Planetary orientation models describe the orientation of the spin axis and prime meridian of planets in inertial space as a function of time. The models are required for the planning and execution of Earth-based or space-based observational work, e.g. to compute viewing geometries and to tie observations to planetary coordinate systems. The current orientation model for Mercury is inadequate because it uses an obsolete spin orientation, neglects oscillations in the spin rate called longitude librations, and relies on a prime meridian that no longer reflects its intended dynamical significance. These effects result in positional errors on the surface of ~1.5 km in latitude and up to several km in longitude, about two orders of magnitude larger than the finest image resolution currently attainable. Here we present an updated orientation model which incorporates modern values of the spin orientation, includes a formulation for longitude librations, and restores the dynamical significance to the prime meridian. We also use modern values of the orbit normal, spin axis orientation, and precession rates to quantify an important relationship between the obliquity and moment of inertia differences. © The Author(s) 2009.

We used a sample of Kepler candidate planets with orbital periods less than 200 days and radii between 1.5 and 30 Earth radii (R⊕) to determine the typical dynamical spacing of neighboring planets. To derive the intrinsic (i.e., free of observational bias) dynamical spacing of neighboring planets, we generated populations of planetary systems following various dynamical spacing distributions, subjected them to synthetic observations by the Kepler spacecraft, and compared the properties of observed planets in our simulations with actual Kepler detections. We found that, on average, neighboring planets are spaced 21.7 mutual Hill radii apart with a standard deviation of 9.5. This dynamical spacing distribution is consistent with that of adjacent planets in the solar system. To test the packed planetary systems hypothesis, the idea that all planetary systems are dynamically packed or filled to capacity, we determined the fraction of systems that are dynamically packed by performing long-term (108years) numerical simulations. In each simulation, we integrated a system with planets spaced according to our best-fit dynamical spacing distribution but containing an additional planet on an intermediate orbit. The fraction of simulations exhibiting signs of instability provides an approximate lower bound on the fraction of systems that are dynamically packed; we found that ≥31%, ≥35%, and ≥45% of two-planet, three-planet, and four-planet systems are dynamically packed, respectively. Such sizeable fractions suggest that many planetary systems are indeed filled to capacity. This feature of planetary systems is another profound constraint that formation and evolution models must satisfy. © 2013. The American Astronomical Society. All rights reserved..

The locations of the fully despun, double synchronous end states of tidal evolution, where the rotation rates of both the primary and secondary components in a binary system synchronize with the mean motion about the center of mass, are derived for spherical components. For a given amount of scaled angular momentum J/. J', the tidal end states are over-plotted on a tidal evolution diagram in terms of mass ratio of the system and the component separation (semimajor axis in units of primary radii). Fully synchronous orbits may not exist for every combination of mass ratio and angular momentum; for example, equal-mass binary systems require J/. J' > 0.44. When fully synchronous orbits exist for prograde systems, tidal evolution naturally expands the orbit to the stable outer synchronous solution. The location of the unstable inner synchronous orbit is typically within two primary radii and often within the radius of the primary itself. With the exception of nearly equal-mass binaries, binary asteroid systems are in the midst of lengthy tidal evolutions, far from their fully synchronous tidal end states. Of those systems with unequal-mass components, few have even reached the stability limit that splits the fully synchronous orbit curves into unstable inner and stable outer solutions.Calculations of material strength based on limiting the tidal evolution time to the age of the Solar System indicate that binary asteroids in the main belt with 100-km-scale primary components are consistent with being made of monolithic or fractured rock as expected for binaries likely formed from sub-catastrophic impacts in the early Solar System. To tidally evolve in their dynamical lifetime, near-Earth binaries with km-scale primaries or smaller created via a spin-up mechanism must be much weaker mechanically than their main-belt counterparts even if formed in the main belt prior to injection into the near-Earth region. Small main-belt binaries, those having primary components less than 10. km in diameter, could bridge the gap between the large main-belt binaries and the near-Earth binaries, as, depending on the age of the systems, small main-belt binaries could either be as strong as the large main-belt binaries or as weak as the near-Earth binaries. The inherent uncertainty in the age of a binary system is the leading source of error in calculation of material properties, capable of affecting the product of rigidity μ and tidal dissipation function Q by orders of magnitude. Several other issues affecting the calculation of μQ are considered, though these typically affect the calculation by no more than a factor of two. We also find indirect evidence within all three groups of binary asteroids that the semimajor axis of the mutual orbit in a binary system may evolve via another mechanism (or mechanisms) in addition to tides with the binary YORP effect being a likely candidate. © 2011 Elsevier Inc.

Observations with the adaptive optics system on the Very Large Telescope reveal that the outer main belt asteroid (702) Alauda has a small satellite with primary to secondary diameter ratio of ∼56. The secondary revolves around the primary in 4.9143 ± 0.007 days at a distance of 1227 ± 24 km, yielding a total system mass of (6.057 ± 0.36) x 1018kg. Combined with an IRAS size measurement, our data yield a bulk density of 1570 ± 500 kg m-3for this B-type asteroid. © 2011. The American Astronomical Society.

