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1.
Analytical description of physical librations of saturnian coorbital satellites Janus and Epimetheus
Janus and Epimetheus are famously known for their distinctive horseshoe-shaped orbits resulting from a 1:1 orbital resonance. Every 4 years these two satellites swap their orbits by a few tens of kilometers as a result of their close encounter. Recently Tiscareno et al. (Tiscareno, M.S., Thomas, P.C., Burns, J.A. [2009]. Icarus 204, 254-261) have proposed a model of rotation based on images from the Cassini orbiter. These authors inferred the amplitude of rotational librational motion in longitude at the orbital period by fitting a shape model to Cassini ISS images. By a quasi-periodic approximation of the orbital motion, we describe how the orbital swap impacts the rotation of the satellites. To that purpose, we have developed a formalism based on quasi-periodic series with long- and short-period librations. In this framework, the amplitude of the libration at the orbital period is found proportional to a term accounting for the orbital swap. We checked the analytical quasi-periodic development by performing a numerical simulation and find both results in good agreement. To complete this study, the results obtained for the short-period librations are studied with the help of an adiabatic-like approach. 相似文献
2.
Epimetheus, a small moon of Saturn, has a rotational libration (an oscillation about synchronous rotation) of 5.9°±1.2°, placing Epimetheus in the company of Earth’s Moon and Mars’ Phobos as the only natural satellites for which forced rotational libration has been detected. The forced libration is caused by the satellite’s slightly eccentric orbit and non-spherical shape.Detection of a moon’s forced libration allows us to probe its interior by comparing the measured amplitude to that predicted by a shape model assuming constant density. A discrepancy between the two would indicate internal density asymmetries. For Epimetheus, the uncertainties in the shape model are large enough to account for the measured libration amplitude. For Janus, on the other hand, although we cannot rule out synchronous rotation, a permanent offset of several degrees between Janus’ minimum moment of inertia (long axis) and the equilibrium sub-Saturn point may indicate that Janus does have modest internal density asymmetries.The rotation states of Janus and Epimetheus experience a perturbation every 4 years, as the two moons “swap” orbits. The sudden change in the orbital periods produces a free libration about synchronous rotation that is subsequently damped by internal friction. We calculate that this free libration is small in amplitude (<0.1°) and decays quickly (a few weeks, at most), and is thus below the current limits for detection using Cassini images. 相似文献
3.
Philippe Robutel Nicolas Rambaux Maryame El Moutamid 《Celestial Mechanics and Dynamical Astronomy》2012,113(1):1-22
The Cassini spacecraft collects high resolution images of the Saturnian satellites and reveals the surface of these new worlds. Tiscareno et?al. succeeded to determine the Epimetheus rotation from the Cassini Imaging Science Subsystem data, initiating studies on the rotation of Epimetheus and its companion Janus (Tiscareno et?al., Icarus 204:254?C261, 2009; Noyelles, Icarus 207:887?C902, 2010; Robutel et?al., Icarus 211:758?C769, 2011). Especially, Epimetheus is characterized by its horseshoe shape orbit and the presence of the swap has to be introduced explicitly into rotational models. During its journey in the Saturnian system, Cassini spacecraft accumulates the observational data of the other satellites and it will be possible to determine the rotational parameters of several of them. To prepare these future observations, we built rotational models of the coorbital (also called Trojan) satellites Telesto, Calypso, Helene, and Polydeuces, in addition to Janus and Epimetheus. Indeed, Telesto and Calypso orbit around the L 4 and L 5 Lagrange points of Saturn-Tethys while Helene and Polydeuces are coorbital of Dione. The goal of this study is to understand how the departure from the Keplerian motion induced by the perturbations of the coorbital body, influences the rotation of these satellites. To this aim, we introduce explicitly the perturbation in the rotational equations by using the formalism developed by érdi (Celest Mech 15:367?C383, 1977) to represent the coorbital motions, and so we describe the rotational motion of the coorbitals, Janus and Epimetheus included, in compact form. 相似文献
4.
