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1.
V.V. Kouprianov 《Icarus》2005,176(1):224-234
The problem of observability of chaotic regimes in the rotation of planetary satellites is studied. The analysis is based on the inertial and orbital data available for all satellites discovered up to now. The Lyapunov spectra of the spatial chaotic rotation and the full range of variation of the spin rate are computed numerically by integrating the equations of the rotational motion; the initial data are taken inside the main chaotic layer near the separatrices of synchronous resonance in phase space. The model of a triaxial satellite in a fixed elliptic orbit is adopted. A short Lyapunov time along with a large range of variation of the spin rate are used as criteria for observability of the chaotic motion. Independently, analysis of stability of the synchronous state with respect to tilting the axis of rotation provides a test for the physical opportunity for a satellite to rotate chaotically. Finally, a calculation of the times of despinning due to tidal evolution shows whether a satellite's spin could evolve close to the synchronous state. Apart from Hyperion, already known to rotate chaotically, only Prometheus and Pandora, the 16th and 17th satellites of Saturn, pass all these four tests.  相似文献   

2.
The chaotic orbital motion of Prometheus and Pandora, the 16th and 17th satellites of Saturn, is studied. Chaos in their orbital motion, as found by Goldreich & Rappaport and Renner & Sicardy, is due to interaction of resonances in the resonance multiplet corresponding to the 121:118 commensurability of the mean motions of the satellites. It is shown rigorously that the system moves in adiabatic regime. The Lyapunov time (the 'time horizon of predictability' of the motion) is calculated analytically and compared to the available numerical–experimental estimates. For this purpose, a method of analytical estimation of the maximum Lyapunov exponent in the perturbed pendulum model of non-linear resonance is applied. The method is based on the separatrix map theory. An analytical estimate of the width of the chaotic layer is made as well, based on the same theory. The ranges of chaotic diffusion in the mean motion are shown to be almost twice as big compared to previous estimates for both satellites.  相似文献   

3.
The system of Saturn's inner satellites is saturated with many resonances. Its structure should be strongly affected by tidal forces driving the satellites through several orbit–orbit resonances. The evolution of these satellites is investigated using analytic and numerical methods. We show that the pair of satellites Prometheus and Pandora has a particularly short lifetime (<20 Myr) if the orbits of the satellites converge without capture into a resonance. The capture of Pandora into a resonance with Prometheus increases the lifetime of the couple by a few tens of Myr. However, resonances of the system are not well separated, and capture results in a chaotic motion. Secondary resonances also disrupt the resonant configurations. In all cases, the converging orbits of these two satellites result in a close encounter. The implications for the origin of Saturn's rings are discussed.  相似文献   

4.
An analysis of the character of the possible dynamics of all hitherto known planetary satellites shows two satellites—Amalthea (J5) and Prometheus (S16)—to have the most unusual structure of the phase space of possible rotational motion. These are the only satellites whose phase space of planar rotation may host synchronous resonances of three different kinds: the α resonance, the β resonance, and a mode corresponding to the period doubling bifurcation of the α resonance. We analyze the stability of these states against the tilt of the rotational axis.  相似文献   

5.
Recent HST images of the saturnian satellites Prometheus and Pandora show that their longitudes deviate from predictions of ephemerides based on Voyager images. Currently Prometheus is lagging and Pandora leading these predictions by somewhat more than 20°. We show that these discrepancies are fully accounted for by gravitational interactions between the two satellites. These peak every 24.8 days at conjunctions and excite chaotic perturbations. The Lyapunov exponent for the Prometheus-Pandora system is of order 0.3 year−1 for satellite masses based on a nominal density of 0.63 g cm−3. Interactions are strongest when the orbits come closest together. This happens at intervals of 6.2 years when their apses are antialigned. In this context, we note the sudden changes of opposite signs in the mean motions of Prometheus and Pandora at the end of 2000 occurred around the time their apsidal lines were antialigned.  相似文献   

