On efficiency of convection of Öpik's cellular convection theory

The physical meaning of the convection efficiency parameter of Öpik's theory is clarified by relating it to that of the mixing-length theory. A compact comparison of both theories is presented to explain the earlier findings of Gough and Weiss (1976), that Öpik's theory becomes indistinguishable from the mixing-length theory when the value of Öpik's cell depth is taken as being equal to 2.44 times the local pressure scale height for the solar convective envelope.     

Low velocity impacts into dust: results from the COLLIDE-2 microgravity experiment

We present the results of the second flight of the Collisions Into Dust Experiment (COLLIDE-2), a space shuttle payload that performs six impact experiments into simulated planetary regolith at speeds between 1 and 100 cm/s. COLLIDE-2 flew on the STS-108 mission in December 2001 following an initial flight in April 1998. The experiment was modified since the first flight to provide higher quality data, and the impact parameters were varied. Spherical quartz projectiles of 1-cm radius were launched into quartz sand and JSC-1 lunar regolith simulant targets 2-cm deep. At impact speeds below ∼20 cm/s the projectile embedded itself in the target material and did not rebound. Some ejecta were produced at ∼10 cm/s. At speeds >25 cm/s the projectile rebounded and significant ejecta was produced. We present coefficients of restitution, ejecta velocities, and limits on ejecta masses. Ejecta velocities are typically less than 10% of the impact velocity, and the fraction of impact kinetic energy partitioned into ejecta kinetic energy is also less than 10%. Taken together with a proposed aerodynamic planetesimal growth mechanism, these results support planetesimal growth at impact speeds above the nominal observed threshold of about 20 cm/s.     

The Distribution of Energy Perturbations at Planetary Close Encounters

Öpiks theory of close encounters allows us to deduce an analytic expression for the distribution of energy perturbations at close encounters between small bodies and planets. The derivation of this expression highlights a simple geometric structure in the plane containing the planet and perpendicular to the unperturbed planetocentric velocity vector. The analytic formulation reproduces well the results of the numerical integrations that first pointed out the asymmetries in the distribution of energy perturbations.     

Analysis of the Space Debris Impacts Risk on the International Space Station

Öpik's analytical expressions relate in a simple way the semimajor axis, eccentricity and inclination of the projectile orbit to the magnitude and direction of the relative velocity vector at impact on a given target on circular orbit. These interesting quantities, along with the impact probability of any given projectile, can be all represented on a suitable projection giving a comprehensive picture of the impact risk on the selected target. By means of this theory a complete analysis of the impact risk on the International Space Station (ISS) is performed. It is found that the large majority of the debris population is on orbits such that a correlation exists between their impact velocity on the ISS and the angle between the velocity vector of the impactor and that of the ISS. The impactor population also is separated in terms of nature of the projectiles, with most of the low-medium velocity ones being particles related to solid rocket motor slag condensates. On the other hand, the highest velocity projectiles are composed mainly by fragments of past in-orbit explosions.The flux of projectiles on the ISS has been calculated for the planned operative lifetime of the Station, by assuming a realistic scenario of the future debris environment evolution and the actual planned altitude profile for the ISS mission. There is a factor 2-3 variation of the flux due to the changing ISS altitude. The most dangerous part of the mission appears to be the central one, when the ISS will orbit at about 450 km above the Earth.     

