An intricate dynamical dance performed by the inner moons of Uranus could end in disaster as it appears that certain pairs of moons have the orbital equivalent to two left feet. 

Uranus is surrounded by 27 moons, which have been named after characters in Shakespeare’s plays, and 13 of these are classed as inner moons. The orbital stability of these moons has been called into question for years, and new simulations show that violent collisions will most likely occur between Cupid and Belinda, and also between Cressida and Desdemona.

The chaotic orbits of Cupid and Belinda are most likely due to resonances. A resonance is the term used when a ratio exists between orbital periods of moons or planets. For example, Neptune and Pluto are in a 3:2 orbital resonance. This means that Neptune circles the Sun three times for every two orbits of Pluto. Resonances can either cause orbits to be stable or unstable, depending on how close the two bodies come to each other.

The complicated interactions between the moons Cupid and Belinda will result in Cupid’s treacherous orbit bringing it precariously close to Belinda’s path, causing a collision between the two. The simulations suggest that this could occur between one thousand and ten million years from now. The future is also bleak for Cressida and Desdemona, where orbital crossing occurring between one hundred thousand and ten million years in the future. There is also a hint that Juliet will collide with the Cressida-Desdemona system, or “Cresdemona”, further down the line.

These timescales are dependent on the density of the moons; however no accurate measurements yet exist. The densities are thus estimated based on other information that is available about the moons. For instance, the fact that they don’t reflect much light means they probably have more rock than ice, which helps astronomers to obtain density values. If the density of these moons turns out to be higher, then the timescales before orbit crossing occurs will be shorter.

The new research also suggests that Uranus may be recycling its moons, as there is only a tiny probability that we should be observing several moons towards the end of their lives. If this is the case, then new moons will replace the destroyed objects by re-accreting from the debris. Evidence for this theory comes from the existence of the ν (nu, pronounced “new”) ring around Uranus. “It’s entirely possible that the ν ring is the debris left over from a previous collision,” explains Robert French from the SETI Institute. “We also have Cupid, which seems to be in a highly unstable orbit, and thus probably hasn’t been there for long. Both suggest that there may have been collisions in the fairly recent past, astronomically speaking.”

Crossing orbits doesn’t necessarily spell doom for other moons in the Solar System. For instance, Saturn’s moons Janus and Epimetheus not only cross orbits safely, they also switch orbits every four years. The reason that Cupid and Belinda can’t share this peculiar fate is because of their mass difference, with Belinda being 100 times more massive than Cupid. In contrast, Janus and Epimetheus have similar masses, and their orbits have low eccentricities, meaning that their orbits are almost circular rather than elliptical.

“As Cupid ‘laps’ Belinda every 70 days, Cupid has almost no effect on Belinda, but massive Belinda has a tremendous effect on tiny Cupid, often causing Cupid’s orbit to change dramatically by increasing its eccentricity,” French tells Skymania News. “As Cupid’s orbit becomes more eccentric, part of the orbit is inside of Belinda’s orbit, and part is outside. This is the ‘crossing’ that will eventually cause a collision.”

The paper is published in the August 2012 issue of Icarus. You can see a stunning view of Uranus, with rings and moons taken from Earth by Mike Brown in this Skymania report.

UK planetary scientist Chris Arridge is working to develop a potential joint mission to Uranus by NASA and the European Space Agency.