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     

The chaotic rotation of Hyperion

A plot of spin rate versus orientation when Hyperion is at the pericenter of its orbit (surface of section) reveals a large chaotic zone surrounding the synchronous spin-orbit state of Hyperion, if the satellite is assumed to be rotating about a principal axis which is normal to its orbit plane. This means that Hyperion's rotation in this zone exhibits large, essentially random variations on a short time scale. The chaotic zone is so large that it surrounds the ½ and 2 states, and libration in the 3/2 state is not possible. Stability analysis shows that for libration in the synchronous and ½ states, the orientation of the spin axis normal to the orbit plane is unstable, whereas rotation in the 2 state is attitude stable. Rotation in the chaotic zone is also attitude unstable. A small deviation of the principal axis from the orbit normal leads to motion through all angles in both the chaotic zone and the attitude unstable libration regions. Measures of the exponential rate of separation of nearby trajectories in phase space (Lyapunov characteristic exponents) for these three-dimensional motions indicate the the tumbling is chaotic and not just a regular motion through large angles. As tidal dissipation drives Hyperion's spin toward a nearly synchronous value, Hyperion necessarily enters the large chaotic zone. At this point Hyperion becomes attitude unstable and begins to tumble. Capture from the chaotic state into the synchronous or ½ state is impossible since they are also attitude unstable. The 3/2 state does not exist. Capture into the stable 2 state is possible, but improbable. It is expected that Hyperion will be found tumbling chaotically.     

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.     

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.     

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.     

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.     

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.     

BVR photometry of Hyperion near the time of the 2005 Cassini encounter

Six nights of BVR photometry and three nights of R photometry were collected over a month-long period shortly after the Cassini encounter with Hyperion on September 24 2005. Our observations were designed to help constrain the rotational state of the chaotically rotating satellite. Fourier analysis of our lightcurve data yields three possible periods: 10.2±0.2, 13.9±0.2, and 19.7±0.4 days. Our B-V and V-R colors agree well with previous ground-based and Voyager 2 measurements.     

Rotational Properties of Cometary Nuclei

We review several techniques used to retrieve rotational parameters from observations. The spin period of a dozen of comets retrieved with these techniques are summarized. We describe how the spin period of comet Hale-Bopp (C/1995 O1) has been calculated with a high accuracy (11.30–11.34 h). Although several authors converged to a spin axis orientation at (α,δ) = (275 ± 15°, -55 ± 5°), detailed studies indicate that the dust jets morphology in 1996–1997 may be incompatible with this orientation. Comet 19P/Borrelly has been recently observed by the Deep Space 1 spacecraft. At the same time, its spin axis orientation and period have been determined by several authors to be respectively (α,δ) = (225 ± 15°, -10 ± 10°)and 26h. These two comets are likely to be in (or close to) a principal axis spin state. We discuss new modeling of the spin state of comet 46P/Wirtanen, the target of the Rosetta mission. The model involves a three-dimensional shape and thermal model, from which the torque of the non gravitational force is calculated at each time step. The moments of inertia are computed for each irregular shape. The results from numerical integrations show that this comet can remain in a principal axis spin state during more than 10 orbits if the spin period does not get above～6 h. If the spin period increases, its nucleus gets rapidly into excited spin states. It shows that even small and very active short-period comets are not necessarily in non principal axis spin states. In the last section, the consequences of recent observations and modeling of the rotational parameters of comet nuclei are discussed, and unsolved problems are presented.     

Rotational evolution of the Sun

The evolutionary behaviour of rotating solar models with different initial angular-momentum distributions has been investigated through the pre-Main-Sequence and Main-Sequence phases. The angular momentum was removed from the convective evelope of the solar models according to the Kawaler's model of magnetic stellar wind (Kawaler, 1988). The models show that (i) the surface rotational velocities of the solar mass stars are independent of initial angular momentum for ages greater than 10⁸ years and (ii) it is not possible to explain the neutrino problem and the sufficient depletion of lithium in the Sun.     

Rotational evolution of solar-type stars

The aim of the present investigation has been to consider rotational evolution of solar-type stars simulated by a polytropic model that possesses differential rotation of Clement's type. A properly defined reduction factor moderates the effects of such a rotation. The present treatment is based upon the general Eulerian equation, governing nonuniform (i.e., nonrigid-body) rotation, which has been set up in a previous investigation. Nonconservative terms, arising when stellar wind torque is under consideration, are taken into account. Data available for the viscosity of the Sun are used to construct a plausible viscosity model. Certain assumptions are made that remove the mathematical difficulties and simplify the physical ground. The obtained results are compared to corresponding estimates of recent observations.     

Rotational dynamics of celestial bodies

In this paper the ‘class of near homoaxial rotations’ is defined, being suitable for treatment of problems of nonuniform rotation of stars. This class is represented by a proper form of the so-called ‘velocity tensor’, the latter describing efficiently the motion of a deformable finite material continuum in the common frame. The ‘class of particular near homoaxial rotations’ is then defined, characterized by simple transformation equations of the velocity tensor in two noninertial frames; namely, in a ‘frame rotating uniformly’ relative to the common frame, and in a ‘frame rotating nonuniformly’ relative to it. A sufficient condition is also derived so that a near homoaxial rotation be reducible to a particular one. ‘Preferred frames’ are then defined in the sense that they preserve a near homoaxial rotation in its class when referring thismotion; that is, such frames keep invariant the intertial class of the motion. Finally, a method is proposed for constructing a nonuniformly rotating preferred frame, to which a near homoaxial rotation is referred simply as ‘radial distortion’.     

