We present a model of the precession dynamics of the Moon that comprises a fluid outer core and a solid inner core. We show that three Cassini states associated with the inner core exist. The tilt angle of the inner core in each of these states is determined by the ratio between the free inner core nutation frequency ($ω_{ficn}$) and the precession frequency $Ω_p = 2π/18.6$ yr $^{-1}$. All three Cassini states are possible if $|ω_{ficn}| > 2π/16.4$ yr $^{-1}$, but only one is possible otherwise. Assuming that the lowest energy state is favoured, this transition marks a discontinuity in the tilt angle of the inner core, transiting from $-33^\circ$ to $17^\circ$ as measured with respect to the mantle figure axis, where negative angles indicate a tilt towards the orbit normal. Possible Lunar interior density structures cover a range of $ω_{ficn}$, from approximately half to twice as large as $Ω_p$, so the precise tilt angle of the inner core remains unknown, though it is likely large because $Ω_p$ is within the resonant band of $ω_{ficn}$. Adopting one specific density model, we suggest an inner core tilt of approximately $-17^\circ$. Viscoelastic deformations within the inner core and melt and growth at the surface of a tilted inner core, both neglected in our model, should reduce this amplitude. If the inner core is larger than approximately 200 km, it may contribute by as much as a few thousandths of a degree on the observed mantle precession angle of $1.543^\circ$.
Analyses of Lunar Laser Ranging data show that the spin-symmetry axis of the Moon is ahead of its expected Cassini state by an angle of $ϕ_p$ = 0.27 arcsec. This indicates the presence of one or more dissipation mechanisms acting on the lunar rotation. A combination of solid-body tides and viscous core-mantle coupling have been proposed in previous studies. Here, we investigate whether viscoelastic deformation within a solid inner core at the centre of the Moon can also account for a part of the observed phase lead angle $ϕ_p$. We build a rotational dynamic model of the Cassini state of the Mo…
We present a model of the Cassini state of Mercury that comprises an inner core, a fluid core and a mantle. Our model includes inertial and gravitational torques between interior regions, and viscous and electromagnetic (EM) coupling at the boundaries of the fluid core. We show that the coupling between Mercury's interior regions is sufficiently strong that the obliquity of the mantle spin axis deviates from that of a rigid planet by no more than 0.01 arcmin. The mantle obliquity decreases with increasing inner core size, but the change between a large and no inner core is limited to 0.015 arc…
Saturn's largest icy moon, Rhea, hosts a tenuous surface-sputtered exosphere composed primarily of molecular oxygen and carbon dioxide. In this Letter, we examine Cassini Plasma Spectrometer velocity space distributions near Rhea and confirm that Cassini detected nongyrotropic fluxes of outflowing CO$_2^+$ during both the R1 and R1.5 encounters. Accounting for this nongyrotropy, we show that these possess comparable alongtrack densities of $\sim$2$\times$10$^{-3}$ cm$^{-3}$. Negatively charged pickup ions, also detected during R1, are surprisingly shown as consistent with mass 26$\pm$3 u which…
The Moon is known to have a small liquid core, and it is thought that in the distant past the core may have produced strong magnetic fields recorded in lunar samples. Here we implement a numerical model of lunar orbital and rotational dynamics that includes the effects of a liquid core. In agreement with previous work, we find that the lunar core is dynamically decoupled from the lunar mantle, and that this decoupling happened very early in lunar history. Our model predicts that the lunar core rotates sub-synchronously, and the difference between the core and the mantle rotational rates was si…
During the thirteen years in orbit around Saturn before its final plunge, the Cassini spacecraft provided more than ten thousand astrometric measurements. Such large amounts of accurate data enable the search for extremely faint signals in the orbital motion of the saturnian moons. Among these, the detection of the dynamical feedback of the rotation of the inner moons of Saturn on their respective orbits becomes possible. Using all the currently available astrometric data associated with Atlas, Prometheus, Pandora, Janus and Epimetheus, we first provide a detailed analysis of the Cassini Imagi…
We compute predictions of the deviation of Mercury's spin axis from an exact Cassini state caused by tidal dissipation, and viscous and electromagnetic (EM) friction at the core-mantle boundary (CMB) and inner core boundary (ICB). Viscous friction at the CMB generates a phase lead, viscous and EM friction at the ICB produce a phase lag; the magnitude of the deviation depends on the inner core size, kinematic viscosity and magnetic field strength, but cannot exceed an upper bound. For a small inner core, viscous friction at the CMB results in a maximum phase lead of 0.027 arcsec. For a large in…
