Daniel J. Scheeres

The Rubble-Pile Asteroid Itokawa as Observed by Hayabusa

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 asteroids orthogonal axes are 535, 294, and 209 meters, the mass is 3.51 × 1010 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.

Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia

The exterior gravitation of a constant-density polyhedron is derived analytically in closed form. Expressions for potential, attraction, and gravity gradient matrix involve one logarithm term per edge and one arctangent term per face, The Laplacian can be used to determine whether a field point is inside or outside the polyhedron, This polyhedral method is well suited to evaluating the gravitational field of an irregularly shaped body such as an asteroid or comet, Conventional harmonic and mascon potential and attraction expressions suffer large errors when evaluated close to a polyhedral model of asteroid 4769 Castalia.

Touchdown of the Hayabusa Spacecraft at the Muses Sea on Itokawa

After global observations of asteroid 25143 Itokawa by the Hayabusa spacecraft, we selected the smooth terrain of the Muses Sea for two touchdowns carried out on 19 and 25 November 2005 UTC for the first asteroid sample collection with an impact sampling mechanism. Here, we report initial findings about geological features, surface condition, regolith grain size, compositional variation, and constraints on the physical properties of this site by using both scientific and housekeeping data during the descent sequence of the first touchdown. Close-up images revealed the first touchdown site as a regolith field densely filled with size-sorted, millimeter- to centimeter-sized grains.

Regolith migration and sorting on asteroid Itokawa.

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 Itokawas small size, implying that they can occur on other small asteroids should those have regolith.

Radar Imaging of Binary Near-Earth Asteroid (66391) 1999 KW4

High-resolution radar images reveal near-Earth asteroid (66391) 1999 KW4 to be a binary system. The ∼1.5-kilometer-diameter primary (Alpha) is an unconsolidated gravitational aggregate with a spin period ∼2.8 hours, bulk density ∼2 grams per cubic centimeter, porosity ∼50%, and an oblate shape dominated by an equatorial ridge at the objects potential-energy minimum. The ∼0.5-kilometer secondary (Beta) is elongated and probably is denser than Alpha. Its average orbit about Alpha is circular with a radius ∼2.5 kilometers and period ∼17.4 hours, 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.

Mass and Local Topography Measurements of Itokawa by Hayabusa

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) × 1010 kilograms, implying a bulk density of (1.95 ± 0.14) grams per cubic centimeter for a volume of (1.84 ± 0.09) × 107 cubic meters and a bulk porosity of ∼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.

Disruption of kilometre- sized asteroids by energetic collisions

Recent numerical studies suggest that ‘rubble-pile’ asteroids (gravitationally bound aggregates of collisional debris) are common in the Solar System, and that self-gravitation may equal or exceed material cohesion for planetary bodies as small as several hundred metres. Because analytical scaling relations for impact cratering and disruption do not extend to this size regime, where gravity and material strength are both important, detailed simulations are needed to predict how small asteroids evolve through impact, and also to ascertain whether powerful explosions offer a viable defence against bodies headed for a collision with Earth. Here we present simulations, using a smooth-particle hydrodynamics code, of energetic impacts into small planetary bodies with internal structure ranging from solid rock to porous aggregate. We find that the outcome of a collision is very sensitive to the configuration of pre-existing fractures and voids in the target. A porous asteroid (or one with deep regolith) damps the propagation of the shock wave from the impactor, sheltering the most distant regions, while greatly enhancing the local deposition of energy. Multiple-component asteroids (such as contact binaries) are also protected, because the shock wave cannot traverse the discontinuity between the components. We conclude that the first impact to significantly fragment an asteroid may determine its subsequent collisional evolution, and that internal structure will greatly influence attempts to disrupt or deflect an asteroid or comet headed towards Earth.

Scaling forces to asteroid surfaces: The role of cohesion

The scaling of physical forces to the extremely low ambient gravitational acceleration regimes found on the surfaces of small asteroids is performed. Resulting from this, it is found that van der Waals cohesive forces between regolith grains on asteroid surfaces should be a dominant force and compete with particle weights and be greater, in general, than electrostatic and solar radiation pressure forces. Based on this scaling, we interpret previous experiments performed on cohesive powders in the terrestrial environment as being relevant for the understanding of processes on asteroid surfaces. The implications of these terrestrial experiments for interpreting observations of asteroid surfaces and macro-porosity are considered, and yield interpretations that differ from previously assumed processes for these environments. Based on this understanding, we propose a new model for the end state of small, rapidly rotating asteroids which allows them to be comprised of relatively fine regolith grains held together by van der Waals cohesive forces.

Nonlinear Mapping of Gaussian Statistics: Theory and Applications to Spacecraft Trajectory Design

This paper discusses the nonlinear propagation of spacecraft trajectory uncertainties via solutions of the Fokker– Planck equation. We first discuss the solutions of the Fokker–Planck equation for a deterministic system with a Gaussian boundary condition. Next, we derive an analytic expression of a nonlinear trajectory solution using a higher-order Taylor series approach, discuss the region of convergence for the solutions, and apply the result to spacecraft applications. Such applications consist of nonlinear propagation of the mean and covariance matrix, design of statistically correct trajectories, and nonlinear statistical targeting. The two-body and Hill three-body problems are chosen as examples and realistic initial uncertainty models are considered. The results show that the nonlinear map of the trajectory uncertainties can be approximated in an analytic form, and there exists an optimal place to perform a correction maneuver, which is not found using the linear method.

Stability Analysis of Planetary Satellite Orbiters: Application to the Europa Orbiter

Thestability oforbit dynamicsaround a planetary satelliteisstudied using analyticaland numerical techniques. The Europa orbiter mission is used to motivate our analysis and to provide specie c numerical data for verie cation of our analytical results. After verie cation, the results are applied to a large number of planetary satellites in the solar system. The motivation is that numerically integrated, low-altitude spacecraft orbits about Europa often impacton thatmoon’ ssurfaceafterashortperiod ofafewdaystoweeks.Numericalintegrationsindicatethatthese impact orbits only occurfor inclinations within » 45 deg of a polarorbit. An analytical study of this problem using averaging theory, which resultsin an approximate, closed-form solution fortheorbiterdynamics, is described. The solution includes the effect of theplanetgravity and theplanetary satellite oblateness, with theassumption that the eccentricity of the nominal orbit is small. This solution is used to compute limits for impacting and nonimpacting orbits at Europa and provides good agreement with numerical computations of these limits performed with highprecision numerical integrations of the motion. The analytical result predicts a set of initial conditions that can postpone impact with the planetary surface for considerable lengths of time.