Orbital evolution of the Galilean satellites: Capture into resonance

C.F. Yoder's scenario 1979 for the capture into resonance of the first three Galilean satellites is reexamined. A more refined dynamical model for the resonance and for the tidal effects is proposed and analyzed. The results agree qualitatively with those of Yoder but differ numerically by 10 to 20%.     

The orbital resonance amongst the Galilean satellites of Jupiter

The resonance amongst three of the Galilean satellites is described in a way intended to demonstrate the similarities it has to the normal two-satellite resonance. The hypothesis that the resonance was formed by the action of tidal forces is discussed. The problem is too complicated to reach any firm conclusions, but the tidal hypothesis does not seem to be a satisfactory explanation.

     

Galilean satellites: 1976 radar results

Radar observations of the Galilean satellites, made in late 1976 using the 12.6-cm radar system of the Arecibo Observatory, have yielded mean geometric albedos of 0.04 ± , 0.69 ± 0.17, 0.37 ± 0.09, and 0.15 ± 0.04, for Io, Europa, Ganymede, and Callisto, respectively. The albedo for Io is about 40% smaller than that obtained approximately a year earlier, while the albedos for the outer three satellites average about 70% larger than the values previously reported for late 1975, raising the possibility of temporal variation. Very little dependence on orbital phase is noted; however, some regional scattering inhomogeneities are seen on the outer three satellites. For Europa, Ganymede, and Callisto, the ratios of the echo received in one mode of circular polarization to that received in the other were: 1.61 ± 0.20 1.48 ± 0.27, and 1.24 ± 0.19, respectively, with the dominant component having the same sence of circularity as that transmitted. This behavior has not previously been encountered in radar studies of solar system objects, whereas the corresponding observations with linear polarization are “normal.” Radii determined from the 1976 radar data for Europa and Ganymede are: 1530 ± 30 and 2670 ± 50 km, in fair agreement with the results from the 1975 radar observations and the best recent optical determinations. Doppler shifts of the radar echoes, useful for the improvement of the orbits of Jupiter and some of the Galilean satellites, are given for 12 nights in 1976 and 10 nights in 1975.     

VLA observations of the Galilean satellites

Jupiter's Galilean satellites I–IV, Io, Europa, Ganymede, and Callisto have been observed with the VLA at 2 and 6 cm. The Jovian system was about 4.46 AU from the Earth at the time the observations were taken. The flux densities for satellites I–IV at 2 cm are 15 ± 2, 5.6 ± 1.2, 22.3 ± 2.0, and 26.0 ± 2.5 mJy, respectively, which corresponds to disk brightness temperatures of 92 ± 13, 47 ± 10, 67 ± 6, and 92 ± 9°K, respectively. At 6 cm flux densities of 1.10 ± 0.2, 0.55 ± 0.12, 2.0 ± 0.2, and 3.15 ± 0.2 mJy were found, corresponding to temperatures of 65 ± 11, 44 ± 10, 55 ± 6, and 105 ± 7°K, respectively. The radio brightness temperatures are lower than the infrared, the latter generally being consistent with the temperature derived from equilibrium with absorbed insolation. The radio temperature are qualitatively consistent with the equilibrium temperature for fast rotating bodies considering the high radio reflectivity (low emissivity) as determined from radar measurements by S. J. Ostro (1982). In Satellites of Jupiter (D. Morrison, Ed.). Univ. of Arizona Press, Tucson).     

Early eclipses of the Galilean satellites

A brief summary of the development of the theory of motion of the Galilean satellites is presented. Over 7700 eclipse observations have been collected and reduced using the Ephemeris E-2. They are of great potential in improving the ephemerides of the satellites and can yield important information on the evolution of the Galilean system.Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980Presently a recipient of the Humboldt Award of the Alexander von Humboldt Foundation at the Astronomisches Rechen-Institut in Heidelberg and on leave from the Jet Propulsion Laboratory     

Four-color photometry of the Galilean satellites

Photometry obtained in 1973 on the uvby system yields high-precision rotational light curves for Io, Europa, and Ganymede at a mean phase angle of ～6°. By combining our observations with photometry obtained by others over a broader range of phase angle, we alsi derive improved values for the phase coefficients and opposition surges of the four Galilean satellites. The values of V(1, 0) obtained by linear extrapolation to zero phase are accurate to ±0.03 magnitudes. We also derive the colors of the sun of the uvby system and use these to obtain albedos of the satellites in four colors.     

