Chaos can explain the seemingly random behavior of two moons of Saturn, JPL researchers say. The moons — Pandora and Prometheus — are more than 100,000 miles off course of where they would be if their orbits followed conventional physics. “With chaotic interactions, a barely perceptible difference in starting conditions can make such a great difference in later positions that the movements are not fully predictable over time. The two moons give each other a gravitational kick each time Pandora passes inside Prometheus, about every 28 days. Because neither’s orbit is quite circular, the distance between them on those occasions — hence the strength of the kick — varies.”
From the Jet Propulsion Laboratory:
Chaos Seen in Movement of Ring-Herding Moons of Saturn
October 11, 2002
Scientists have a new explanation for weird movements of two small moons that shepherd one of Saturn’s rings: Pandora, which keeps the narrow F ring from spreading outward, and Prometheus, which rides herd along the same ring’s inner edge.
Observations of the pair in recent years found them far from where they should have been based on orbital movements calculated from NASA’s Voyager spacecraft observations during Saturn flybys in 1980 and 1981. Pandora is about 20 degrees farther around in its orbit than it would be if it had followed standard physics for the past two decades. Prometheus lags behind its predicted position by about the same amount. At the size of these moons’ orbits, 20 degrees is more than 160,000 kilometers (100,000 miles).
“Chaotic gravitational interactions between them can fully account for these discrepancies,” said Dr. Nicole Rappaport of NASA’s Jet Propulsion Laboratory, Pasadena, Calif. She and Prof. Peter Goldreich of the California Institute of Technology, Pasadena, reported the new explanation this week at the annual meeting of the American Astronomical Society’s Division of Planetary Sciences in Birmingham, Ala.
With chaotic interactions, a barely perceptible difference in starting conditions can make such a great difference in later positions that the movements are not fully predictable over time. The two moons give each other a gravitational kick each time Pandora passes inside Prometheus, about every 28 days. Because neither’s orbit is quite circular, the distance between them on those occasions — hence the strength of the kick — varies. The perturbations lead to changes in motion that are not periodic or predictable, say Rappaport and Goldreich.
They had predicted 20 years ago that Pandora’s motion might be chaotic. “This is like a dream come true,” Goldreich said of the observations that fit the prediction. For him, it’s a recurring dream, since he and Dr. Scott Tremaine, then a post-doctoral fellow at Caltech, also predicted the very existence of shepherd moons — confirmed later by Voyager — as an explanation for the narrowness of the F ring.
By the principle of action and reaction, the same transfer of momentum by which Pandora pushes F ring particles inward toward Saturn and Prometheus pushes them outward should also gradually push the two moons away from the ring. The effects of Saturn’s wider A ring, which is just inside the F ring, are even more important in pushing the moons outward. The F ring would slowly widen. So, although the discovery of the shepherd moons fulfilled a scientific prediction explaining the current narrowness of the F ring, it led to more questions about the longer-term history and fate of the ring and shepherds.
One theory among several has been that the ring must be quite young to still be so narrow, perhaps about 10 million-years-old. But in proportion to the age of Saturn itself, that would be as if the ring were created in the last three minutes of a 24-hour day, and some scientists believe it unlikely that we would happen to witness such a rare event. Another theory, proposed by Rappaport, Goldreich and Tremaine in 1982, is that Pandora’s movement includes an element of chaos.
The story took a further twist in the mid-1990s, while Saturn’s rings were edge-on toward Earth so the timing was good for observing Prometheus and Pandora with NASA’s Hubble Space Telescope. Analysis of those and subsequent observations by several researchers in New York and Massachusetts revealed that each moon was about 20 degrees from where normal orbital mechanics would have put it. This was an amazing discovery. For the first time ever, astronomers found that they could not predict the orbits of objects in the sky.
Goldreich and Rappaport have demonstrated that chaotic orbits of the F ring shepherds could produce changes in location very similar to those observed with the Hubble Space Telescope. “The chaos is due to the gravitational interactions between the two moons,” Rappaport said. “This is the first observation ever of chaotic orbital motions in the solar system.” A larger moon of Saturn, Hyperion, is already known to have chaotic rotation around its axis.
Goldreich and Rappaport hope they have found the piece of the puzzle that will help resolve the problem of the age of the rings.
JPL, NASA’s lead center for robotic exploration of the solar system, is managed for NASA by the California Institute of Technology, Pasadena.
Contacts: JPL/Guy Webster (818) 354-6278
California Institute of Technology/Robert Tindol (626) 395-3631