The fate of ejecta from Hyperion

Ejecta from Saturn's moon Hyperion are subject to powerful perturbations from nearby Titan, which control their ultimate fate. We have performed numerical integrations to simulate a simplified system consisting of Saturn (including optical flattening as well as dynamical oblateness), its main ring system (treated as a massless flat annulus), the moons Tethys, Dione, Titan, Hyperion, and Iapetus, and the Sun (treated simply as a massive satellite). At several different points in Hyperion's orbit, 1050 massless particles, more or less evenly distributed over latitude and longitude, were ejected radially outward from 1 km above Hyperion's mean radius at speeds 10% faster than escape speed from Hyperion. Most of these particles were removed within the first few thousand years, but ∼3% of them survived the entire 100,000-year duration of the simulations. Ejecta from Hyperion are much more widely scattered than previously thought, and can cross the orbits of all of Saturn's satellites. About 9% of all the particles escaped from the saturnian system, but Titan accreted ∼78% of the total, while Hyperion reaccreted only ∼5%. This low efficiency of reaccretion may help to account for Hyperion's small size and rugged shape. Only ∼1% of all the particles hit other satellites, and another ∼1% impacted Saturn itself, while ∼3% of them struck its main rings. The high proportion of impacts into Saturn's rings is surprising; these collisions show a broad decline in impact speed with time, suggesting that Hyperion ejecta gradually spread inwards. Additional simulations were used to investigate the dependence of ejecta evolution on launch speed, the mass of Hyperion, and the presence of the Sun. In general, the wide distribution of ejecta from Hyperion suggests that it does contribute to “Population II” craters on the inner satellites of Saturn. Ejecta which escape from a satellite into temporary orbit about its planet, but later reimpact into the same moon or another one produce “poltorary” impacts, intermediate in character between primary and secondary impacts. It may be possible to distinguish poltorary craters from primary and secondary craters on the basis of morphology.     

Rotational modeling of Hyperion

Saturn’s moon, Hyperion, is subject to strongly-varying solid body torques from its primary and lacks a stable spin state resonant with its orbital frequency. In fact, its rotation is chaotic, with a Lyapunov timescale on the order of 100 days. In 2005, Cassini made three close passes of Hyperion at intervals of 40 and 67 days, when the moon was imaged extensively and the spin state could be measured. Curiously, the spin axis was observed at the same location within the body, within errors, during all three fly-bys—~ 30° from the long axis of the moon and rotating between 4.2 and 4.5 times faster than the synchronous rate. Our dynamical modeling predicts that the rotation axis should be precessing within the body, with a period of ~ 16 days. If the spin axis retains its orientation during all three fly-bys, then this puts a strong constraint on the in-body precessional period, and thus the moments of inertia. However, the location of the principal axes in our model are derived from the shape model of Hyperion, assuming a uniform composition. This may not be a valid assumption, as Hyperion has significant void space, as shown by its density of 544± 50  kg m⁻³ (Thomas et al. in Nature 448:50, 2007). This paper will examine both a rotation model with principal axes fixed by the shape model, and one with offsets from the shape model. We favor the latter interpretation, which produces a best-fit with principal axes offset of ~ 30° from the shape model, placing the A axis at the spin axis in 2005, but returns a lower reduced χ ² than the best-fit fixed-axes model.     

Topography and geology of Hyperion

I have mapped the Saturnian satellite Hyperion using Voyager 2 images obtained in 1981 and a shape model derived from the results of Thomas et al. (1995). The results are presented in tabular and graphic form, including detailed shaded relief maps of the satellite. The shape is approximated by a triaxial ellipsoid with axes of 270, 201 and 336 km. The volume is estimated to be 9.5 ± 2.0 × 10⁶ km³. Geological interpretations were augmented by the use of super-resolution image composites. The surface is heavily cratered. A system of scarps and an isolated mountain are interpreted as the rim and central peak of an impact crater with a diameter similar to the mean diameter of the satellite itself, the largest crater with recognizable impact morphology in relation to the size of the body yet observed in the solar system. The crater density dates that impact, not the formation of Hyperion. Grooves are identified in several images, and form part of a zone of fracturing radial to a prominent crater.University of Western Ontario     