Rotational circulation-preserving magnetogeostrophic flows

It has been shown that the only steady, inviscid, magnetogeostrophic rotational circulation-preverving motion whose magnetic field line pattern is that of the irrotational motion is a complex-lamellar motion whose magnetic field magnitude bears a constant value on a magnetic field line.     

Rotational dynamics of a deformable medium

The aim of the present investigation has been to derive from the fundamental Cauchy's first law of continuum mechanics the explicit form of the Eulerian general equation which governs the three-axial generalized rotation about the centre of mass of a self-gravitating deformable finite material continuum, viscolinear (i.e., Newtonian) or not, consisting of compressible fluid of arbitrary viscosity, in an external field of force. The generalized rotation is a superposition of the so-called rigid-body (i.e., time dependent only) rotation of the continuum plus a nonrigidbody (i.e., position-time dependent) rotation of its configurations.In Section 2, which follows brief introductory remarks outlining the problem, we develop a mathematical theory which describes the whole phenomenon in terms of two rotation tensors corresponding, respectively, to the rigid-body and nonrigid-body rotation modes. In Section 3, we derive the differmation vectors of velocity and acceleration. The equations we have obtained are a very general version of Navier Stokes' equations, which were not given in previous investigations. In Section 4, we perform integration of the left-hand side of Cauchy's first law, cross-multiplied by the position vector, without any restriction. In Section 6, integration of the right-hand side of the same law, cross-multiplied by the position vector, is carried out, by taking account of actually simplifying assumptions stated in Section 5. All the integral terms occurring in both sides are expressed explicitly by quantities evaluated in terms of components of properly defined moments.Finally, in Section 7, the system of the general Eulerian equations is set up; and some easy modifications are given, which describe nicely physical models of special interest; while the concluding Section 8 contains a general discussion of the results.     

Rotational Modulation of Microwave Solar Flux

Time series data of 10.7 cm solar flux for one solar cycle (1985–1995 years) was processed through autocorrelation. Rotation modulation with varying persistence and period was quite evident. The persistence of modulation seems to have no relation with sunspot numbers. The persistence of modulation is more noticeable during 1985–1986, 1989–1990, and 1990–1991. In other years the modulation is seen, but its persistence is less. The sidereal rotation period varies from 24.07 days to 26.44 days with no systematic relation with sunspot numbers. The results indicate that the solar corona rotates slightly faster than photospheric features. The solar flux was split into two parts, i.e., background emission which remains unaffected by solar rotation and the localized emission which produces the observed rotational modulation. Both these parts show a direct relation with the sunspot numbers. The magnitude of localized emission almost diminishes during the period of low sunspot number, whereas background emission remains at a 33% level even when almost no sunspots may be present. The localized regions appear to shift on the solar surface in heliolongitudes.     

Rotational fission of contact binary asteroids

The energetics and dynamics of contact binary asteroids as they approach and pass the rotational fission limit is studied. We presume that the asteroids are subject to an external torque, such as from the YORP effect, that increases their angular momentum. Furthermore, we assume the asteroids can be described by a fairly minimal model comprised of a sphere and ellipsoid resting on each other. The minimum energy configurations for contact binary asteroids at different levels of angular momentum are computed and discussed. We find distinct transitions between different configurations as the angular momentum of the system is increased. These indicate that rapidly rotating contact binary asteroids may seek out clearly different relative configurations than slowly rotating systems. We find a single end state of the systems prior to rotational fission, and distinct dynamical outcomes as a function of mass distribution and shape when the rotational fission limit is exceeded. Our theoretical results agree qualitatively with observed properties of near-Earth asteroids, and can be used to help explain the spin-rate barrier, contact binaries, and the observed morphology of most NEO binaries.     

Rotational dynamics of celestial deformable bodies

In a previous paper of this series (Tokis, 1974b), we have discussed the solution of the Eulerian equation which governs the axial rotation, applied to the effects of viscous friction exhibited in binary systems which consist of a close pair of fluid bodies of arbitrary structure. The aim of the present paper will be to give an application of those results to the Earth-Moon system. It is shown that synchronism between the axial rotation of the Earth and the revolution of the Moon will occur at the value of 650 h, in a time scale which depends strongly on the value of the mean viscosity of the Earth (regarded as spherical or spheroidal). In particular, the variation of rotational angular velocity of the Earth over the next ten centuries commencing from 1900 A.D., depends sensitively on the value of viscosity. On the other hand, the time for synchronism of axial rotation of the Moon is not affected by the viscosity for values between 10²⁴g cm^?1 s^?1 and 10²⁷g cm^?1 s^?1.     

Rotational dynamics of deformable celestial bodies

1.40M . C¹²+C¹²Mg²⁴+. Bruenn (1972) . , ( ), . , URCA . ( , ) . .