On the basis of the strong mathematical and physical parallels between orbit-orbit and spin-orbit resonances, the dynamics of mutual orbit perturbations between two satellites about a massive planet are examined, exploiting an approach previously adopted in the study of spin-orbit coupling. The satellites are assumed to have arbitrary mass ratio and to move in non-intersecting orbits of arbitrary size and eccentricity. Resonances are found to exist when the mean orbital periods are commensurable with respect to some rotating axis, which condition also involves the apsidal and nodal motions of both satellites. In any resonant state the satellites are effectively trapped in separate potential wells, and a single variable is found to describe the simultaneous librations of both satellites. The librations in longitude are 180° out-of-phase, with fixed amplitude ratio that depends only on their relative masses and semimajor axes. At the same time the stroboscopic longitude of conjunction also librates about the commensurate axis with the same period. The theory is applicable to Saturn's resonant pairs Titan-Hyperion and Mimas-Tethys, and in these cases our calculated libration periods are in reasonably good agreement with the observed periods.This research supported under a grant from the California Institute of Technology President's Fund and NASA Contract NAS 7-100. 相似文献
5.
Sarah J. Morrison Peter C. Thomas Matthew S. Tiscareno Joseph A. Burns Joseph Veverka 《Icarus》2009,204(1):262-270
High-resolution images from the Cassini Imaging Science Subsystem (ISS) show parallel sets of grooves on Epimetheus and Pandora. Grooves have previously been observed on other satellites and asteroids, including Phobos, Gaspra, Ida, Eros, and minor occurrences on Phoebe. Sets of parallel grooves are so far observed only on satellites known or likely to be subject to significant tidal stresses, such as forced librations. Grooves on asteroids and on satellites not subject to significant forced librations occur in more globally disorganized patterns that may reflect impacts, varying internal structures, or even thermal stresses. The patterns and individual morphologies of grooves on the tidally-affected satellites suggest fracturing in weak materials due to tidal stresses and forced librations. 相似文献
6.
We analyze the interactions between Saturn's coorbital satellites, Janus and Epimetheus, and the outer edge of the A ring, which is presumably maintained by these moons at their 7:6 resonance. Using two distinct but conceptually related methods, we show that ring torques are driving these satellites into a tighter lock. Unless there is a counterbalancing force which we have neglected, their orbital configuration will evolve from the current horseshoe-type lock to one of tadpole orbits around a single Lagrange point in ～20 myr. This finding adds an additional member to the list of short time scale problems associated with the interactions between Saturn's rings and its inner moons 相似文献
7.
Abimael Bengochea Manuel Falconi Ernesto Pérez-Chavela 《Astrophysics and Space Science》2011,333(2):399-408
We present some families of horseshoe periodic orbits in the general planar three-body problem for the case of two equal masses.
The considered system is a symmetric version of the one formed by Saturn, Janus and Epimetheus. We use a mass ratio equal
to 35×10−5, corresponding to 105 times the Saturn-Janus mass parameter of the restricted case; for this mass ratio the satellites have a significantly bigger
influence on the planet than in the classical Saturn, Janus and Epimetheus system. To obtain periodic orbits, we search those
horseshoe orbits passing through two reversible configurations. A particular kind of periodic orbits where the minor bodies
follow the same path is discussed. 相似文献
8.
An analytical model that describes the evolution of ring particles that are co-orbital with two larger bodies on near-circular and near-planar orbits has been formulated. This can be used to estimate the lifetime of the particles within the ring. All the examples investigated, such as the Janus-Epimetheus (JE) system, indicate that the particles should be removed from the co-orbital region within half a synodic period (∼4 years for JE). Numerical modelling confirms the predictions of the model. When the masses are on eccentric orbits the particles remain within the co-orbital system for longer. Our results suggest that the ring associated with Janus and Epimetheus must be continually fed with material, probably by meteoroid impacts on the two satellites. 相似文献
9.
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
10.
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
11.
