager 2 and new images from the Hubble Space Telescope.

Robert French and Mark Showalter of the SETI Institute decided to run orbital simulations to see if the new moons were also in danger.

The result: "Something bad always happened," French says. "Almost no matter what assumptions we make, Cupid is going to die."

Tale of woe

The most important plot points are the moons' orbits and their masses, which reveal how they will affect each other via gravitational interactions. But the moons are so small and dim that little is known about them except for their sizes and their relative positions when telescopes happened to be looking.

French and Showalter ran thousands of simulations to see if a trend emerged, varying the masses of the moons and re-calculating their orbits each time. They checked the solutions to see if any moons crossed orbits, a sign that they are nearly certain to collide.

"It almost didn't matter what the masses were: certain pairs of moons almost always crossed orbits on very short time stamps," says French. "There were never systems where it was stable and nothing happened."

In the first act, Cupid smacks into the larger moon Belinda sometime between 1000 and 10 million years from now, depending on initial conditions. What happens next depends a lot on the moons' as-yet-unknown compositions. They could bounce off each other, stick together or break apart into tiny pieces.

In some settings, French and Showalter assume Cupid and Belinda will merge to form a single moon called CupBel. From there, the next pair of doomed moons is Cressida and Desdemona, fated to crash in 100,000 to 10 million years. If those moons merge, the resulting body, Cresdemona, takes out the moon Juliet, and CupBel collides with Perdita.

But just as the bloodbath in Hamlet ends with the prince's death, Uranus's satellites calm down after the carnage, French says.

Recycling rings

The authors think Cupid and Belinda are more likely to break apart than stick together. However, even that scenario leads to multiple collisions, which could solve another of the planet's mysteries.

Material close to a planet tends to get pulled apart into rings, while debris that's sufficiently far away can clump together to form moons. In addition to a traditional set of rings and moons, Uranus has a small, faint ring in an anomalous place, just inside the orbit of Cupid. That moon, meanwhile, has such a short life expectancy that French is surprised it exists.

"So we have this ring that shouldn't be there because it should be a moon, and a moon that shouldn't be there because it should smack into something and create a ring," he says. "Perhaps there is a cycle going on."

French suggests that the inner moons and rings are constantly recycling in a process similar to what's happening in Saturn's F ring. "Maybe this isn't the end of Cupid's life," he says. "Maybe it's the middle or the beginning, and it's just not going to last very long."

But Hal Levison, of the Southwest Research Institute in Colorado, says he's dubious that the Uranian moons are players in a cosmic tragedy. Levison is a co-author of the Nice model of the solar system, in which the planets started out in unstable orbits and tossed each other around until they found the stable positions they inhabit today.

The situation in the early solar system was just as chaotic as what's happening now around Uranus, he says, but the planets still found a peaceful ending.

Journal reference: Icarus, DOI: 10.1016/j.icarus.2012.06.031

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