High-resolution images of the surface of asteroid Itokawa from the Hayabusa mission reveal it to be covered with unconsolidated millimeter-sized and larger gravels. Locations and morphologic characteristics of this gravel indicate that Itokawa has experienced considerable vibrations, which have triggered global-scale granular processes in its dry, vacuum, microgravity environment. These processes likely include granular convection, landslide-like granular migrations, and particle sorting, resulting in the segregation of the fine gravels into areas of potential lows. Granular processes become major resurfacing processes because of Itokawa's small size, implying that they can occur on other small asteroids should they have regolith.

Radar and optical observations reveal that the continuous increase in the spin rate of near-Earth asteroid (54509) 2000 PH5 can be attributed to the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect, a torque due to sunlight. The change in spin rate is in reasonable agreement with theoretical predictions for the YORP acceleration of a body with the radar-determined size, shape, and spin state of 2000 PH5. The detection of asteroid spin-up supports the YORP effect as an explanation for the anomalous distribution of spin rates for asteroids under 10 km in diameter and as a binary formation mechanism.

Dynamical simulations of the coupled rotational and orbital dynamics of binary near-Earth asteroid (66391) 1999 KW4 suggest that it is excited due to perturbations from the sun during perihelion passages. Excitation of the mutual orbit will stimulate complex internal motions, including periodic fluctuations in the orbit and in the magnitude of the angular momentum of the primary component, and oscillations in the rotational dynamics and orbital mechanics of the smaller component that cause its attitude relative to uniform rotation to have large variation within some orbits and to hardly vary within others. The primary's proximity to its rotational stability limit suggests an origin from spin-up and disruption of a loosely bound precursor within the past million years.

High-resolution radar images reveal near-Earth asteroid (66391) 1999 KW4 to be a binary system. The ~1.5-km-diameter primary (Alpha) is an unconsolidated gravitational aggregate with spin period ~ 2.8 h, bulk density ~2 g cm(-3), porosity ~ 50%, and an oblate shape dominated by an equatorial ridge at the object's potential energy minimum. The ~0.5-km secondary (Beta) is elongated and probably is denser than Alpha. Its average orbit about Alpha is circular with radius ~2.5 km and period ~17.4 h, and its average rotation is synchronous with the long axis pointed toward Alpha, but librational departures from that orientation are evident. Exotic physical and dynamical properties may be common among near-Earth binaries.

The ranging instrument aboard the Hayabusa spacecraft measured the surface topography of asteroid 25143 Itokawa and its mass. A typical rough area is similar in roughness to debris located on the interior wall of a large crater on asteroid 433 Eros, which suggests a surface structure on Itokawa similar to crater ejecta on Eros. The mass of Itokawa was estimated as (3.58 +/- 0.18) x 10(10) kilograms, implying a bulk density of (1.95 +/- 0.14) grams per cubic centimeter for a volume of (1.84 +/- 0.09) x 10(7) cubic meters and a bulk porosity of approximately 40%, which is similar to that of angular sands, when assuming an LL (low iron chondritic) meteorite composition. Combined with surface observations, these data indicate that Itokawa is the first subkilometer-sized small asteroid showing a rubble-pile body rather than a solid monolithic asteroid.

During the interval from September through early December 2005, the Hayabusa spacecraft was in close proximity to near-Earth asteroid 25143 Itokawa, and a variety of data were taken on its shape, mass, and surface topography as well as its mineralogic and elemental abundances. The asteroid's orthogonal axes are 535, 294, and 209 meters, the mass is 3.51 x 10(10) kilograms, and the estimated bulk density is 1.9 +/- 0.13 grams per cubic centimeter. The correspondence between the smooth areas on the surface (Muses Sea and Sagamihara) and the gravitationally low regions suggests mass movement and an effective resurfacing process by impact jolting. Itokawa is considered to be a rubble-pile body because of its low bulk density, high porosity, boulder-rich appearance, and shape. The existence of very large boulders and pillars suggests an early collisional breakup of a preexisting parent asteroid followed by a re-agglomeration into a rubble-pile object.

Equilibrium conditions for a mutually attracting general mass distribution and point mass are stated. The equilibrium conditions can be reduced to six equations in six unknowns, plus the existence of integrals of motion consisting of the total angular momentum and energy of the system. The equilibrium conditions are further reduced to two independent equations, and their theoretical properties are studied. We state a set of necessary and sufficient conditions for an equilibrium that is well suited to the computation of certain classes of equilibria. These equations are solved for nonsymmetric gravity fields of interest, using a real asteroid shape model for the general gravity fields. The stability of the resulting equilibria are also noted.

The fuel optimality of third-body driven plane changes (i.e., plane changes performed by using third-body forces) over one-impulse transfers is investigated numerically and analytically. In particular, the range of third-body driven plane changes that are realizable is shown to be restricted and one impulse must be used in the uncovered regions. However, when third-body driven plane changes are realizable, it is shown that they are always optimal above a certain critical value (about 40 degrees ) that depends on the initial condition. Contour plots of optimal DeltaV values to perform a desired plane changes are given.

The stability of relative equilibrium solutions for the interaction of two massive bodies is explored. We restrict ourselves to the interaction between an ellipsoid and a sphere, both with finite mass. The study of this problem has application to modeling the relative dynamics of binary asteroids, the motion of spacecraft about small bodies, and the dynamics of gravity gradient satellites. The relative equilibrium can be parameterized by a few constants, including the mass ratio of the two bodies, the shape of the ellipsoid, and the normalized distance between the two bodies. Planar stability is characterized over this range of parameter values. When restricted to motion in the symmetry plane, the dynamical problem can be reduced to a two-degrees of freedom Hamiltonian system, which allows for an efficient computation of stability characteristics of the relative equilibria. Future work will look at full stability of these relative equilibria.

The purpose of this paper is to describe the general setting for the application of techniques from geometric mechanics and dynamical systems to the problem of asteroid pairs. The paper also gives some preliminary results on transport calculations and the associated problem of calculating binary asteroid escape rates. The dynamics of an asteroid pair, consisting of two irregularly shaped asteroids interacting through their gravitational potential is an example of a full-body problem or FBP in which two or more extended bodies interact. One of the interesting features of the binary asteroid problem is that there is coupling between their translational and rotational degrees of freedom. General FBPs have a wide range of other interesting aspects as well, including the 6-DOF guidance, control, and dynamics of vehicles, the dynamics of interacting or ionizing molecules, the evolution of small body, planetary, or stellar systems, and almost any other problem in which distributed bodies interact with each other or with an external field. This paper focuses on the specific case of asteroid pairs using techniques that are generally applicable to many other FBPs. This particular full two-body problem (F2BP) concerns the dynamical evolution of two rigid bodies mutually interacting via a gravitational field. Motivation comes from planetary science, where these interactions play a key role in the evolution of asteroid rotation states and binary asteroid systems. The techniques that are applied to this problem fall into two main categories. The first is the use of geometric mechanics to obtain a description of the reduced phase space, which opens the door to a number of powerful techniques, such as the energy-momentum method for determining the stability of equilibria and the use of variational integrators for greater accuracy in simulation. Second, techniques from computational dynamic systems are used to determine phase space structures that are important for transport phenomena and dynamic evolution.