Synchronous spin-orbital resonance locking of large planetary satellites

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.     

Possible Effect of the Earth’s Inertial Induction on the Orbital Decay of LAGEOS

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.     

Rotational dynamics of planetary satellites: A survey of regular and chaotic behavior

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.     

Infrared albedos and rotation curves of the Galilean satellites

Infrared (1.5–5 μm) albedos and rotation curves of the Galilean satellites have been obtained. The data suggest that the rotational variation in the infrared is less than ±10% for all four satellites. While no conclusion about rotational variation could be reached for Io, the 1.57 μm data for the outer three satellites marginally suggest phase correlation with the visual variation. The geometric albedos obtained are in general agreement with earlier results. For Io, the absorption feature near 1.5 μm found by Pilcher et al. (1972) is confirmed, thus contradicting the flat spectrum measured by Fink et al. (1973). Io and Ganymede were observed in the 1.57 μm bandpass as they reappeared from eclipse. The curve for Io shows a slight (<10%) overshoot similar to those sometimes reported for visual measurements. This result is based on a single reappearance, and is extremely tentative.     

Influence of the coorbital resonance on the rotation of the Trojan satellites of Saturn

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.     

Report of the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements: 2003

Every three years the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements revises tables giving the directions of the north poles of rotation and the prime meridians of the planets, satellites, and asteroids. This report introduces a system of cartographic coordinates for asteroids and comets. A topographic reference surface for Mars is recommended. Tables for the rotational elements of the planets and satellites and size and shape of the planets and satellites are not included, since there were no changes to the values. They are available in the previous report (Celest. Mech. Dyn. Astron., 82, 83–110, 2002), a version of which is also available on a web site.     

Modeling Uranian mutual event light curves

Salient features of the analysis of the mutual event light curves of planetary satellites are presented. The need to carefully evaluate the flux contribution of the occulting/eclipsing satellite to the total flux is illustrated. Albedo variations on the satellites will produce signatures on the mutual event light curves. The partial events of the upcoming mutual event series of the uranian satellites can be modeled taking into account the albedo variations inferred from the maps of the southern regions imaged by Voyager 2 when only these regions are occulted/eclipsed. This will enable a robust determination of the astrometric parameters. The shape and asymmetry of the mutual event light curves along with the rotational light curves of the satellites obtained simultaneously during the planet's equinox crossing period can be utilized to obtain a coarse albedo map of the northern hemisphere of the satellites. These studies will also help in investigating possible changes in the known southern regions since the 1986 encounter of Voyager 2.     

Spectrophotometry of the small satellites of Saturn and their relationship to Iapetus, Phoebe, and Hyperion

We have obtained broadband spectrophotometric observations of four of the recently discovered small satellites of Saturn (Gladman et al., 2001, Nature 412, 163-166). The new data enable an understanding of the provenance, composition, and interrelationships among these satellites and the other satellites of Saturn, particularly Iapetus, Phoebe, and Hyperion. Temporal coverage of one satellite (S21 Tarvos) was sufficient to determine a partial rotational lightcurve. Our major findings include: (1) the satellites are red and similar in color, comparable to D-type asteroids, some KBOs, Iapetus, and Hyperion; (2) none of the satellites, including those from the “Phoebe Group” has any spectrophotometric relationship to Phoebe; and (3) S21 Tarvos exhibits a rotational lightcurve, although the data are not well-constrained and more observations are required to fit a definitive period. Dust created by meteoritic impacts and ejected from these satellites and additional undiscovered ones may be the source of the exogenous material deposited on the low-albedo side of Iapetus. Recent work which states that the small irregular satellites of Saturn have impacted Phoebe at least 6-7 times in the age of the Solar System (Nesvorny et al., 2003, Astron. J. 126, 398-429), suggests that such collisions may have propelled additional material from both Phoebe and the small irregular satellites toward Iapetus. The accretion of material from outer retrograde satellites may be a process that also occurs on Callisto and the uranian satellites.     