Internal structures of the Galilean satellites

New models for the interiors of Io, Ganymede, and Callisto are proposed. The model of Io consists of a thin, high-rigidity outer layer separated from a solid interior by a thin, molten or partially molten shell. The modulus of rigidity of the outer layer must be at least 100 times larger than that of the underlying partially molten shell. These layers have thicknesses of order 100 km or less. The near-surface partially molten layer was most likely produced early in Io's history as a consequence of accretional heating; enhanced tidal heating in the outer rigid layer has kept the underlying region partially molten to the present day. The model of Ganymede consists of an ice outer layer, a shell of undifferentiated, primordial ice-silicate mixture, and a rock core. Accretional heating is responsible for melting the ice in the outer layers of Ganymede's initially homogeneous ice-silicate interior. Most of the rock in this outer layer accumulates in a shell on top of Ganymede's early cold and rigid central region; the water in the outer layer quickly refreezes. Heating of the undifferentiated region by the decay of radioactive elements in the silicate fraction would gradually warm it and reduce its viscosity. The rock layer would become gravitationally unstable and sink through the undifferentiated materials to form a rock core. Callisto's heavily cratered surface strongly suggests that relatively little, if any, ice-rock differentiation has occured in its interior.     

Mid-eclipse brightening of the Galilean satellites

Brinkmann (1973) has suggested that the Galilean satellites might briefly manifest a brightening at mid-eclipse due to a concentration of light refracted into the geometric umbra of Jupiter by the atmosphere around the terminator. Results obtained using two different models of the Jovian atmosphere indicate that such a brightening is unlikely even for Callisto due to the probable aerosol concentration in the Jovian atmosphere at the relevant altitudes.     

Cratering rates on the Galilean satellites

We exploit recent theoretical advances toward the origin and orbital evolution of comets and asteroids to obtain revised estimates for cratering rates in the jovian system. We find that most, probably more than 90%, of the craters on the Galilean satellites are caused by the impact of Jupiter-family comets (JFCs). These are comets with short periods, in generally low-inclination orbits, whose dynamics are dominated by Jupiter. Nearly isotropic comets (long period and Halley-type) contribute at the 1-10% level. Trojan asteroids might also be important at the 1-10% level; if they are important, they would be especially important for smaller craters. Main belt asteroids are currently unimportant, as each 20-km crater made on Ganymede implies the disruption of a 200-km diameter parental asteroid, a destruction rate far beyond the resources of today's asteroid belt. Twenty-kilometer diameter craters are made by kilometer-size impactors; such events occur on a Galilean satellite about once in a million years. The paucity of 20-km craters on Europa indicates that its surface is of order 10 Ma. Lightly cratered surfaces on Ganymede are nominally of order 0.5-1.0 Ga. The uncertainty in these estimates is about a factor of five. Callisto is old, probably more than 4 Ga. It is too heavily cratered to be accounted for by the current flux of JFCs. The lack of pronounced apex-antapex asymmetries on Ganymede may be compatible with crater equilibrium, but it is more easily understood as evidence for nonsynchronous rotation of an icy carapace.     

UBV photometry of the Galilean satellites

UBV observations of the Galilean satellites made at Lowell Observatory and Cerro Tololo Inter-American Observatory during 1973 and 1974 are reported. The dependence of brightness on solar phase angle for various faces of each satellite is determined. Significant differences in this dependence are found between different faces of the same satellite, between satellites, and between the present results and those of previous investigators. Rotational light and color-index curves are presented for the satellites and compared with earlier work. An apparent secular brightening of all four satellites between 1973 and 1974 is discussed.     

