Could Ariel have been heated by tidal friction?

For significant dissipation in Ariel, the past existence of an orbital resonance to force and maintain a substantial eccentricity in the orbit is hypothesized. The absolute maximum dissipation rate would be reduced both by the time necessary to establish the resonance in the first place and by a consequently larger minimum Q. The actual heating rate was much less than this maximum so even the existence of a 2/1 resonance may not be sufficient to account for Ariel's smooth sufrace

Why no orbital resonances among the satellites of Uranus?

Most of the orbital resonances among the satellites of the major planets are thought to be assembled by differential tidal expansion of their orbits. Why this has not occurred for the Uranus system can be investigated by determining the resonances which would be encountered for various values of Uranus' tidal effective Q. The comparison and the possible escape of Ariel-Umbriel from the 5:3 resonance mean that it is not unreasonable that no orbital resonances are found among these satellites

Some effects of elasticity on lunar rotation

A general Hamiltonian function for a rotating moon in the field of the earth is expanded in terms of parameters orienting the spin angular momentum relative to the principal axes of the moon and relative to coordinate axes fixed in the orbit plane. The effects of elastic distortion are included as modifications of the moment of inertia tensor, where the magnitude of the distortion is parameterized by the Love number k sub 2

Determination of parameters related to the interior of Mercury

Bounds on (C-A)/C for Mercury as a function of the uncertainty in the value of the obliquity are determined. The high precision of 1 min of arc which is required for reasonable bounds on (C-A)/C cannot be obtained by either earth based observations or the television imagery of the Mariner 73 flyby. Among other methods discussed, one involving both landers and orbiters could determine unambiguously not only (C-A)/C but also (B-A)/C and C/sq MR

The ring arcs of Neptune

After the corotation resonance with an exterior satellite proved inapplicable to the Neptune ring arc confinement, a search for other mechanisms settled on the possible influence of Neptune's magnetic field. The areas of greater optical depth around the ring are much dustier than the low optical depth regions. These particles reside in a plasma; therefore, they must carry some charge. The components of Neptune's magnetic field on the equator at the radius of the ring arcs as a function of Neptunian longitude are shown. The components are those of an offset tilted dipole model. Although the dipole model is probably not a good approximation so close to the planet, the magnitude of the field that is given is probably close to the actual value. The possible importance of the magnetic field on the smallest particles in the ring is indicated by the ratio of the magnetic field on the smallest particles in the ring is indicated by the ratio of the magnetic force to the central gravitation attraction with the field strength of B = 0.01 gauss at the ring distance. A preferred position in the orbit for magnetically perturbed particles seems to require a commensurability between the rotation of the planet and the motion of the particle in the orbit. The period of rotation is assumed to be that of the radio bursts at 16.11 hours. However, without a model for the radio emission, one cannot be absolutely sure. Jupiter's decametric radiation depends on Io's orbital position as well as the rotation, so a synodic periodicity might be appropriate. But the latter radiation is highly directed, whereas Neptune's was seen all along the spacecraft trajectory on the 16.11 hour schedule, i.e., with no shifts in phase relative to a fixed longitude on the planet. The ring orbital period is 10.536 hours which is not commensurate with the rotation period. If the 16.11 hours is interpreted as a synodic period between the rotation and a satellite motion, the closest rotation periods to 16 hours are 15.9 hours if the satellite is 1989N4 and 18.2 hours if the satellite is Triton. The former is near a 3:2 resonance with the ring particle motion. The problem deserves some more thought before a possible herding of small particles by the magnetic field is abandoned

Orbital resonances, unusual configurations and exotic rotation states among planetary satellites

Several examples of satellite dynamics are presented where significant progress has been made in understanding a complex problem, where a long-standing problem has finally been solved, where newly discovered configurations have motivated novel descriptions or where an entirely new phenomenon has been revealed. The origin of orbital resonances in satellites and the solution of the problem of the origin and evolution of the three body Laplace resonance among the Galilean satellites are among the topics discussed