6.
A plot of spin rate versus orientation when Hyperion is at the pericenter of its orbit (surface of section) reveals a large chaotic zone surrounding the synchronous spin-orbit state of Hyperion, if the satellite is assumed to be rotating about a principal axis which is normal to its orbit plane. This means that Hyperion's rotation in this zone exhibits large, essentially random variations on a short time scale. The chaotic zone is so large that it surrounds the ½ and 2 states, and libration in the 3/2 state is not possible. Stability analysis shows that for libration in the synchronous and ½ states, the orientation of the spin axis normal to the orbit plane is unstable, whereas rotation in the 2 state is attitude stable. Rotation in the chaotic zone is also attitude unstable. A small deviation of the principal axis from the orbit normal leads to motion through all angles in both the chaotic zone and the attitude unstable libration regions. Measures of the exponential rate of separation of nearby trajectories in phase space (Lyapunov characteristic exponents) for these three-dimensional motions indicate the the tumbling is chaotic and not just a regular motion through large angles. As tidal dissipation drives Hyperion's spin toward a nearly synchronous value, Hyperion necessarily enters the large chaotic zone. At this point Hyperion becomes attitude unstable and begins to tumble. Capture from the chaotic state into the synchronous or ½ state is impossible since they are also attitude unstable. The 3/2 state does not exist. Capture into the stable 2 state is possible, but improbable. It is expected that Hyperion will be found tumbling chaotically.  相似文献   

7.
Saturn's F ring has been the subject of study due to its peculiar structure and the proximity to two satellites, named Prometheus (interior) and Pandora (exterior to the ring), which cause perturbations to the ring particles. Early results from Voyager data have proposed that the ring is populated with centimetre- and micrometre-sized particles. The Cassini spacecraft also detected a less dense part in the ring with width of 700 km. Small particles suffer the effects of solar radiation. Burns et al. showed that due to effects of one component of the solar radiation, the Poynting–Robertson drag, a ring particle will decay in the direction of the planet in a time much shorter than the age of the Solar system. In this work, we have analysed a sample of dust particles (1, 3, 5 and 10 μm) under the effects of solar radiation, the Poynting–Robertson drag and the radiation pressure components and the gravitational effects of the satellites Prometheus and Pandora. In this case, the high increase of the eccentricity of the particles leads almost all of them to collide with the outer edge of the A ring. The inclusion of the oblateness of Saturn in this system significantly changes the outcome, since the large variation of the eccentricity is reduced by the oblateness effect. As a result, there is an increase in the lifetime of the particle in the envelope region. Our results show that even the small dust particles, which are very sensitive to the effects of solar radiation, have an orbital evolution similar to larger particles located in the F ring. The fate of all particles is a collision with Prometheus or Pandora in less than 30 years. On the other hand, collisions of these particles with moonlets/clumps present in the F ring could change this scenario.  相似文献   

8.
We demonstrate that the chaotic orbits of Prometheus and Pandora are due to interactions associated with the 121:118 mean motion resonance. Differential precession splits this resonance into a quartet of components equally spaced in frequency. Libration widths of the individual components exceed the splitting, resulting in resonance overlap which causes the chaos. Mean motions of Prometheus and Pandora wander chaotically in zones of width 1.8 and 3.1 deg yr−1, respectively. A model with 1.5 degrees of freedom captures the essential features of the chaotic dynamics. We use it to show that the Lyapunov exponent of 0.3 yr−1 arises because the critical argument of the dominant member of the resonant quartet makes approximately two separatrix crossings every 6.2 year precessional cycle.  相似文献   

9.
Topographic models of Saturn's F-Ring shepherd satellites Prometheus and Pandora were derived from the shapes of limbs and terminators in Voyager images, modified locally to accommodate large craters and ridges. The models are presented here in tabular and graphic form, including the first published maps of the satellites. The shape of Prometheus is approximated by a triaxial ellipsoid with axes of 145, 85 and 60 km. The volume is estimated to be 3.9 ± 1.0 × 105 km3, significantly smaller than previous estimates. A system of prominent ridges and valleys cross the north polar region. Prometheus appears to be less heavily cratered than the other small satellites near the edge of the rings, though this may be an artifact of the low resolution of available images. Pandora is approximated by a triaxial ellipsoid with axes of 114, 84 and 62 km. The volume is estimated to be 3.1 ± 1.0 × 105 km3. Its surface appears to be very heavily cratered.  相似文献   