Hydrocode modeling of oblique impacts: The fate of the projectile

Abstract— All impacts are oblique to some degree. Only rarely do projectiles strike a planetary surface (near) vertically. The effects of an oblique impact event on the target are well known, producing craters that appear circular even for low impact angles (>15° with respect to the surface). However, we still have much to learn about the fate of the projectile, especially in oblique impact events. This work investigates the effect of angle of impact on the projectile. Sandia National Laboratories' three‐dimensional hydrocode CTH was used for a series of high‐resolution simulations (50 cells per projectile radius) with varying angle of impact. Simulations were carried out for impacts at 90, 60, 45, 30, and 15° from the horizontal, while keeping projectile size (5 km in radius), type (dunite), and impact velocity (20 km/s) constant. The three‐dimensional hydrocode simulations presented here show that in oblique impacts the distribution of shock pressure inside the projectile (and in the target as well) is highly complex, possessing only bilateral symmetry, even for a spherical projectile. Available experimental data suggest that only the vertical component of the impact velocity plays a role in an impact. If this were correct, simple theoretical considerations indicate that shock pressure, temperature, and energy would depend on sin²θ, where θ is the angle of impact (measured from the horizontal). However, our numerical simulations show that the mean shock pressure in the projectile is better fit by a sin θ dependence, whereas shock temperature and energy depend on sin^3/2 θ. This demonstrates that in impact events the shock wave is the result of complex processes that cannot be described by simple empirical rules. The mass of shock melt or vapor in the projectile decreases drastically for low impact angles as a result of the weakening of the shock for decreasing impact angles. In particular, for asteroidal impacts the amount of projectile vaporized is always limited to a small fraction of the projectile mass. In cometary impacts, however, most of the projectile is vaporized even at low impact angles. In the oblique impact simulations a large fraction of the projectile material retains a net downrange motion. In agreement with experimental work, the simulations show that for low impact angles (30 and 15°), a downrange focusing of projectile material occurs, and a significant amount of it travels at velocities larger than the escape velocity of Earth.     

Limits for the Firehose Instability in Space Plasmas

Electromagnetic instabilities in high-β plasmas, where β is the ratio of the kinetic plasma energy to the magnetic energy, have a broad range of astrophysical applications. The presence of temperature anisotropies T _∥ /T _⊥ >1 (where ∥ and ⊥ denote directions relative to the background magnetic field) in solar flares and the solar wind is sustained by the observations and robust acceleration mechanisms that heat plasma particles in the parallel direction. The surplus of parallel kinetic energy can excite either the Weibel-like instability (WI) of the ordinary mode perpendicular to the magnetic field or the firehose instability (FHI) of the circularly polarized waves at parallel propagation. The interplay of these two instabilities is examined. The growth rates and the thresholds provided by the kinetic Vlasov – Maxwell theory are compared. The WI is the fastest growing one with a growth rate that is several orders of magnitude larger than that of the FHI. These instabilities are however inhibited by the ambient magnetic field by introducing a temperature anisotropy threshold. The WI admits a larger anisotropy threshold, so that, under this threshold, the FHI remains the principal mechanism of relaxation. The criteria provided here by describing the interplay of the WI and FHI are relevant for the existence of these two instabilities in any space plasma system characterized by an excess of parallel kinetic energy.     

Deflection of near-Earth asteroids by kinetic energy impacts from retrograde orbits

Previous studies of non-nuclear diversion of near Earth asteroids have largely ignored the use of pure kinetic energy impacts, partly due to apparent limits on impact speeds of 10-. Here, I will consider the use of a near-term solar sail to deliver an inert projectile onto a retrograde solar orbit, thus raising impact speeds to at least . Such high-energy orbits increase the energy liberated during impact by a factor of 40 or more, while reducing the required projectile mass by at least 95%. This considerable reduction in projectile mass allows kilometre-sized asteroids to be diverted with current launch vehicles, near-term technologies and at a cost comparable to a modest deep space mission.     

Energy partition into translational and rotational motion of fragments in catastrophic disruption by impact: An experiment and asteroid cases

Translational kinetic energy E_t and rotational kinetic energy E_r of the fragments produced in the laboratory catastrophic disruption of a basalt sphere by the impact of a high-speed projectile were determined. It was found that the maximum value of E_t/E_t is of the orders of 10⁻², which is not so different in the order of magnitude from the value estimated for family asteroids in spite of the great difference of the scale. However, the laboratory value is significantly higher than the value for the family.     

