Penetration depth for shallow impact cratering

We present data for the penetration of a variety of spheres, dropped from rest, into a level non-cohesive granular medium. We improve upon our earlier work [Uehara {\it et al.} Phys. Rev. Lett. {\bf 90}, 194301 (2003)] in three regards. First, we explore the behavior vs sphere diameter and density more systematically, by holding one of these parameters constant while varying the other. Second, we prepare the granular medium more reproducibly and, third, we measure the penetration depth more accurately. The new data support our previous conclusion that the penetration depth is proportional to the 1/2 power of sphere density, the 2/3 power of sphere diameter, and the 1/3 power of total drop distance

Consequences of asteroid fragmentation during impact hazard mitigation

The consequences of the fragmentation of an Earth-threatening asteroid due to an attempted deflection are examined in this paper. The minimum required energy for a successful impulsive deflection of a threatening object is computed and compared to the energy required to break up a small size asteroid. The results show that the fragmentation of an asteroid that underwent an impulsive deflection, such as a kinetic impact or a nuclear explosion, is a very plausible event.Astatistical model is used to approximate the number and size of the fragments as well as the distribution of velocities at the instant after the deflection attempt takes place. This distribution of velocities is a function of the energy provided by the deflection attempt, whereas the number and size of the asteroidal fragments is a function of the size of the largest fragment. The model also takes into account the gravity forces that could lead to a reaggregation of the asteroid after fragmentation. The probability distribution of the pieces after the deflection is then propagated forward in time until the encounter with Earth. A probability damage factor (i.e., expected damage caused by a given size fragment multiplied by its impact probability) is then computed and analyzed for different plausible scenarios, characterized by different levels of deflection energies and lead times

Dynamics of grain ejection by sphere impact on a granular bed

The dynamics of grain ejection consecutive to a sphere impacting a granular material is investigated experimentally and the variations of the characteristics of grain ejection with the control parameters are quantitatively studied. The time evolution of the corona formed by the ejected grains is reported, mainly in terms of its diameter and height, and favourably compared with a simple ballistic model. A key characteristic of the granular corona is that the angle formed by its edge with the horizontal granular surface remains constant during the ejection process, which again can be reproduced by the ballistic model. The number and the kinetic energy of the ejected grains is evaluated and allows for the calculation of an effective restitution coefficient characterizing the complex collision process between the impacting sphere and the fine granular target. The effective restitution coefficient is found to be constant when varying the control parameters.Comment: 9 page

On the deflection of asteroids with mirrors

This paper presents an analysis of an asteroid deflection method based on multiple solar concentrators. A model of the deflection through the sublimation of the surface material of an asteroid is presented, with simulation results showing the achievable orbital deflection with, and without, accounting for the effects of mirror contamination due to the ejected debris plume. A second model with simulation results is presented analyzing an enhancement of the Yarkovsky effect, which provides a significant deflection even when the surface temperature is not high enough to sublimate. Finally the dynamical model of solar concentrators in the proximity of an irregular celestial body are discussed, together with a Lyapunov-based controller to maintain the spacecraft concentrators at a required distance from the asteroid

Note on restoring manifest rotational symmetry in hyperfine and fine structure in light-front QED

We study the part of the renormalized, cutoff QED light-front Hamiltonian that does not change particle number. The Hamiltonian contains interactions that must be treated in second-order bound state perturbation theory to obtain hyperfine structure. We show that a simple unitary transformation leads directly to the familiar Breit-Fermi spin-spin and tensor interactions, which can be treated in degenerate first-order bound-state perturbation theory, thus simplifying analytic light-front QED calculations. To the order in momenta we need to consider, this transformation is equivalent to a Melosh rotation. We also study how the similarity transformation affects spin-orbit interactions.Comment: 17 pages, latex fil

Mirror formation control in the vicinity of an asteroid

Two strategies are presented for the positioning and control of a spacecraft formation designed to focus sunlight onto a point on the surface of asteroid, thereby sublimating the material and ejecting debris creating thrust. In the first approach, the formation is located at artficial equilibrium points around the asteroid and controlled using the force from the solar radiation pressure. The second approach determines the optimal periodic formation orbits, subject to the gravitational perturbations from the asteroid, the solar radiation pressure and the control acceleration derived from a control law

Low-speed impact craters in loose granular media

We report on craters formed by balls dropped into dry, non-cohesive, granular media. By explicit variation of ball density $\rho_{b}$, diameter $D_{b}$, and drop height $H$, the crater diameter is confirmed to scale as the 1/4 power of the energy of the ball at impact: $D_{c}\sim(\rho_{b}{D_{b}}^{3}H)^{1/4}$. Against expectation, a different scaling law is discovered for the crater depth: $d\sim({\rho_{b}}^{3/2}{D_{b}}^{2}H)^{1/3}$. The scaling with properties of the medium is also established. The crater depth has significance for granular mechanics in that it relates to the stopping force on the ball.Comment: experiment; 4 pages, 3 figure

Variation in Magnetic Fabrics at Low Shock Pressure Due to Experimental Impact Cratering

Magnetic fabrics provide important clues for understanding impact cratering processes. However, only a few magnetic fabric studies for experimentally shocked material have been reported so far. In the framework of MEMIN (Multidisciplinary Experimental and Modeling Impact Research Network), we conducted two impact experiments on blocks of Maggia gneiss with the foliation oriented perpendicular (A38) and parallel (A37) to the target surface. Maggia gneiss has plenty of biotite bands forming a strong rock foliation. The bulk magnetic susceptibility varies from 0.376 × 10$^{−3}$ to 1.298 × 10$^{−3}$ SI in unshocked and from 0.443 × 10$^{−3}$ to 3.940 × 10$^{−3}$ SI in shocked gneiss. The thermomagnetic curves reveal a Verwey transition at −147 °C and a Curie temperature between 576 and 579 °C in unshocked and shocked samples, indicating nearly pure magnetite, which carries the magnetic fabrics. In A37 and A38 kinking is prominent from the point source down to a depth of 2 and 4.2 d$_{p}$ (projectile diameter) or 1 and 2.1 cm, respectively. Kinking, folding, and fracturing changed the position of magnetite grains with respect to each other to reorient the magnetic fabrics. Reorientation of magnetic fabrics is conspicuous down to 20 d$_{p}$ (10 cm) in A38, where no other impact‐related deformation is visible. The reorientation of magnetic fabrics may, therefore, aid in identifying impact processes at very low pressures, starting at 0.1 GPa, when other common indicators are absent

Front Form Spinors in Weinberg-Soper Formalism and Melosh Transformations for any Spin

Using the Weinberg-Soper formalism we construct the front form $(j,0)\oplus(0,j)$ spinors. Explicit expressions for the generalised Melosh transformations up to spin two are obtained. The formalism, without explicitly invoking any wave equations, reproduces spin one half front-form results of Melosh, Lepage and Brodsky, and Dziembowski.Comment: 16 Pages, RevTex. We continue to receive reprint requests for this paper. So we now archive it her