10.
A numerical investigation of the chaotic rotation of large planetary satellites before their synchronous spin-orbital resonance locking with regard to tidal friction is carried out. The rotational dynamics of seven large satellites greater than 1000 km in diameter and with known inertial parameters (Io, Europa, Ganymede, Callisto (J1–J4), Tethys (S3), Iapetus (S8), and Ariel (U1)) in the epoch of synchronous resonance locking is modeled. All of these satellites have a small dynamic asymmetry. The planar case is considered in which the satellite’s axis of rotation is orthogonal to the plane of orbit. The satellites possessing an initial rapid rotation pass through various resonant states during the tidal evolution. Here, the probability of their locking into these states exists. The numerical experiments presented in this paper have shown that, with a rather high arbitrariness in the choice of initial states, the satellites during the course of the tidal evolution of their rotational motion have passed without interruption through the regions of the 5: 2, 2: 1, and 3: 2 resonances in the phase space and are locked into the 1: 1 resonance. The estimate for the tidal deceleration time is obtained both theoretically and on the numerical experimental basis.  相似文献   

11.
Utilizing topographic models of Saturn's F-ring shepherd satellites Prometheus (S16 1980S27) and Pandora (S15 1980S26), derived by Stooke (1994), and supposing that their mass density is constant, we derived basic geometrical and dynamical characteristics of the moons. They include the volume and mass, the mean radii, the tensor of inertia, and Stokes coefficients of the harmonic expansions of external gravitational potential. The best fitting ellipsoid approximations of the topography were calculated. A simple method of determining the gravitational potential on the surface of an irregular satellite is presented. Examples of equipotential surfaces of the satellites are shown  相似文献   

12.
Saturn’s narrow F ring is flanked by two nearby small satellites, Prometheus and Pandora, discovered in Voyager images taken in 1980 and 1981 (Synnott et al., 1983, Icarus 53, 156-158). Observations with the Hubble Space Telescope (HST) during the ring plane crossings (RPX) of 1995 led to the unexpected finding that Prometheus was ∼19° behind its predicted orbital longitude, based on the Synnott et al. (1983) Voyager ephemeris (Bosh and Rivkin, 1996 Science 272, 518-521; Nicholson et al., 1996, Science 272, 509-515). Whereas Pandora was at its predicted location in August 1995, McGhee (2000, Ph.D. thesis, Cornell University) found from the May and November 1995 RPX data that Pandora also deviates from the Synnott et al. (1983) Voyager ephemeris. Using archival HST data from 1994, previously unexamined RPX images, and a large series of targeted WFPC2 observations between 1996 and 2002, we have determined highly accurate sky-plane positions for Prometheus, Pandora, and nine other satellites found in our images. We compare the Prometheus and Pandora measurements to the predictions of substantially revised and improved ephemerides for the two satellites based on an extensive analysis of a large set of Voyager images (Murray et al., 2000, Bull. Am. Astron. Soc. 32, 1090; Evans, 2001 Ph.D. thesis, Queen Mary College). From December 1994 to December 2000, Prometheus’ orbital longitude lag was changing by −0.71° year−1 relative to the new Voyager ephemeris. In contrast, Pandora is ahead of the revised Voyager prediction. From 1994 to 2000, its longitude offset changed by +0.44° year−1, showing in addition an ∼585 day oscillatory component with amplitude ΔλCR0 = 0.65 ± 0.07° whose phase matches the expected perturbation due to the nearby 3:2 corotation resonance with Mimas, modulated by the 71-year libration in the longitude of Mimas due to its 4:2 resonance with Tethys. We determine orbital elements for freely precessing equatorial orbits from fits to the 1994-2000 HST observations, from which we conclude that Prometheus’ semimajor axis was 0.31 km larger, and Pandora’s was 0.20 km smaller, than during the Voyager epoch. Subsequent observations in 2001-2002 reveal a new twist in the meanderings of these satellites: Prometheus’ mean motion changed suddenly by an additional −0.77° year−1, equivalent to a further increase in semimajor axis of 0.33 km, at the same time that Pandora’s mean motion changed by +0.92° year−1, corresponding to a change of −0.42 km in its semimajor axis. There is an apparent anticorrelation of the motions of these two moons seen in the 2001-2002 observations, as well as over the 20-year interval since the Voyager epoch. This suggests a common origin for their wanderings, perhaps through direct exchange of energy between the satellites as the result of resonances, possibly involving the F ring.  相似文献   