Viscous boundary layer between the solar wind and cometary plasmas

The interaction between the solar wind and cometary ionospheres downstream from the subsolar region is modeled in terms of viscous MHD flow theory. Calculations of the flow stremalines within the mixing region indicate that, as a result of viscous action, both the solar wind particles and the cometary material should be gradually directed towards the interior of the plasma wake to reinforce the formation of a type 1 tail. This behavior supports the notion that a transverse force acting on cometary plasma particles is actually responsible for the collapse of tail ray structures as suggested by Öpik (1964), Wurm (1968, 1975) and Wurm and Mammano (1972).     

Deformation and melting of steel projectiles in hypervelocity cratering experiments

Abstract– We carried out hypervelocity cratering experiments with steel projectiles and sandstone targets to investigate the structural and mineralogical changes that occur upon impact in the projectile and target. The masses of coherent projectile relics that were recovered in different experiments ranged between 58% and 92% of their initial projectile masses. A significant trend between impact energy, the presence of water in the target, and the mass of projectile relics could not be found. However, projectile fragmentation seems to be enhanced if the target contains substantial amounts of water. Two experiments that were performed with 1 cm sized steel projectiles impacting at 3400 and 5300 m s^?1 vertically onto dry Seeberger sandstone were investigated in detail. The recovered projectiles are intensely plastically deformed. Deformation mechanisms include dislocation glide and dislocation creep. The latter led to the formation of subgrains and micrometer‐sized dynamically recrystallized grains. In case of the 5300 m s^?1 impact experiment, this deformation is followed by grain annealing. In addition, brittle fracturing and friction‐controlled melting at the surface along with melting and boiling of iron and silica were observed in both experiments. We estimated that heating and melting of the projectile impacting at 5300 m s^?1 consumed 4.4% of the total impact energy and was converted into thermal energy and heat of fusion. Beside the formation of centimeter‐sized projectile relics, projectile matter is distributed in the ejecta as spherules, unmelted fragments, and intermingled iron‐silica aggregates.     

Projectile preservation during oblique hypervelocity impacts

Impact angle plays a significant role in determining the fate of the projectile. In this study, we use a suite of hypervelocity impact experiments to reveal how impact angle affects the preservation, distribution, and physical state of projectile residues in impact craters. Diverse types of projectiles, including amorphous silicates, crystalline silicates, and aluminum, in two sizes (6.35 and 12.7 mm), were launched into blocks of copper or 6061 aluminum at speeds between 1.9 and 5.7 km s⁻¹. Crater interiors preserve projectile residues in all cases, including conditions relevant to the asteroid belt. These residues consist of projectile fragments or projectile-rich glasses, depending on impact conditions. During oblique impacts at 30° and 45°, the uprange crater wall preserves crystalline fragments of the projectile. The fragments of water-rich projectiles such as antigorite remain hydrated. Several factors contribute to enhanced preservation on the uprange wall, including a weaker shock uprange, uprange acceleration as the shock reflects off the back of the projectile, and rapid quenching of melts along the projectile–target interface. These findings have two broader implications. First, the results suggest a new collection strategy for flyby sample return missions. Second, these results predict that the M-type asteroid Psyche should bear exogenic, impactor-derived debris.     

Experimental Investigation of Shock Wave Attenuation in Basalt

Shock compression experiments on Kinosaki basalt were carried out in the interest of studying collisional phenomena in the solar nebula. Shock waves of 7 and 31 GPa were generated using a thin flyer plate, and a shock wave of 16 GPa was generated using a thick cylindrical projectile. By employing in-material manganin and carbon pressure gauges, the shock wave attenuation was examined and the propagation velocities of the shock wave and rarefaction wave were measured.The attenuation mechanism consists of two effects: the rarefaction wave and geometrical expansion. The rarefaction effect includes the reflected wave and the edge wave. The efficiency of these mechanisms depends on the geometry of the projectile, initially induced pressure, and materials of the target and projectile.As a result of the experiments, a cylindrical impactor created an isobaric region of size almost equal to the projectile radius. The shock wave in the far field was attenuated similarly with the power of −1.7 to −1.8 of the propagation distance under our experimental conditions. The shock wave generated using a thin flyer plate was attenuated by the rarefaction wave generated on the back surface of the flyer plate and by geometrical expansion effects. The shock wave generated using a thick projectile was attenuated by edge-wave and by geometrical expansion effects.According to elastic theory, the rigidity of basalt at 7 and 31 GPa was calculated as 35±7 and 0±3 GPa, respectively, using the measured rarefaction wave velocities. The decayed shock pressure was related to the ejection velocity of the impact fragments, which were obtained in previous disruption experiments. The attenuation rates in previous experiments were consistent with ours. The previous impact scaling parameter called “nondimensional impact stress (PI)” has been improved.     