Hyperion: Analysis of Voyager observations

A total of 82 images of Hyperion was returned by the Voyager spacecraft; the most detailed views have a nominal resolution of 8.7 km/line pair. Hyperion had a rotation period of about 13 days and a spin vector lying close to its orbital plane at the time of the Voyager 2 encounter in 1981. The satellite's shape is very irregular, and cannot be approximated suitably by an ellipsoid. The largest cross section (A × C) is about 370 × 225 km; the B × C cross section is approximately 280 × 225 km. Most prominent among the surface features is a 120-km-diameter crater with an estimated depth of 10 km, and a series of arcuate scarps 300 km long that have relief in excess of 5 km. The density of large craters of Hyperion is smaller than that on other small Saturnian satellites and suggests the possibility that the last significant fragmentation of Hyperion occurred near the end of or after initial heavy bombardment. Voyager photometry yields an average normal reflectance of the surface material of 0.21 in the clear filter (0.47 μm) and evidence of slight albedo mottling over the surface. The disk-integrated phase coefficient between phase angles of 22° and 82° is 0.018 mag/de; there is little indication of a strong opposition effect in Voyager data down to phase angles of 3°. Hyperion's average color is definitely redder than that of Phobe, but matches that of the dark material on the leading hemisphere of Iapetus quite well. The satellite's albedo and color are consistent with those of contaminated water ice but since no mass determinations of Hyperion exist we do not know whether the bulk composition is icy or rocky.     

Regular and chaotic orbits in a self-consistent triaxial stellar system with slow figure rotation

We created a self-consistent triaxial stellar system through the cold disipationless collapse of 100,000 particles whose evolution was followed with a multipolar code. The resulting system rotates slowly even though its total angular momentum is zero, i.e., it offers an example of figure rotation. The potential of the system was subsequently approximated with interpolating formulae yielding a smooth potential stationary in the rotating frame. The Lyapunov exponents could then be computed for a randomly selected sample of 3,472 of the bodies that make up the system, allowing the recognition of regular and partially and fully chaotic orbits. The regular orbits were Fourier analyzed and classified using their locations on the frequency map. A comparison with a similar non-rotating model showed that the fraction of chaotic orbits is slightly but significantly enhanced in the rotating model; alternatively, there are no significant differences between the corresponding fractions neither of partially and fully chaotic orbits nor of long axis tubes, short axis tubes, boxes and boxlets among the regular orbits. This is a reasonable result because the rotation causes a breaking of the symmetry that may increase chaotic effects, but the rotation velocity is probably too small to produce any other significant differences. The increase in the fraction of chaotic orbits in the rotating system seems to be due mainly to the effect of the Coriolis force, rather than the centrifugal force, in good agreement with the results of other investigations.     

Hyperion: Collisional disruption of a resonant satellite

Hyperion is an irregularly shaped object of about 285 km in mean diameter, which appears as the likely remmant of a catastrophic collisional evolution. Since the peculiar orbit of this satellite (in $\text{4}\text{3}$ resonance locking with Titan) provides an effective mechanism to prevent any reaccretion of secondary fragments originated in a breakup event, the present Hyperion is probably the “core” of a disrupted precursor. This contrasts with the other, regularly shaped small satellites of Saturn, which, according to B.A. Smith et al. [Science215, 504–537 (1982)], were disrupted several times but could reaccrete from narrow rings of collisional fragments. The numerical experiments performed to explore the region of the phase space surrounding the present orbit show that most fragments ejected with a relative velocity $\text{?0.1}\text{km}\text{/}\text{sec}$ rapidly attain chaotic-type orbits, having repeated close encounters with Titan. Ejection velocities of this order of magnitude are indeed expected for a collision at a velocity of ～ 10 km/sec with a projectile-to-target mass ratio of the order of 10^?3; similar effects could be produced by less energetic but nearly grazing collisions. Such events are not likely to displace the largest remnant (i.e., the present Hyperion) outside the stable region of the phase space associated with the resonance, but could be responsible for the large amplitude of the observed orbital libration.     