Using astrometric observations spanning more than a century and including a large set of Cassini data, we determine Saturn's tidal parameters through their current effects on the orbits of the eight main and four coorbital moons. We have used the latter to make the first determination of Saturn's Love number, $k_2=0.390 \pm 0.024$, a value larger than the commonly used theoretical value of 0.341 (Gavrilov & Zharkov, 1977), but compatible with more recent models (Helled & Guillot, 2013) for which $k_2$ ranges from 0.355 to 0.382. Depending on the assumed spin for Saturn's interior, the new cons…
For terrestrial exoplanets with thin atmospheres or no atmospheres, the surface contributes light to the reflected light signal of the planet. Measurement of the variety of disk-integrated brightnesses of bodies in the Solar System and the variation with illumination and wavelength is essential for both planning imaging observations of directly imaged exoplanets and interpreting the eventual datasets. Here we measure the change in brightness of the Galilean satellites as a function of planetocentric longitude, illumination phase angle, and wavelength. The data span a range of wavelengths from …
The Cassini Division in Saturn's rings contains a series of eight named gaps, three of which contain dense ringlets. Observations of stellar occultations by the Visual and Infrared Mapping Spectrometer onboard the Cassini spacecraft have yielded ~40 accurate and precise measurements of the radial position of the edges of all of these gaps and ringlets. These data reveal suggestive patterns in the shapes of many of the gap edges: the outer edges of the 5 gaps without ringlets are circular to within 1 km, while the inner edges of 6 of the gaps are eccentric, with apsidal precession rates consist…
The purpose of this work is to determine the location and stability of the Cassini states of a celestial body with an inviscid fluid core surrounded by a perfectly rigid mantle. Both situations where the rotation speed is either non-resonant or trapped in a p:1 spin-orbit resonance where p is a half integer are addressed. The rotation dynamics is described by the Poincaré-Hough model which assumes a simple motion of the core. The problem is written in a non-canonical Hamiltonian formalism. The secular evolution is obtained without any truncation in obliquity, eccentricity nor inclination. The …
Some of the small inner moons of Uranus have very closely-spaced orbits. Multiple numerical studies have found that the moons Cressida and Desdemona, within the Portia sub-group, are likely to collide in less than 100 Myr. The subsequent discovery of three new moons (Cupid, Perdita, and Mab) made the system even more crowded. In particular, it has been suggested that the Belinda group (Cupid, Belinda, and Perdita) will become unstable in as little as 10$^5$ years. Here we revisit the issue of the stability of the inner moons of Uranus using updated orbital elements and considering tidal dissip…
We present numerically-derived orbits and mass estimates for the inner Saturnian satellites, Atlas, Prometheus, Pandora, Janus and Epimetheus from a fit to 2580 new Cassini ISS astrometric observations spanning February 2004 to August 2013. The observations are provided in a supplementary table. We estimate GM_ Atlas=0.384+/-0.001 x 10^(-3)km^3s^(-2), a value 13% smaller than the previously published estimate but with an order of magnitude reduction in the uncertainty. We also find GM_ Prometheus=10.677+/-0.006x10(-3)km^3s^(-2), GM_Pandora=9.133+/-0.009x10^(-3)km^3s^(-2), GM_Janus=126.51+/-0.0…
The spin axes of the mantle, fluid core and solid inner core of the Moon precess at frequency $Ω_p=2π/18.6$ yr$^{-1}$ though with different orientations, leading to viscous friction at the core-mantle boundary (CMB) and inner core boundary (ICB). Here, we use a rotational model of the Moon with a range of inner core and outer core radii to investigate the relative importance of viscous dissipation at the CMB and ICB, and to show how this dissipation is connected to the phase lead angle ($ϕ_p$) of the mantle ahead of its Cassini state. We show that when the inner core radius is $>80$ km and the…
Saturn's rings are rock-poor, containing 90%-95% ice by mass. As a group, Saturn's moons interior to and including Tethys are also about 90% ice. Tethys itself contains <6% rock by mass, in contrast to its similar-mass outer neighbor Dione, which contains >40% rock. Here we simulate the evolution of a massive primordial ice-rich ring and the production of satellites as ring material spreads beyond the Roche limit. We describe the Roche-interior ring with an analytic model, and use an N-body code to describe material beyond the Roche limit. We track the accretion and interactions of spawned sat…
The Cassini spacecraft revealed the spectacular, highly irregular shapes of the small inner moons of Saturn, ranging from the unique "ravioli-like" forms of Pan and Atlas to the highly elongated structure of Prometheus. Closest to Saturn, these bodies provide important clues regarding the formation process of small moons in close orbits around their host planet, but their range of irregular shapes has not been explained yet. Here we show that the spectrum of shapes among Saturn's small moons is a natural outcome of merging collisions among similar-sized moonlets possessing physical properties …