The Dependence of Satellite Galaxy Kinematics on Galaxy Properties

The relations between the kinematics of satellites and the properties of hosts and satellites themselves are investigated in this paper. Our sample of hosts and satellites is selected from the Sloan Digital Sky Survey (SDSS) data by adopting a self-adapted method developed by van den Bosch et al. Consistent with the previous studies, the average velocity dispersion increases with the mass of host galaxy, and is larger for red hosts than for blue hosts. We find that, on average, the velocity dispersion is independent of satellite mass around red hosts, however it increases with the satellite mass around blue hosts, and red satellites have a larger velocity dispersion than their blue counterparts. Our further investigations show that in the same halo, the velocity dispersion is independent of satellite mass, regardless of the host color. Interestingly, around red hosts, the red satellites tend to have a smaller velocity dispersion than the blue ones. It implies some interesting processes. In addition, we also find that if host galaxies only have red or blue (high mass or low mass) satellites, the system with red (high mass) satellites has a larger velocity dispersion than that with blue (low mass) satellites. It suggests that satellite properties are important for the measurement of dark halo mass.     

Unusual rotation modes of minor planetary satellites

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.     

The rotation states predominant among the planetary satellites

On the basis of tidal despinning timescale arguments, Peale showed in 1977 that the majority of irregular satellites (with unknown rotation states) are expected to reside close to their initial (fast) rotation states. Here we investigate the problem of the current typical rotation states among all known satellites from a viewpoint of dynamical stability. We explore location of the known planetary satellites on the (ω₀, e) stability diagram, where ω₀ is an inertial parameter of a satellite and e is its orbital eccentricity. We show that most of the satellites with unknown rotation states cannot rotate synchronously, because no stable synchronous 1:1 spin-orbit state exists for them. They rotate either much faster than synchronously (those tidally unevolved) or, what is much less probable, chaotically (tidally-evolved objects or captured slow rotators).     

Sizes, shapes, and albedos of the inner satellites of Neptune

Based on 87 resolved Voyager images of the five innermost satellites of Neptune, their shapes were measured and fit by tri-axial ellipsoids with the semi-axes of 48 × 30 × 26 km for Naiad, 54 × 50 × 26 km for Thalassa, 90 × 74 × 64 km for Despina, 102 × 92 × 72 km for Galatea, and 108 × 102 × 84 km for Larissa. Thomas and Veverka published a similar shape for Larissa (104 × 89 km, J. Geophys. Res. 96, 19261-19268, 1991). The other satellites had no published shapes. Using Voyager photometry of the six inner satellites by the same authors and the revised sizes, including the published size of Proteus, the reflectivity within this inner system was found to vary by about 30%. Geometric albedos in the visible are estimated between 0.07 for Naiad and 0.10 for Proteus. The rotational lightcurves of these satellites seem to be due to satellite shapes.     

Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites

This paper is the entire report of the IAU Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites, including three annexes. Tables give the recemmended values for the directions of the north poles of rotation and the prime meridians of the planets and satellites. Reference surfaces for mapping these bodies are described. The annexes discuss the guiding principles, given in the body of the report, present explanatory notes, and provide a bibliography of the rotational elements and reference surfaces of the planets and satellites, definitions, and algebraic expressions of relevant parameters.     

Topography on satellite surfaces and the shape of asteroids

Calculations of the topography and shape of planetary bodies are presented for two sets of models. One set of models deals with the effects of static loading on bodies, taking into account strengths of materials, density, and size. The other set considers the effects of creep deformation on model bodies of differing composition, size and temperature. Application of these models to asteroids and satellites of the major planets indicates that model, even the largest asteroids could retain highly nonspherical shapes, and the four large satellites of Jupiter could sustain statically loaded topography on the order of 10 km. (2) If silicate asteroids have not been heated to near the melting temperature of silicates, initial topography should survive for at least 109 yr under creep deformation. Topography on an insulated icy asteroid will be rapidly reduced if it is of larger scale than the insulating layer, no matter what the thermal history. (3) Of the Galilean satellites of Jupiter, J1 and J2 should retain topography created on silicate surfaces since their formation (or since the surfaces were near the silicate melting temperature. If ice layers of any significant thickness exist, topography on a scale smaller than the layer's thickness will be reduced rapidly. (4) J4 and J3 probably fit an icy model throughout and topography of all scales may be reduced with relaxation times < 10⁶yr. These satellites are thus likely to preserve only very recent features on their surfaces, in contrast to the other Galilean satellites. If melting has taken place since formation, these conclusions become even stronger. (5) Of the satellites of the other planets, only Titan appears likely to have undergone topographic reduction by creep, under the models presented. However, if ices other than water are present in large proportion on these satellites relaxation times for topography may be shorter than calculated from the water ice models.     