M. A. Vashkov’yak 《Astronomy Letters》2001,27(7):455-463
Based on data for twelve recently discovered outer satellites of Saturn, we investigate their orbital evolution on long time scales. For our analysis, we use the previously obtained general solution of Hill’s double-averaged problem, which was refined for libration orbits, and numerical integration of the averaged system of equations in elements with allowance for Saturn’s orbital evolution. The following basic quantitative parameters of evolving orbits are determined: extreme eccentricities and inclinations, as well as circulation periods of the pericenter arguments and of the longitudes of the ascending nodes. For four new satellite orbits, we have revealed the libration pattern of variations in pericenter arguments and determined the ranges and periods of their variations. Based on characteristic features of the orbits of Saturn’s new satellites, we propose their natural classification. 相似文献
12.
G. Filacchione F. Capaccioni J.N. Cuzzi A. Coradini P.D. Nicholson R.H. Brown F. Tosi R. Jaumann 《Icarus》2010,206(2):507-523
We report the detailed analysis of the spectrophotometric properties of Saturn’s icy satellites as derived by full-disk observations obtained by visual and infrared mapping spectrometer (VIMS) experiment aboard Cassini. In this paper, we have extended the coverage until the end of the Cassini’s nominal mission (June 1st 2008), while a previous paper (Filacchione, G., and 28 colleagues [2007]. Icarus 186, 259-290, hereby referred to as Paper I) reported the preliminary results of this study.During the four years of nominal mission, VIMS has observed the entire population of Saturn’s icy satellites allowing us to make a comparative analysis of the VIS-NIR spectral properties of the major satellites (Mimas, Enceladus, Tethys, Dione, Rhea, Hyperion, Iapetus) and irregular moons (Atlas, Prometheus, Pandora, Janus, Epimetheus, Telesto, Calypso, Phoebe). The results we discuss here are derived from the entire dataset available at June 2008 which consists of 1417 full-disk observations acquired from a variety of distances and inclinations from the equatorial plane, with different phase angles and hemispheric coverage. The most important spectrophotometric indicators (as defined in Paper I: I/F continua at 0.55 μm, 1.822 μm and 3.547 μm, visible spectral slopes, water and carbon dioxide bands depths and positions) are calculated for each observation in order to investigate the disk-integrated composition of the satellites, the distribution of water ice respect to “contaminants” abundances and typical regolith grain properties. These quantities vary from the almost pure water ice surfaces of Enceladus and Calypso to the organic and carbon dioxide rich Hyperion, Iapetus and Phoebe. Janus visible colors are intermediate between these two classes having a slightly positive spectral slope. These results could help to decipher the origins and evolutionary history of the minor moons of the Saturn’s system. We introduce a polar representation of the spectrophotometric parameters as function of the solar phase angle (along radial distance) and of the effective longitude interval illuminated by the Sun and covered by VIMS during the observation (in azimuth) to better investigate the spatial distribution of the spectrophotometric quantities across the regular satellites hemispheres. Finally, we report the observed spectral positions of the 4.26 μm band of the carbon dioxide present in the surface material of three outermost moons Hyperion, Iapetus and Phoebe. 相似文献
13.
14.