Eclipse spectrophotometry of the Galilean satellites

Narrowband spectrophotometry of satellite eclipses is presented for each of the Galilean satellites. Comparing the partially eclipsed full-phase satellite disk to the uneclopsed disk can reveal colorimetric inhomogeneities on the surface. The trailing half-disk of Ganymede is slightly blue compared to the leading half-disk. The trailing and leading half-disks of Callisto are similar to each other, as are the northern and southern half-disks. The northern half-disk shows evidence of blue and red portions. The trailing half-disk of Europa is redder than the leading half-disk.     

The icy Galilean satellites: ultraviolet phase curve analysis

Ultraviolet disk-integrated solar phase curves of the icy galilean satellites Europa, Ganymede, and Callisto are presented, using combined data sets from the International Ultraviolet Explorer (IUE), Hubble Space Telescope (HST), and the Galileo Ultraviolet Spectrometer. Global, disk-integrated solar phase curves for all three satellites, in addition to disk-integrated solar phase curves for Europa's leading, trailing, jovian, and anti-jovian hemispheres, are modeled using Hapke's equations for 7 broadband UV wavelengths between 260 and 320 nm. The sparse coverage in solar phase angle, particularly for Ganymede and Callisto, and the noise in the data sets poorly constrain some of the photometric parameter values in the model. However, the results are sufficient for forming a preliminary relationship between the effects of particle bombardment on icy surfaces and photometric scattering properties at ultraviolet wavelengths. Callisto exhibits a large UV opposition surge and a surface comprised of relatively low-backward scattering particles. Europa's surface displays a dichotomy between the jovian and anti-jovian hemispheres (the anti-jovian hemisphere is more backward scattering), while a less pronounced hemispherical variation was detected between the leading and trailing hemispheres. Europa's surface, with the exception of the trailing hemisphere region, appears to have become less backscattering between the late-1970s-early-1980s and the mid-1990s. These results are commensurate with the bombardment history of these surfaces by magnetospheric charged particles.     

Galilean satellites and the Galileo space mission

The Galileo spacecraft arrived at Jupiter in December 1995 to start its two-year mission of exploring the Jovian system, The spacecraft will complete eleven orbits around Jupiter and have ten more close encounters with the outer three Galilean satellites, after the initial close approach to lo on December 7, 1995, Since the lo encounter occurred closer to lo than originally designed, the spacecraft energy change was greater than nominally planned and resulted in an initial spacecraft orbital period about 7 days less than that designed in the nominal tour, A 100-km change in the Io-encounter distance results in an 8-day change in initial period of the spacecraft. Hence the first Ganymede encounter was moved forward one week, and the aim points for the first two Ganymede encounters were altered, but all other encounters would occur on their nominal dates and at the nominal altitudes, This was accomplished without expending spacecraft fuel and resulted in the first Ganymede flyby occurring on June 27, 1996 rather than the nominally scheduled July 4.Earth- and spacecraft-based data were employed in developing ephemerides in support of the Galileo space mission. An analysis of CCD astrometric observations from 1992–1994, of photographic observations from 1967–1993, of mutual event astrometric data from 1973–1991, of Jovian eclipse timing data from 1652-1983, of Doppler data from 1987–1991, and of optical navigation data from the Voyager spacecraft encounter in 1979, produced the satellite ephemerides for the Galileo space mission.     

How fast do Galilean satellites spin?

Each of the Galilean satellites, as well as most other satellites whose initial rotations have been substantially altered by tidal dissipation, has been widely assumed to rotate synchronously with its orbital mean motion. Such rotation would require a small permanent asymmetry in the mass distribution in order to overcome the small mean tidal torque. Since Io and Europa may be substantially fluid, they may not have the strenght to support the required permanent asymmetry. Thus, each may rotate at the unknown but slightly nonsynchronous rate that corresponds to zero mean tidal torque. This behaviour may be observable by Galileo spacecraft imaging. It may help explain the longitudinal variation of volcanism on Io and the cracking of Europa's crust.     