Assessment of Kinetic Energy of Meteoroids Detected by Satellite-Based Light Sensors

Radiation energies of bright flashes caused by disintegration of large meteoroids in the atmosphere have been measured using optical sensors on board geostationary satellites. Light curves versus time are available for some of the events. We have worked out several numerical techniques to derive the kinetic energy of the meteoroids that produced the flashes. Spectral opacities of vapor of various types of meteoroids were calculated for a wide range of possible temperatures and densities. Coefficients of conversion of kinetic energy to radiation energy were computed for chondritic and iron meteoroids 10 cm to 10 m in size using radiation–hydrodynamics numerical simulations. Luminous efficiency increases with body size and initial velocity. Some analytical approximations are presented for average conversion coefficients for irons and H-chondrites. A mean value of this coefficient for large meteoroids (1–10 m in size) is about 5–10%. The theory was tested by analyzing the light curves of several events in detail.Kinetic energies of impactors and energy–frequency distribution of 51 bolides, detected during 22 months of systematic observations in 1994–1996, are determined using theoretical values of luminous efficiencies and heat-transfer coefficients. The number of impacts in the energy range from 0.25 to 4 kt TNT is 25 per year and per total surface of the Earth.The energy–frequency distribution is in a rather good agreement with that derived from acoustic observations and the lunar crater record. Acoustic systems have registered one 1 Mt event in 12 years of observation. Optical systems have not detected such an event as yet due to a shorter time of observation. The probability of a 1 Mt impact was estimated by extrapolation of the observational data.     

N-Body Simulations of Planetesimal Evolution: Effect of Varying Impactor Mass Ratio

We present results from direct N-body simulations of collisions between gravitational aggregates of varying size as part of a study to parameterize planetesimal growth in the Solar System. We find that as the ratio of projectile to target mass departs from unity, the impact angle has less effect on the outcome. At the same time, the probability of planetesimal growth increases. Conversely, for a fixed impact energy, collisions between impactors with mass ratio near unity are more dispersive than those with impactor mass ratio far from unity. We derive an expression for the accretion probability as a function of mass ratio. For an average mass ratio of 1:5, we find an accretion probability of ∼60% over all impact parameters. We also compute the critical specific dispersal energy Q*_D as a function of projectile size. Extrapolating to a projectile size of 1 m with a 1-km target, we find Q*_D=10³−10⁴ J kg⁻¹, in agreement with several other collision models that use fundamentally different techniques. Our model assumes that the components of each gravitational aggregate are identical and indestructible over the range of sampled impact speeds. In future work we hope to incorporate a simple fracture model to extend the range of applicable speeds and we plan to implement our results in a large-scale planetesimal evolution code.     

Modeling repulsive gravity with creation

There is a growing interest among cosmologists for theories with negative energy scalar fields and creation, in order to model a repulsive gravity. The classical steady state cosmology proposed by Bondi, Gold & Hoyle in 1948, was the first such theory which used a negative kinetic energy creation field to invoke creation of matter. We emphasize that creation plays a very crucial role in cosmology and provides a natural explanation to the various explosive phenomena occurring in local (z < 0.1) and extra galactic universe. We exemplify this point of view by considering the resurrected version of this theory — the quasi-steady state theory, which tries to relate creation events directly to the large scale dynamics of the universe and supplies more natural explanations of the observed phenomena. Although the theory predicts a decelerating universe at the present era, it explains successfully the recent SNe Ia observations (which require an accelerating universe in the standard cosmology), as we show in this paper by performing a Bayesian analysis of the data.     

