Weird Saturn Moon Movements Explained
11 Oct 2002
(Source: American Astronomical Society - Division for Planetary Sciences)
DPS Press Release
Embargoed until 9:30 AM, Fri., Oct. 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 Voyager spacecraft observations during Saturn flybys in 1980 and 1981. Pandora is about 20 degrees farther around in its orbit that 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 100,000 miles (160,000 kilometers).
"Chaotic gravitational interactions between them can fully account for these discrepancies," said Dr. Nicole Rappaport of NASA's Jet Propulsion Laboratory, Pasadena, Calif. 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 Caltech scientist Peter 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. The explanation involves the transfer of angular momentum from Prometheus to the F ring to Pandora. This results in ring particles being pushed away from each satellite, and therefore concentrating in a narrow ring.
The discovery of the so-called "F ring shepherds" by the Voyager spacecraft represented a striking success of scientific prediction. But, as is generally the case, this discovery led to more questions. The most intriguing question was the age of the rings.
While the presence of an F ring shepherd on each side of the F ring could explain the ring's narrowness, the same theory predicted that the satellites ought to move away from the rings. Indeed, from the principle of action and reaction, the same effect that pushes the ring particles away from the satellites, also pushes the satellites away from the rings. Most importantly, Saturn more massive A ring pushes both satellites out.
For the inner shepherd, Prometheus, it was conceivable that it was in a kind of equilibrium between the action of the wide A ring pushing it outward, and that of the F ring, pushing it inward. The problem was more difficult for Pandora, the outer shepherd. What could maintain this satellite so close to the F ring?
Some researchers concluded that the rings are young. Indeed, if the F ring and Pandora had just formed (some 10 million years ago), then Pandora would not have had the time yet to get away from the F ring. Other researchers did not think it was very likely that we were witnessing such a rare event.
For a while, until the orbits of the satellites were established, it appeared that Pandora might be involved in an orbital resonance with Mimas, which is itself involved in another orbital resonance with Tethys. These orbital resonances are characterized by nearly commensurable orbital periods. The most interesting property of a resonant configuration is that it allows the transfer of angular momentum from one satellite to the other.
When it was clear that Pandora was not in a resonance with Mimas, Borderies (former name of Rappaport), Goldreich and Tremaine proposed the idea, 20 years ago, that the motion of Prometheus and Pandora might be chaotic. They wrote: "A most interesting possibility is that S26 [earlier name of Pandora] is transferring angular momentum to Mimas even though the two bodies are not in an exact resonance. This could be accomplished if the motion of S26 were chaotic, i.e., if the value of its mean motion were undergoing a slow random walk."
Another chapter of the story took place in 1996. During the years 1995 and 1996, the Earth crossed the plane of Saturn rings. This was a good opportunity to observe Prometheus and Pandora with the Hubble Space Telescope.
These observations, which were analyzed independently by Prof. Phillip Nicholson of Cornell University on one hand, and Dr. Amanda Bosh of Boston University and Dr. Andrew Rivkin of the Massachusetts Institute of Technology on the other hand, revealed that Prometheus was lagging its predicted longitude by about 20 degrees. Four years later, Colleen McGhee, then a graduate student at Cornell, found that Pandora was leading the Voyager ephemeris by a similar amount. Several researchers, including Prof. Richard French of Wellesley College, subsequently verified the reality of the discrepancies.
This was an amazing discovery. For the first time ever, astronomers found that they could not predict the orbits of objects in the sky. Several hypotheses were investigated. Maybe there were undiscovered satellites moving on the orbits of Prometheus and Pandora? Although this might seem exotic at first view, we know of a group of asteroids with the same orbit as Jupiter, and Voyager discovered that a satellite of Saturn, Epimetheus, is moving in a sort of dance with Janus.
Are there large clumps of particles or small satellites within the F ring, which somehow perturbed the orbits of Prometheus and Pandora? This was another hypothesis.
For several years, none of the attempts made by the dynamicists provided a clear explanation of the puzzle. Then Goldreich and Rappaport demonstrated that the orbits of the F ring shepherds are chaotic and that the chaos leads to changes in longitude very similar to those observed with the Hubble Space Telescope. The chaos is due to the gravitational interactions between the two satellites.
What is the cause of the chaos? Goldreich and Rappaport are investigating the role of overlapping resonances. These occur where several mean motion commensurabilities occur very close to each other. If a body is present in such a location, it will tend to jump from one resonant configuration to another, in an unpredictable fashion.
The discovery that the orbits of Prometheus and Pandora are chaotic is important for several reasons. First, it represents the first observation ever of chaotic orbital motions in the solar system. We knew already of one satellite in chaotic rotation around its axis. This satellite is Hyperion, a major satellite of Saturn.
Second, the discovery of the chaotic motion of Prometheus and Pandora is expected to open a suite of new discoveries. In particular, Goldreich and Rappaport hope that they have found the piece of the puzzle that will resolve the problem of the age of the rings.
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