The Faraday rotation of sunspots

In this paper the numerical solutions of the Unno-Beckers's equations for the magneto-sensitive line Fei 5250.216 are used to demonstrate the importance and role of Faraday rotation in sunspot magnetic fields and to study the influence of this effect on the measurements of the azimuth of the transverse field. We propose a method to determine the intrinsic direction of the transverse field with the observed azimuthal angle of the plane of linear polarization.     

The rotation of small asteroids

The addition of the unbiased sample of R. P. Binzel and J. D. Mulholland (Icarus56, 519–533) nearly triples the sample size of photoelectrically determined rotational parameters for main belt asteroids with estimated diameters (D) ≤30 km. Nonparametric stattistical tests which require no assumptions about the distributions or variances of the samples are used to examine rotational parameters for all D ≤ 30 km asteroids. A comparison of photoelectric and photographic results shows that the techniques have a highly significant difference in the range of detected frequencies. This difference does not allow photographic and photoelectric observations to be combined for meaningful statistical tests since a photographic bias toward smaller sample variances can induce statistical results that appear overly significant. Photographic observations also show a highly significant bias toward detecting asteroids with larger lightcurve amplitudes. The fit of a Maxwellian to the observed rotational frequency distribution can be rejected at a highly significant confidence level but the observed distribution can be acceptably fit by two Maxwellian distributions, which is consistent with the hypothesis that there are separate populations of slow and fast rotating asteroids. The frequency distributions of <15 km main belt asteroids and Earth and Mars crossers are not found to differ significantly. However, the larger mean lightcurve amplitude of the Earth and Mars crossing asteroids is found to be statistically significant. This latter result is interesting in view of the lack of any strong inverse amplitude versus diameter relation for small asteroids. No significant diameter dependence on rotational frequency is seen among only D ≤ 30 km asteroids. However, the inverse frequency versus diameter relation for D ≤ 120 km asteroids found by S. F. Dermott, A. W. Harris, and C. D. Murray (Icarus, in press) is found to be statistically significant using a linear least-squares analysis of photoelectric data only. No significant diameter dependence on rotational lightcurve amplitude is seen using linear least-squares analysis of photoelectric data for D≤30 and D≤90 km asteroids. However, a significant inverse amplitude versus diameter relation is found when this analysis is extended to D≤120 km asteroids. This finding may be consistent with the hypothesis of Dermott et al. that near 120 km there is a transition between primordial asteroids and their collisional fragments.     

The axial rotation of asteroids

The observed fact that light changes of the asteroids exhibit no beat periods is interpreted as an indication that they do not wobble in space like spinning tops, but spin about only one axis (possibly — but not necessarily — inclined but little to the plane of their orbits). Since, moreover, the damping of three-dimensional rotation by jovi-solar attraction would require a time which is long in comparison with the age of the solar system, it is concluded that the present uni-axial rotation must represent a property preserved from the time when the asteroids were formed. This would seem to testify against their origin by collisional fragmentation of larger bodies; for in such a case the resulting solid splinters would still today be characterized by a random distribution of their angular momenta in three dimensions.The writer owes this assurance to Dr. Thomas Gehrels (private information).     

The rotation of Janus and Epimetheus

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.     

The rotation of 53 Be stars

Through spectral observations we obtained the rotational velocity Vsini for 53 Be stars, and estimated the values of V and i on the basis of Hutching's method. We analysed the effect of rotation on the width of emission lines and used the emission peak separation to determine the relative size of the shell and the photosphere and the dilution factor. We discuss in depth fast rotating models where stellar winds are present and their relation to the Be phenomenon.     