13.
Stéfan Renner  Bruno Sicardy 《Icarus》2005,174(1):230-240
Hubble Space Telescope (HST) images of Prometheus and Pandora show longitude discrepancies of about 20° with respect to the Voyager ephemerides, with an abrupt change in mean motion at the end of 2000 (French et al., 2003, Icarus 162, 143-170; French and McGhee, 2003, Bull. Am. Astron. Soc. 34, 06.07). These discrepancies are anti-correlated and arise from chaotic interactions between the two moons, occurring at interval of 6.2 yr, when their apses are anti-aligned (Goldreich and Rappaport, 2003a, Icarus 162, 391-399). This behavior is attributed to the overlap of four 121:118 apse-type mean motion resonances (Goldreich and Rappaport, 2003b, Icarus 166, 320-327). We study the Prometheus-Pandora system using a Radau-type integrator taking into account Saturn's oblateness up to and including terms in J6, plus the effects of the major satellites. We first confirm the chaotic behavior of Prometheus and Pandora. By fitting the numerical integrations to the HST data (French et al., 2003, Icarus 162, 143-170; French and McGhee, 2003, Bull. Am. Astron. Soc. 34, 06.07), we derive the satellite masses. The resulting GM values (with their standard 3-σ errors) for Prometheus and Pandora are respectively and . Using the nominal shape of the two moons (Thomas, 1989, Icarus 77, 248-274), we derive Prometheus and Pandora's densities, 0.40+0.03−0.07 and 0.49+0.05−0.09 g cm−3, respectively. Our numerical fits also enable us to constrain the time of the latest apse anti-alignment in 2000. Finally, using our fit, we predict the orbital positions of the two satellites during the Cassini tour, and provide a lower limit of the uncertainties due to chaos. These uncertainties amount to about 0.2° in mean longitude at the arrival of the Cassini spacecraft in July 2004, and to about 3° in 2008, at the end of the nominal tour.  相似文献   

14.
We have obtained numerically integrated orbits for Saturn's coorbital satellites, Janus and Epimetheus, together with Saturn's F-ring shepherding satellites, Prometheus and Pandora. The orbits are fit to astrometric observations acquired with the Hubble Space Telescope and from Earth-based observatories and to imaging data acquired from the Voyager spacecraft. The observations cover the 38 year period from the 1966 Saturn ring plane crossing to the spring of 2004. In the process of determining the orbits we have found masses for all four satellites. The densities derived from the masses for Janus, Epimetheus, Prometheus, and Pandora in units of g cm−3 are , , , and , respectively.  相似文献   

15.
The Cassini-Huygens arrival into the Saturnian system brought a large amount of data about the satellites and rings. Two diffuse rings were found in the region between the A ring and Prometheus. R/2004 S1 is coorbital to Atlas and R/2004 S2 is close to Prometheus. In this work we analysed the closest approach between Prometheus and both rings. As a result we found that the satellite removes particles from R/2004 S2 ring. Long-term numerical simulations showed that some particles can cross the F ring region . The well known region of the F ring, where small satellites are present and particles are being taking from the ring, gains a new insight with the presence of particles from R/2004 S2 ring. The computation of the Lyapunov Characteristic Exponent reveled that the R/2004 S2 ring lies in a chaotic region while R/2004 S1 ring and Atlas are in a stable region. Atlas is responsible for the formation of three regimes in the R/2004 S1 ring, as expected for a satellite embedded in a ring.  相似文献   

16.
Most of the positions of faint satellite images obtained during the 1966 Saturn ring plane crossing fit the period of the coorbital satellites 1980 S1 and 1980 S3. In 1966 the satellites were separated by 137° in orbital longitude. Until the mutual interaction of the satellites is understood and applied to derive the precise orbital motion, the 1966 and 1980 observations cannot be linked.  相似文献   