We investigated the underlying architecture of planetary systems by deriving the distribution of planet multiplicity (number of planets) and the distribution of orbital inclinations based on the sample of planet candidates discovered by the Kepler mission. The scope of our study included solar-like stars and planets with orbital periods less than 200 days and with radii between 1.5 and 30 Earth radii, and was based on Kepler planet candidates detected during Quarters 1-6. We created models of planetary systems with different distributions of planet multiplicity and inclinations, simulated observations of these systems by Kepler, and compared the properties of the transits of detectable objects to actual Kepler planet detections. Specifically, we compared with both the Kepler sample's transit numbers and normalized transit duration ratios in order to determine each model's goodness of fit. We did not include any constraints from radial velocity surveys. Based on our best-fit models, 75%-80% of planetary systems have one or two planets with orbital periods less than 200 days. In addition, over 85% of planets have orbital inclinations less than 3° (relative to a common reference plane). This high degree of coplanarity is comparable to that seen in our solar system. These results have implications for planet formation and evolution theories. Low inclinations are consistent with planets forming in a protoplanetary disk, followed by evolution without significant and lasting perturbations from other bodies capable of increasing inclinations. © 2012. The American Astronomical Society. All rights reserved..

We derive the locations of the fully synchronous end states of tidal evolution for binary asteroid systems having one spherical component and one oblate- or prolate-spheroid component. Departures from a spherical shape, at levels observed among binary asteroids, can result in the lack of a stable tidal end state for particular combinations of the system mass fraction and angular momentum, in which case the binary must collapse to contact. We illustrate our analytical results with near-Earth Asteroids (8567) 1996 HW1, (66391) 1999 KW4, and 69230 Hermes. © 2013 Elsevier Inc.

Sylvia is a triple asteroid system located in the main belt. We report new adaptive optics observations of this system that extend the baseline of existing astrometric observations to a decade. We present the first fully dynamical three-body model for this system by fitting to all available astrometric measurements. This model simultaneously fits for individual masses, orbits, and primary oblateness. We find that Sylvia is composed of a dominant central mass surrounded by two satellites orbiting at 706.5 ± 2.5km and 1357 ± 4.0km, i.e., about 5 and nearly 10 primary radii. We derive individual masses of 1.484+0.016- 0.014× 1019kg for the primary (corresponding to a density of 1.29 ± 0.39g cm-3), 7.33+4.7- 2.3× 1014kg for the inner satellite, and 9.32+20.7- 8.3× 1014kg for the outer satellite. The oblateness of the primary induces substantial precession and the J2value can be constrained to the range of 0.0985-0.1. The orbits of the satellites are relatively circular with eccentricities less than 0.04. The spin axis of the primary body and the orbital poles of both satellites are all aligned within about 2deg of each other, indicating a nearly coplanar configuration and suggestive of satellite formation in or near the equatorial plane of the primary. We also investigate the past orbital evolution of the system by simulating the effects of a recent passage through 3:1 mean-motion eccentricity-type resonances. In some scenarios this allow us to place constraints on interior structure and past eccentricities. © 2012. The American Astronomical Society. All rights reserved.

We have identified and quantified semimajor axis drifts in near-Earth asteroids (NEAs) by performing orbital fits to optical and radar astrometry of all numbered NEAs. We focus on a subset of 54 NEAs that exhibit some of the most reliable and strongest drift rates. Our selection criteria include a Yarkovsky sensitivity metric that quantifies the detectability of semimajor axis drift in any given data set, a signal-to-noise metric, and orbital coverage requirements. In 42 cases, the observed drifts (∼10-3AUMyr-1) agree well with numerical estimates of Yarkovsky drifts. This agreement suggests that the Yarkovsky effect is the dominant non-gravitational process affecting these orbits, and allows us to derive constraints on asteroid physical properties. In 12 cases, the drifts exceed nominal Yarkovsky predictions, which could be due to inaccuracies in our knowledge of physical properties, faulty astrometry, or modeling errors. If these high rates cannot be ruled out by further observations or improvements in modeling, they would be indicative of the presence of an additional non-gravitational force, such as that resulting from a loss of mass of order a kilogram per second. We define the Yarkovsky efficiency fYas the ratio of the change in orbital energy to incident solar radiation energy, and we find that typical Yarkovsky efficiencies are ∼10-5. © 2012. The American Astronomical Society. All rights reserved.

The combination of the radio tracking of the MErcury Surface, Space ENvironment, GEochemistry, and Ranging spacecraft and Earth-based radar measurements of the planet's spin state gives three fundamental quantities for the determination of the interior structure of Mercury: mean density ρ, moment of inertia C, and moment of inertia of the outer solid shell C m. This work focuses on the additional information that can be gained by a determination of the change in gravitational potential due to planetary tides, as parameterized by the tidal potential Love number k2. We investigate the tidal response for sets of interior models that are compatible with the available constraints (ρ, C, and Cm). We show that the tidal response correlates with the size of the liquid core and the mean density of material below the outer solid shell and that it is affected by the rheology of the outer solid shell of the planet, which depends on its temperature and mineralogy. For a mantle grain size of 1cm, we calculate that the tidal k 2 of Mercury is in the range 0.45 to 0.52. Some of the current models for the interior structure of Mercury are compatible with the existence of a solid FeS layer at the top of the core. Such a layer, if present, would increase the tidal response of the planet. Key Points We present models of the tidal deformation of Mercury based on MESSENGER results Tides are sensitive to size and density of the core and rheology of outer shell The presence of a FeS layer would increase the tidal response ©2014. American Geophysical Union. All Rights Reserved.

We describe the current state of knowledge about Mercury's interior structure. We review the available observational constraints, including mass, size, density, gravity field, spin state, composition, and tidal response. These data enable the construction of models that represent the distribution of mass inside Mercury. In particular, we infer radial profiles of the pressure, density, and gravity in the core, mantle, and crust. We also examine Mercury's rotational dynamics and the influence of an inner core on the spin state and the determination of the moment of inertia. Finally, we discuss the wide-ranging implications of Mercury's internal structure on its thermal evolution, surface geology, capture in a unique spin-orbit resonance, and magnetic field generation.