A Quantitative Criterion for Defining Planets

A simple metric can be used to determine whether a planet or exoplanet can clear its orbital zone during a characteristic time scale, such as the lifetime of the host star on the main sequence. This criterion requires only estimates of star mass, planet mass, and orbital period, making it possible to immediately classify 99% of all known exoplanets. All 8 planets and all classifiable exoplanets satisfy the criterion. This metric may be useful in generalizing and simplifying the definition of a planet.Comment: Accepted for publication in the Astronomical Journal; 7 pages, 6 figure

The Role of Kozai Cycles in Near-Earth Binary Asteroids

We investigate the Kozai mechanism in the context of near-Earth binaries and the Sun. The Kozai effect can lead to changes in eccentricity and inclination of the binary orbit, but it can be weakened or completely suppressed by other sources of pericenter precession, such as the oblateness of the primary body. Through numerical integrations including primary oblateness and 3 bodies (the two binary components and the Sun), we show that Kozai cycles cannot occur for the closely-separated near-Earth binaries in our sample. We demonstrate that this is due to pericenter precession around the oblate primary, even for very small oblateness values. Since the majority of observed near-Earth binaries are not well-separated, we predict that Kozai cycles do not play an important role in the orbital evolution of most near-Earth binaries. For a hypothetical wide binary modeled after 1998 ST27, the separation is large at 16 primary radii and so the orbital effects of primary oblateness are lessened. For this wide binary, we illustrate the possible excursions in eccentricity and inclination due to Kozai cycles as well as depict stable orientations for the binary's orbital plane. Unstable orientations lead to collisions between binary components, and we suggest that the Kozai effect acting in wide binaries may be a route to the formation of near-Earth contact binaries.Comment: 9 pages, accepted to A

Are Planetary Systems Filled to Capacity? A Study Based on Kepler Results

We used a sample of Kepler candidate planets with orbital periods less than 200 days and radii between 1.5 and 30 Earth radii 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 (10^8 years) 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 2-planet, 3-planet, and 4-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.Comment: 8 pages, 4 figures, accepted to Ap

Near-Earth Asteroid Satellite Spins Under Spin-Orbit Coupling

We develop a fourth-order numerical integrator to simulate the coupled spin and orbital motions of two rigid bodies having arbitrary mass distributions under the influence of their mutual gravitational potential. We simulate the dynamics of components in well-characterized binary and triple near-Earth asteroid systems and use surface of section plots to map the possible spin configurations of the satellites. For asynchronous satellites, the analysis reveals large regions of phase space where the spin state of the satellite is chaotic. For synchronous satellites, we show that libration amplitudes can reach detectable values even for moderately elongated shapes. The presence of chaotic regions in the phase space has important consequences for the evolution of binary asteroids. It may substantially increase spin synchronization timescales, explain the observed fraction of asynchronous binaries, delay BYORP-type evolution, and extend the lifetime of binaries. The variations in spin rate due to large librations also affect the analysis and interpretation of lightcurve and radar observations.Comment: 12 pages, 11 figures, Published in A

Improved Algorithms for Radar-based Reconstruction of Asteroid Shapes

We describe our implementation of a global-parameter optimizer and Square Root Information Filter (SRIF) into the asteroid-modelling software SHAPE. We compare the performance of our new optimizer with that of the existing sequential optimizer when operating on various forms of simulated data and actual asteroid radar data. In all cases, the new implementation performs substantially better than its predecessor: it converges faster, produces shape models that are more accurate, and solves for spin axis orientations more reliably. We discuss potential future changes to improve SHAPE's fitting speed and accuracy.Comment: 12 pages, 9 figure

Tidal End States of Binary Asteroid Systems with a Nonspherical Component

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.Comment: 13 pages, 3 figures, published in Icaru

Prospects of dynamical determination of General Relativity parameter beta and solar quadrupole moment J2 with asteroid radar astronomy

We evaluated the prospects of quantifying the parameterized post-Newtonian parameter beta and solar quadrupole moment J2 with observations of near-Earth asteroids with large orbital precession rates (9 to 27 arcsec century$^{-1}$). We considered existing optical and radar astrometry, as well as radar astrometry that can realistically be obtained with the Arecibo planetary radar in the next five years. Our sensitivity calculations relied on a traditional covariance analysis and Monte Carlo simulations. We found that independent estimates of beta and J2 can be obtained with precisions of $6\times10^{-4}$ and $3\times10^{-8}$, respectively. Because we assumed rather conservative observational uncertainties, as is the usual practice when reporting radar astrometry, it is likely that the actual precision will be closer to $2\times10^{-4}$ and $10^{-8}$, respectively. A purely dynamical determination of solar oblateness with asteroid radar astronomy may therefore rival the helioseismology determination.Comment: The astrophysical journal (ApJ), in pres

Asteroid Systems: Binaries, Triples, and Pairs

In the past decade, the number of known binary near-Earth asteroids has more than quadrupled and the number of known large main belt asteroids with satellites has doubled. Half a dozen triple asteroids have been discovered, and the previously unrecognized populations of asteroid pairs and small main belt binaries have been identified. The current observational evidence confirms that small (<20 km) binaries form by rotational fission and establishes that the YORP effect powers the spin-up process. A unifying paradigm based on rotational fission and post-fission dynamics can explain the formation of small binaries, triples, and pairs. Large (>20 km) binaries with small satellites are most likely created during large collisions.Comment: 31 pages, 12 figures. Chapter in the book ASTEROIDS IV (in press

Binary Asteroid Encounters with Terrestrial Planets: Timescales and Effects

Many asteroids that make close encounters with terrestrial planets are in a binary configuration. Here we calculate the relevant encounter timescales and investigate the effects of encounters on a binary's mutual orbit. We use a combination of analytical and numerical approaches with a wide range of initial conditions. Our test cases include generic binaries with close, moderate, and wide separations, as well as seven well-characterized near-Earth binaries. We find that close approaches (<10 Earth radii) occur for almost all binaries on 1-10 million year timescales. At such distances, our results suggest substantial modifications to a binary's semi-major axis, eccentricity, and inclination, which we quantify. Encounters within 30 Earth radii typically occur on sub-million year timescales and significantly affect the wider binaries. Important processes in the lives of near-Earth binaries, such as tidal and radiative evolution, can be altered or stopped by planetary encounters.Comment: 8 pages, accepted to A

Mercury's Internal Structure

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.Comment: 36 pages, 11 figures, in press, to appear in "Mercury - The View after MESSENGER", S. C. Solomon, B. J. Anderson, L. R. Nittler (editors), Cambridge University Pres