17.
《Planetary and Space Science》2006,54(9-10):1014-1023
Faint rings of micrometre-sized dust particles embrace many planets in the Solar system. As a rule, they are replenished by ejecta from embedded atmosphereless moons. On a number of occasions, the ejecta are generated by hypervelocity meteoroid impacts into the moons. Small ejecta fragments are then swiftly shifted into rings by an array of non-gravitational forces, e.g. radiation pressure or plasma drag. A significant fraction of ejecta mass, however, is contained in relatively big, multi-micrometre fragments which are subject to gravity only. Having escaped from the satellite, they stay close to its orbit and form a belt around planet. This belt is itself a source of ring dust through collisional disruption of its particles. Here the contributions of belts to the respective rings are estimated for selected satellites of Jupiter and Saturn. The belts under review could supply substantially more dust to rings than the direct ejecta from satellites and should be taken into account when estimating ring dust budgets. The belts are very difficult to observe, however, and some of them remain a theoretical proposition. We find an appealing evidence for the belts due to Amalthea and Thebe around Jupiter, and for the belt due to Enceladus around Saturn.  相似文献   

18.
The nominal tour of the Cassini mission enabled the first spectra and solar phase curves of the small inner satellites of Saturn. We present spectra from the Visual Infrared Mapping Spectrometer (VIMS) and the Imaging Science Subsystem (ISS) that span the 0.25-5.1 μm spectral range. The composition of Atlas, Pandora, Janus, Epimetheus, Calypso, and Telesto is primarily water ice, with a small amount (∼5%) of contaminant, which most likely consists of hydrocarbons. The optical properties of the “shepherd” satellites and the coorbitals are tied to the A-ring, while those of the Tethys Lagrangians are tied to the E-ring of Saturn. The color of the satellites becomes progressively bluer with distance from Saturn, presumably from the increased influence of the E-ring; Telesto is as blue as Enceladus. Janus and Epimetheus have very similar spectra, although the latter appears to have a thicker coating of ring material. For at least four of the satellites, we find evidence for the spectral line at 0.68 μm that Vilas et al. [Vilas, F., Larsen, S.M., Stockstill, K.R., Gaffley, M.J., 1996. Icarus 124, 262-267] attributed to hydrated iron minerals on Iapetus and Hyperion. However, it is difficult to produce a spectral mixing model that includes this component. We find no evidence for CO2 on any of the small satellites. There was a sufficient excursion in solar phase angle to create solar phase curves for Janus and Telesto. They bear a close similarity to the solar phase curves of the medium-sized inner icy satellites. Preliminary spectral modeling suggests that the contaminant on these bodies is not the same as the exogenously placed low-albedo material on Iapetus, but is rather a native material. The lack of CO2 on the small inner satellites also suggests that their low-albedo material is distinct from that on Iapetus, Phoebe, and Hyperion.  相似文献   

19.
After the discovery of a huge number of satellites around Jupiter, Saturn, and Uranus, it is necessary to collect together information about all of the planetary satellite systems and to define the possible classification of objects and types of their motion. We give physical parameters of the satellites: their masses, sizes, apparent magnitudes in opposition, and geometrical albedos. We present some of the orbital quantities that characterize the orbits, their shapes and orientation in space, as well as data on the rotation of satellites. The emphasis is on the peculiarities of their motion—the forces acting on them, the main orbital perturbations, and the influence of commensurabilities in the mean motions of satellites. We list references to the main theories of their motion.  相似文献   

20.
The chaotic behaviour of the motion of the planets in our Solar System is well established. In this work to model a hypothetical extrasolar planetary system our Solar System was modified in such a way that we replaced the Earth by a more massive planet and let the other planets and all the orbital elements unchanged. The major result of former numerical experiments with a modified Solar System was the appearance of a chaotic window at κ E ∈ (4, 6), where the dynamical state of the system was highly chaotic and even the body with the smallest mass escaped in some cases. On the contrary for very large values of the mass of the Earth, even greater than that of Jupiter regular dynamical behaviour was observed. In this paper the investigations are extended to the complete Solar System and showed, that this chaotic window does still exist. Tests in different ‘Solar Systems’ clarified that including only Jupiter and Saturn with their actual masses together with a more ‘massive’ Earth (4 < κ E < 6) perturbs the orbit of Mars so that it can even be ejected from the system. Using the results of the Laplace‐Lagrange secular theory we found secular resonances acting between the motions of the nodes of Mars, Jupiter and Saturn. These secular resonances give rise to strong chaos, which is the cause of the appearance of the instability window. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

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