The rotation rates of accreting planetesimals

There are obtained upper limits for the relative velocity at infinity of accreting planetesimals for a nearly constant mass of the largest accreting planetesimal and also in the case of variable mass. We conclude, that while the larger planets cannot be brought to the stage of rotational instability by stochastic collisions, the asteroids could be brought. provided that the relative velocities in the asteroid belt were larger than about 2 km s^–1.     

The equatorial photospheric rotation rate

The equatorial photospheric rotation rate has been observed on 14 days in 1978–1980. The resulting rotation rate, = 14.14±0.04°/day, is 2% slower than the rate as observed for long-lived sunspots.Stationed at Kitt Peak National Observatory.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.     

The rotation of the solar atmosphere

A model of the solar atmosphere is presented in which we discuss the conservation of angular momentum for the two basic states in which the solar gas can be: namely, either confined by closed field lines or outflowing along open magnetic field lines. It can be shown that the boundary conditions are in general different for these two cases. From this we obtain the results that in the closed configuration the gas can corotate at the solar surface with the magnetic field lines and its angular velocity will then increase with height, whereas for a gas flowing along an open field line the angular velocity will decrease. An exception to the latter case can be found where the open magnetic field lines are strongly nonradial and where the density is a slowly varying function of radius. In such regions the angular velocity may initially increase with height, reach a maximum and then decrease.Kitt Peak National Observatory Contribution No. 439.Operated by The Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Infrared reflectance spectra of Hyperion,Titania, and Triton

Medium-resolution infrared (1–2.5 μm; Δλ/λ ∽ 0.05) photometry of Triton, Titania, and Hyperion and medium-resolution (1.5–2.4 μm; Δλ/λ ? 0.01) spectroscopy of Triton are presented. Hyperion and Titania have spectra roughly similar to the laboratory spectrum of water frost, while the spectrum of Triton is inconsistent with the spectra of frosts likely to be major surface constituents.     

The slow rotation of 253 Mathilde

CCD photometry of the NEAR mission fly-by target 253 Mathilde is presented. Measurements taken during 52 nights of observations, from February to June 1995, allow a rotation period of 17.406±0.010 days and a lightcurve amplitude of 0.45±0.02 mag to be determined. A B-V color index of 0.67±0.02 and a V-R of 0.35±0.02 are measured, which are compatible with C-type membership. The determination of the phase relation results in H = 10.28±0.03 and G = 0.12±0.06. Indications that the lightcurve is not strictly singly-periodic are found. A power-spectrum analysis detects a secondary frequency f₂ = 0.0322±0.0010 d⁻¹, which is interpreted as evidence for a complex rotation state.     

Eight-color photometry of Hyperion,Iapetus, and Phoebe

Eight-color spectrophotometry was obtained of Phoebe, Hyperion, and the dark side of Iapetus. Our observed V magnitudes and Voyager-derived diameters yield geometric albedos of 0.07 for Iapetus (with some bright-side contamination), 0.06 for Phoebe, and limits of 0.19 to 0.25 for Hyperion (using the satellite's maximum and minimum dimensions, respectively). Hyperion and Iapetus have quite reddish spectra similar to each other and the spectra of D-type asteroids. Hyperion, however, has a much higher albedo than the dark side of Iapetus or any D-type asteroid measured to date. The mean spectrum of Phoebe is much flatter, with a broad absorption feature near 1 μm. Therefore the surface materials of Phoebe and the dark side of Iapetus are optically quite different, a result that constraints the possible modes of interaction between Phoebe and the other two satellites.     

The Earth's rotation: Definition of the pole and of the angle of sidereal rotation

The use of new techniques for measuring the Earth's orientation in space and the intrinsic qualities of their attached terrestrial and celestial reference frames have now raised the accuracy of the computed polar coordinates and the angle of sidereal rotation to a level usually better than 0.001. The conceptual and conventional definitions of the Earth's pole of rotation and of the Universal Time UT1 must accordingly be given with the same order of precision. This paper gives a review of the past and present definitions of the celestial pole and UT1 as well as an evaluation of their deficiencies. Some necessary improvements in these definitions are proposed.