Two small satellites of Pluto, S/2005 P1 (hereafter P1) and S/2005 P2 (hereafter P2), have recently been discovered outside the orbit of Charon, and their orbits are nearly circular and nearly coplanar with that of Charon. Because the mass ratio of Charon-Pluto is ∼0.1, the orbits of P2 and P1 are significantly non-Keplerian even if P2 and P1 have negligible masses. We present an analytic theory, with P2 and P1 treated as test particles, which shows that the motion can be represented by the superposition of the circular motion of a guiding center, the forced oscillations due to the non-axisymmetric components of the potential rotating at the mean motion of Pluto-Charon, the epicyclic motion, and the vertical motion. The analytic theory shows that the azimuthal periods of P2 and P1 are shorter than the Keplerian orbital periods, and this deviation from Kepler's third law is already detected in the unperturbed Keplerian fit of Buie and coworkers. In this analytic theory, the periapse and ascending node of each of the small satellites precess at nearly equal rates in opposite directions. From direct numerical orbit integrations, we show the increasing influence of the proximity of P2 and P1 to the 3:2 mean-motion commensurability on their orbital motion as their masses increase within the ranges allowed by the albedo uncertainties. If the geometric albedos of P2 and P1 are high and of order of that of Charon, the masses of P2 and P1 are sufficiently low that their orbits are well described by the analytic theory. The variation in the orbital radius of P2 due to the forced oscillations is comparable in magnitude to that due to the best-fit Keplerian eccentricity, and there is at present no evidence that P2 has any significant epicyclic eccentricity. However, the orbit of P1 has a significant epicyclic eccentricity, and the prograde precession of its longitude of periapse with a period of 5300 days should be easily detectable. If the albedos of P2 and P1 are as low as that of comets, the large inferred masses induce significant short-term variations in the epicyclic eccentricities and/or periapse longitudes on the 400-500-day timescales due to the proximity to the 3:2 commensurability. In fact, for the maximum inferred masses, P2 and P1 may be in the 3:2 mean-motion resonance, with the resonance variable involving the periapse longitude of P1 librating. Observations that sample the orbits of P2 and P1 well on the 400-500-day timescales should provide strong constraints on the masses of P2 and P1 in the near future. 相似文献
15.
Planetary perturbations of Mercury's orbit lead to forced librations in longitude in addition to the 88-day forced libration induced by Mercury's orbital motion. The forced librations are a combination of many periods, but 5.93 and 5.66 years dominate. These two periods result from the perturbations by Jupiter and Venus respectively, and they lead to a 125-year modulation of the libration amplitude corresponding to the beat frequency. Other periods are also identified with Jupiter and Venus perturbations as well as with those of the Earth, and these and other periods in the perturbations cause several arc second fluctuations in the libration extremes. The maxima of these extremes are about 30″ above and the minima about 7″ above the superposed ∼60″, 88-day libration during the 125-year modulation. Knowledge of the nature of the long-period forced librations is important for the interpretation of the details of Mercury's rotation state to be obtained from radar and spacecraft observations. We show that the measurement of the 88-day libration amplitude for the purposes of determining Mercury's core properties is not compromised by the additional librations, because of the latter's small amplitude and long period. If the free libration in longitude has an amplitude that is large compared with that of the forced libration, its ∼10-year period will dominate the libration spectrum with the 88-day forced libration and the long-period librations from the orbital perturbations superposed. If the free libration has an amplitude that is comparable to those of the long-period forced libration, it will be revealed by erratic amplitude, period and phase on the likely time span of a series of observations. However, a significant free libration component is not expected because of relatively rapid damping. 相似文献
16.
M. A. Vashkov’yak 《Astronomy Letters》2003,29(10):695-703
We used data on the recently discovered three outer Neptunian satellites to analyze the long-period evolution of their orbits. We estimated the ranges of eccentricities and inclinations as well as approximate circulation periods of the pericenter arguments and the longitudes of the ascending nodes. The results were mainly obtained by using two different versions of the averaged Hill problem. Plane sections of the phase space of satellite orbital elements are given. We discuss the peculiarity of the evolution of several satellite orbits related to the librational variation of the pericenter argument ω. The ω-librators of Saturn’s system were found to qualitatively differ from the libration orbit in the system of Jupiter. 相似文献
17.
由于星际探测事业的发展,对土星卫星的定位精度要求愈来愈高,经典的分析法定轨方法已难以适应,在当今计算技术条件高度发展的背景下,本文给出了土星卫星的数值法定轨方案,采用了土星卫星运动的高精度力学模型,并运用１８７４－１９８９这１００多年间的观测资料,引用现代最小二乘估计,对土星卫生进行精密定轨。该方案可以在引用同样的力学模型的前提下,对土星各颗卫星进行定轨,亦可同时进行多颗卫星的定轨。相应的软件比较 相似文献
18.