Radar observations of the icy Galilean satellites

We report 12.6-cm-wavelength radar observations of Europa, Ganymede, and Callisto made at the Arecibo Observatory in November 1977 and February 1979. When combined with previous observations, our results establish firmly the distinguishing radar properties of these satellites: (i) high geometric albedos, α; (ii) circular polarization ratios, μ_C, which anomalously exceed unity; (iii) linear polarization ratios, μ_L, which are approximately 0.5; and (iv) diffuse scattering which varies as cosⁿθ, where θ is angle of incidence and 1 ? n ? 2. We tabulate weighted-mean values of α, μ_C, μ_L, and n derived from observations between 1975 and 1979. The values of μ_C for Ganymede and Europa are nearly identical and significantly larger than that for Callisto. The values of n for Ganymede and Callisto are nearly identical and significantly smaller than that for Europa. Although significant albedo and/or polarization features are common in the radar spectra, the fractional rms fluctuation in disk-integrated properties is only ～10%. No time variation in the radar properties has been evident during 1976–1979.     

Surface color variations of the Galilean satellites

Color variations of the four Galilean satellites have been monitored during the summer of 1971 with the McDonald Observatory area-scanning photometer. All were found to vary with orbital phase, with the exception of Europa in B-V. The curves suggest complex variations in surface make-up with some large features, possibly the result of interaction with the Jovian environment.     

Observations of Jupiter's Galilean satellites using astrolabes

Jupiter's Galilean satellites have been observed at the Quito (1964) and Haute-Provence (1965) Observatories for experimental purposes; the results show that the astrolabe can give an efficient contribution in this field, and that a permanent survey would be useful.     

Problems on the Galilean satellites of Jupiter

The purpose of this paper is to present a critical review of some problems concerning the dynamics of Jupiter's Galilean system of satellites. Theory, ephemeris and observation are considered.Two theories were proposed by Ferraz-Mello and by Sagnier. The main characteristics of these theories are that the frequencies are allowed to be kept fixed for all times from the earlier stages, and so to have a purely trigonometric solution.For a completely satisfactory work we need many more observations than actually exist. Two kinds of observations seem to be the best suitable: long-focus photographic plates and photometric records of mutual events.The most recent photographic observations are discussed in order to state guidelines for future work. The problem of the precision of Sampson's tables is discussed on the grounds of the recent observations.Paper presented at IAU Colloquium, No. 28, Ithaca, N.Y., August, 1974.     

Tidal evolution of the Galilean satellites: A linearized theory

The Laplace resonance among the Galilean satellites Io, Europa, and Ganymede is traditionally reduced to a pendulum-like dynamical problem by neglecting short-period variations of several orbital elements. However, some of these variations that can now be neglected may once have had longer periods, comparable to the “pendulum” period, if the system was formerly in deep resonance (pairs of periods even closer to the ratio 2:1 than they are now). In that case, the dynamical system cannot be reduced to fewer than nine dimensions. The nine-dimensional system is linearized here in order to study small variations about equilibrium. When tidal effects are included, the resulting evolution is substantially the same as was indicated by the pendulum approach, except that evolution out of deep resonance is found to be somewhat slower than suggested by extrapolation of the pendulum results. This slower rate helps support my hypothesis that the system may have evolved from deep resonance, although other factors still need to be considered to determine whether that hypothesis is quantitatively viable.     

Libration of Laplace's argument in the Galilean satellites theory

In the Galilean satellites motion, the Laplace argument ₁3₂+2₃ librates around the value . The amplitude of libration is very small so that the classical theories have not been set up to take into account large librations. On the other hand large librations have to be considered when we describe possible scenarii of capture into resonance by tidal effects. The aim of this paper is to present a new way of applying Hamiltonian perturbation methods to the problem of the Galilean satellites in such a way that the theory is valid for large librations. Preliminary results from such a theory are discussed.