Secular Evolution of Hierarchical Planetary Systems

(Abridged) We investigate the dynamical evolution of coplanar hierarchical two-planet systems where the ratio of the orbital semimajor axes alpha=a_1/a_2 is small. The orbital parameters obtained from a multiple Kepler fit to the radial velocity variations of a star are best interpreted as Jacobi coordinates and Jacobi coordinates should be used in any analyses of hierarchical planetary systems. An approximate theory that can be applied to coplanar hierarchical two-planet systems with a wide range of masses m_j and orbital eccentricities e_j is the octupole-level secular perturbation theory (OSPT). The OSPT shows that if the ratio of the maximum orbital angular momenta, lambda \approx (m_1/m_2) alpha^{1/2}, for given a_j is approximately equal to a critical value lambda_{crit}, then libration of the difference in the longitudes of periapse, w_1-w_2, about either 0 or 180 deg. is almost certain, with possibly large amplitude variations of both e_j. We establish that the OSPT is highly accurate for systems with alpha<0.1 and reasonably accurate even for systems with alpha as large as 1/3, provided that alpha is not too close to a significant mean-motion commensurability or above the stability boundary. The HD 168443 system is not in a secular resonance and its w_1-w_2 circulates. The HD 12661 system is the first extrasolar planetary system found to have w_1-w_2 librating about 180 deg. The libration of w_1-w_2 and the large-amplitude variations of both e_j in the HD 12661 system are consistent with the analytic results on systems with lambda \approx lambda_{crit}. The HD 12661 system with the best- fit orbital parameters and sin i = 1 is affected by the close proximity to the 11:2 commensurability, but small changes in the outer orbital period can result in configurations that are not affected by mean-motion commensurabilities.Comment: 32 pages, including 8 figures; uses AASTeX v5.0; accepted for publication in Ap

A Primordial Origin of the Laplace Relation Among the Galilean Satellites

Understanding the origin of the orbital resonances of the Galilean satellites of Jupiter will constrain the longevity of the extensive volcanism on Io, may explain a liquid ocean on Europa, and may guide studies of the dissipative properties of stars and Jupiter-like planets. The differential migration of the newly formed Galilean satellites due to interactions with a circumjovian disk can lead to the primordial formation of the Laplace relation n_1 - 3 n_2 + 2 n_3 = 0, where the n_i are the mean orbital angular velocities of Io, Europa, and Ganymede, respectively. This contrasts with the formation of the resonances by differential expansion of the orbits from tidal torques from Jupiter.Comment: 13 pages, including 4 figures; uses scicite.st

Newly discovered brown dwarfs not seen in microlensing time scale frequency distribution?

The 2-Micron All Sky Survey (2MASS) (Skrutskie et al. 1997) and the DEep Near Infrared Survey of the southern sky (DENIS) (Epchtein et al. 1997) have revealed a heretofore unknown population of free brown dwarfs that has extended the local mass function down to as small as 0.01M_sun (Reid et al. 1999). If this local proportion of brown dwarfs extends throughout the Galaxy---in particular in the Galactic bulge---one expects an increase in the predicted fraction of short time scale microlensing events in directions toward the Galactic bulge. Zhao et al.(1996) have indicated that a mass function with 30-60% of the lens mass in brown dwarfs is not consistent with empirical microlensing data. Here we show that even the much lower mass fraction (~ 10%) of brown dwarfs inferred from the new discoveries appears inconsistent with the data. The added brown dwarfs do indeed increase the expected number of short time scale events, but they appear to drive the peak in the time scale frequency distribution to time scales smaller than that observed, and do not otherwise match the observed distribution. A reasonably good match to the empirical data (Alcock et al. 1996) is obtained by increasing the fraction of stars in the range 0.08<m<0.7M_sun considerably above that deduced from several star counts. However, all inferences from microlensing about the appropriate stellar mass function must be qualified by the meagerness of the microlensing data and the uncertainties in the Galactic model.Comment: 5 pages, 1 figure. PS file using aas2pp4.sty. To appear in ApJ Letter