The theory of velocity dependent inertial induction, based upon extended Mach’s principle, has been able to generate many interesting results related to celestial mechanics and cosmological problems. Because of the extremely minute magnitude of the effect its presence can be detected through the motion of accurately observed bodies like Earth satellites. LAGEOS I and II are medium altitude satellites with nearly circular orbits. The motions of these satellites are accurately recorded and the past data of a few decades help to test many theories including the general theory of relativity. Therefore, it is hoped that the effect of the Earth’s inertial induction can have any detectable effect on the motion of these satellites. It is established that the semi-major axis of LAGEOS I is decreasing at the rate of 1.3 mm/d. As the atmospheric drag is negligible at that altitude, a proper explanation of the secular change has been wanting, and, therefore, this paper examines the effect of the Earth’s inertial induction effect on LAGEOS I. Past researches have established that Yarkovsky thermal drag, charged and neutral particle drag might be the possible mechanisms for this orbital decay. Inertial induction is found to generate a perturbing force that results in 0.33 mm/d decay of the semi major axis. Some other changes are also predicted and the phenomenon also helps to explain the observed changes in the orbits of a few other satellites. The results indicate the feasibility of the theory of inertial induction i.e. the dynamic gravitation phenomenon of the Earth on its satellites as a possible partial cause for orbital decay. 相似文献
19.
V. P. Epishev V. I. Kudak V. M. Perig I. I. Motrunich I. F. Naybauer E. J. Novak O. Yu. But 《Astrophysical Bulletin》2018,73(3):363-372
We report the results of an analysis of the variation of the proper rotation of several destabilized satellites over many-year long time intervals. The cause of the cyclic variations of the proper rotation period of “Midas-7” satellite, which has been orbiting the Earth since 1963 at an altitude of 3700 km, have long been unclear. These variations could not be explained either by the influence of the terrestrial atmosphere and terrestrial magnetic field, or by solar activity. Based on the results of 40-year long observations of “Midas-4,” “Midas-6,”, and “Midas-7” satellites it was established that their proper rotation exhibits not only dissipative braking variations, but also long-period variations with the periods of 477 days (“Midas-4”), 466 days (“Midas-6”), and 346 days (“Midas-7”) with different amplitudes. These variations in the case of the above satellites have well-defined resonance nature. An explanation of the processes found is proposed based on the results of this study and simulations of the observed orbital dynamics of the satellites. Long-period variations of the proper spacecraft rotation arise as a result of the combined effect of the gravitational fields of the Earth, Moon, and Sun depending on the orientation of their orbital planes in space. The amplitudes of such variations is determined by the inclination of satellite orbits to the equator: the closer it is to the pole (i.e., to 90?), the stronger the effect. 相似文献
20.
Systematic observations of faint satellites were conducted at Pic-du-Midi with a focal coronograph from 1980 March 20 to 24, during which 150 exposures covering 17 hr were obtained; in addition, the 1966 discovery plates of satellites S10 Janus were reexamined together with other 1966 observations. Janus had its greatest eastern elongation on 1966 December 15.720 (±0.003) + light time, at a distance of 2.53Req. It is recognized that some of the observations thought to be 1966 S2 were in fact reobservations of Janus a few days after its discovery. Among the 1980 observations, differences in magnitudes indicate that is satellite 1980 S1 which corresponds to Janus; its greatest eastern elongation was observed on March 23.876 (±0.002) + light time. Subjected to corrections for librations, the mean period over the past 14 years has most probably one of three values: P1 = 0.69458 day, P2 = 06.9448 day or P3 = 0.69438 day. The fainter satellite, S11, which is also 1980 S3, gravitates in an orbit similar to that of Janus and was leading it by +190° in March 1980; this difference of longitude was +224° in December 1966. An object of magnitude 15–16 was seen not detached from the ring; it could be a condensation in the external part of the rings or an additional faint inner satellite. 相似文献