The Cassini state equilibrium associated with the precession of the Moon predicts that the mantle, fluid core and solid inner core precess at different angles. We present estimates of the dissipation from viscous friction associated with the differential precession at the core-mantle boundary (CMB), $Q_{cmb}$, and at the inner core boundary (ICB), $Q_{icb}$, as a function of the evolving lunar orbit. We focus on the latter and show that, provided the inner core was larger than 100 km, $Q_{icb}$ may have been as high as $10^{10}-10^{11}$ W for most of the lunar history for a broad range of core…
The solar system contains solids of all sizes, ranging from km-size bodies to nano-sized particles. Nanograins have been detected in situ in the Earth's atmosphere, near cometary and giant planet environments, and more recently in the solar wind at 1 AU. These latter nano grains are thought to be formed in the inner solar system dust cloud, mainly through collisional break-up of larger grains and are then picked-up and accelerated by the magnetized solar wind because of their large charge-to-mass ratio. In the present paper, we analyze the low frequency bursty noise identified in the Cassini r…
We use a hybrid numerical approach to simulate the formation of the Moon from an impact-generated disk, consisting of a fluid model for the disk inside the Roche limit and an N-body code to describe accretion outside the Roche limit. As the inner disk spreads due to a thermally regulated viscosity, material is delivered across the Roche limit and accretes into moonlets that are added to the N-body simulation. Contrary to an accretion timescale of a few months obtained with prior pure N-body codes, here the final stage of the Moon's growth is controlled by the slow spreading of the inner disk, …
The $η$ ring is one of the narrow rings of Uranus, consisting of a dense core that is 1-2 km wide and a diffuse outer sheet spanning about 40 km. Its dense core lies just exterior to the 3:2 Inner Lindblad Resonance of the small moon Cressida. We fit the $η$ ring radius residuals and longitudes from a complete set of both ground-based and Voyager stellar and radio occultations of the Uranian rings spanning 1977-2002. We find variations in the radial position of the $η$ ring that are likely generated by this resonance, and take the form of a 3-lobed structure rotating at an angular rate equal t…
The lunar geological record contains a rich archive of the history of the inner Solar System, including information relevant to understanding the origin and evolution of the Earth-Moon system, the geological evolution of rocky planets, and our local cosmic environment. This paper provides a brief review of lunar exploration to-date, and describes how future exploration initiatives will further advance our understanding of the origin and evolution of the Moon, the Earth-Moon system, and of the Solar System more generally. It is concluded that further advances will require the placing of new sci…
As the number of discovered extrasolar planets has been increasing, diversity of planetary systems requires studies of new formation scenarios. It is important to study satellite formation in circumplanetary disks, which is often viewed as analogous to formation of rocky planets in protoplanetary disks. We investigated satellite formation from satellitesimals around giant planets through N-body simulations that include gravitational interactions with a circumplanetary gas disk. Our main aim is to reproduce the observable properties of the Galilean satellites around Jupiter through numerical si…
We use the tidal deformations of the Moon induced by the Earth and the Sun as a tool for studying the inner structure of our satellite. Based on measurements of the degree-two tidal Love numbers k2 and h2 and dissipation coefficients from the GRAIL mission, Lunar Laser Ranging and Laser Altimetry on board of the LRO spacecraft, we perform Monte Carlo samplings for 120,000 possible combinations of thicknesses and viscosities for two classes of the lunar models. The first one includes a uniform core, a low viscosity zone (LVZ) at the core-mantle boundary, a mantle and a crust. The second one has…
We present fully three-dimensional equations to describe the rotations of a body made of a deformable mantle and a fluid core. The model in its essence is similar to that used by INPOP (Integration Planétaire de l'Observatoire de Paris), e.g. Viswanathan et al. (2019), and by JPL (Jet Propulsion Laboratory), e.g. Folkner et al. (2014), to represent the Moon. The intended advantages of our model are: straightforward use of any linear-viscoelastic model for the rheology of the mantle; easy numerical implementation in time-domain (no time lags are necessary); all parameters, including those relat…
The inner structure of the earth is still a topic of discussion. Seismic measurements showed a structure of solid, liquid, solid which describes the mantle, outer core and inner core with the inner core in the center. The analysis of waveform doublets suggests now that the inner core is out of center and even of faster rotation than the mantel and crust. From the sum of Buoyancy and Gravity on the earth inner core, the position energy is plotted and together with the tangential tidal acceleration, it is derived that Earth Inner Core cannot be in a center position without additional force. The …