利用光变曲线估计猎鹰九号火箭末级的旋转状态研究

光度观测是地基观测空间目标的主要手段之一,利用光度信息能够估计空间目标的相关特征信息.为了更好地了解空间目标的旋转状态,选取具有代表性的猎鹰九号火箭末级作为研究对象,由其光变信息研究旋转状态.首先利用云南天文台1.2 m光学望远镜获取猎鹰九号火箭末级的光度数据,再对目标星等进行斜距归一化,得到目标光变信息并分析目标星等...     

Asteroids with satellites: Analysis of observational data

The volume of observational information on asteroids and trans-Neptunians with satellites has significantly increased in recent years. In this paper we study the dependence of asteroid duplicity on the main physical parameters of the primary: the size and rotation rate. The proportion of binary asteroids is shown to grow rapidly with the rotation rate of the primary. The pattern of dependence between asteroid duplicity and size is more complex, with peaks in the area of small (<10 km) and large (>100 km) bodies. Noteworthy is the small number of binaries among typical-sized asteroids (10–150 km). All the orbits of asteroidal satellites whose rotation direction is known are shown to be prograde and have small eccentricities and inclinations.     

Triaxiality of satellites and small bodies in the Solar System

The triaxial figures are very common shape of most of planetary satellites as well as of smaell bodies as asteroids. There are 21 satellites in the Solar System triaxial figures of which were detected in situ evidently (Davies et al., 1995). However, the total number of triaxiaxial satellites in the Solar System should be in fact larger. In this paper the general theory of triaxiality due to tidal forces is discussed in regard to the very recent numerical data. Since they orbit synchronously, as a rule: their orbital periods are equal to the rotational periods, the tidal forces may be responsible for their triaxial figures. On the other hand the origin of triaxiality of asteroids due to another process and the of their figures cannot be axplained by the tidal effects.     

The relative motion of two spheroidal rigid bodies

We consider two spheroidal rigid bodies of comparable size constituting the components of an isolated binary system. We assume that (1) the bodies are homogeneous oblate ellipsoids of revolution, and (2) the meridional eccentricities of both components are small parameters.We obtain seven nonlinear differential equations governing simultaneously the relative motion of the two centroids and the rotational motion of each set of body axes. We seek solutions to these equations in the form of infinite series in the two meridional eccentricities.In the zero-order approximation (i. e., when the meridional eccentricities are neglected), the equations of motion separate into two independent subsystems. In this instance, the relative motion of the centroids is taken as a Kepler elliptic orbit of small eccentricity, whereas for each set of body axes we choose a composite motion consisting of a regular precession about an inertial axis and a uniform rotation about a body axis.The first part of the paper deals with the representation of the total potential energy of the binary system as an infinite series of the meridional eccentricities. For this purpose, we had to (1) derive a formula for representing the directional derivative of a solid harmonic as a combination of lower order harmonics, and (2) obtain the general term of a biaxial harmonic as a polynomial in the angular variables.In the second part, we expound a recurrent procedure whereby the approximations of various orders can be determined in terms of lower-order approximations. The rotational motion gives rise to linear differential equations with constant coefficients. In dealing with the translational motion, differential equations of the Hill type are encountered and are solved by means of power series in the orbital eccentricity. We give explicit solutions for the first-order approximation alone and identify critical values of the parameters which cause the motion to become unstable.The generality of the approach is tantamount to studying the evolution and asymptotic stability of the motion.Research performed under NASA Contract NAS5-11123.     

中高轨卫星广播星历精度分析

GPS广播星历参数具有物理意义明确、参数少、精度高等优点,可以考虑将它应用于其他卫星导航系统。但是GPS系统的卫星构成比较单一,而其他卫星导航系统可能包含中地球轨道 (MEO)、倾斜地球同步轨道(IGSO)和地球静止轨道(GEO)等多种不同类型的中高轨卫星。分析了采用GPS广播星历参数时,MEO、IGSO和GEO卫星的广播星历拟合精度,特别讨论了轨道倾角接近于0的GEO卫星的广播星历拟合精度,并给出了相应的改进措施。计算表明,对于 MEO卫星,2 h的广播星历拟合精度(三维位置)可达厘米级;对于IGSO卫星和轨道倾角较大的GEO卫星,4 h的广播星历拟合精度约为0．1 m,径向位置误差在厘米量级;而对于轨道倾角接近于0的GEO卫星,若不采取特殊措施,由于轨道倾角和升交点经度统计相关,其广播星历拟合精度很差,为此提出了一种坐标转换方法。采用此方法后的广播星历拟合精度可达0．1 m,径向位置误差为厘米量级。