Galactic cosmic ray modulation from 1965–1970

Numerical solutions of the cosmic-ray equation of transport within the solar cavity and including the effects of diffusion, convection, and energy losses due to adiabatic deceleration, have been used to reproduce the modulation of galactic electrons, protons and helium nuclei observed during the period 1965–1970. Kinetic energies between 10 and 10⁴ MeV/nucleon are considered. Computed and observed spectra (where data is available) are given for the years 1965, 1968, 1969 and 1970 together with the diffusion coefficients. These diffusion coefficients are assumed to be of separable form in rigidity and radial dependence, and are consistent with the available magneticfield power spectra. The force-field solutions are given for these diffusion coefficients and galactic spectra and compared with the numerical solutions. For each of the above years we have (i) determined the radial density gradients near Earth; (ii) found the mean energy losses suffered by galactic particles as they diffuse to the vicinity of the Earth's orbit; (iii) shown quantitatively the exclusion of low-energy galactic protons and helium nuclei from near Earth by convective effects; and (iv), for nuclei of a given energy near Earth, obtained their distribution in energy before entering the solar cavity. It is shown that the energy losses and convection lead to near-Earth nuclei spectra at kinetic energies ≤100 MeV/nucleon in which the differential intensity is proportional to the kinetic energy with little dependence on the form of the galactic spectrum. This dependence is in agreement with the observed spectra of all species of atomic nuclei and we argue that this provides strong observational evidence for the presence of energy losses in the propagation process; and for the exclusion of low energy galactic nuclei from near Earth.     

Dynamical tides in close binary systems

The aim of the present paper will be to investigate the circumstances under which an irreversible dissipation of the kinetic energy into heat is generated by the dynamical tides in close binary systems if (a) their orbit is eccentric; (b) the axial rotation of the components is not synchronized with the revolution; or (c) the equatorial planes are inclined to that of the orbit.In Section 2 the explicit form of the viscous dissipation function will be set up in terms of the velocity-components of spheroidal deformation arising from the tides; in Section 3, the principal partial tides contributing to the dissipation will be detailed; Section 4 will be devoted to a determination of the extent of stellar viscosity — both gas and radiative; while in the concluding Section 5 quantitative estimates will be given of the actual rate at which the kinetic energy of dynamical tides gets dissipated into heat by viscous friction in stellar plasma.The results disclose that the amount of heat produced per unit time by tidal interaction between components of actual close binaries equals only about 10^–10th part of their nuclear energy production; and cannot, therefore, affect the internal structure of evolution of the constituent stars to any appreciable extent. Moreover, it is shown that the kinetic energy of their axial rotation can be influenced by tidal friction only on a nuclear, rather than gravitational (Kelvin) time-scale — as long as plasma or radiative viscosity constitute the sole sources of dissipation. However, the emergence of turbulent viscosity in secondary components of late spectral types, which have evolved away from the Main Sequence, can accelerate the dissipation 10⁵–10⁶ times, and thus give rise to appreciable changes in the elements of the system (particularly, in the orbital periods) over time intervals of the order of 10⁵–10⁶ years. Lastly, it is pointed out that, in close binary systems consisting of a pair of white dwarfs, a dissipation of the kinetic energy through viscous tides in degenerate fermion-gas could produce enough heat to account, by itself, for the observed luminosity of such objects.     

Power spectral analysis of Jupiter’s clouds and kinetic energy from Cassini

We present suggestive evidence for an inverse energy cascade within Jupiter’s atmosphere through a calculation of the power spectrum of its kinetic energy and its cloud patterns. Using Cassini observations, we composed full-longitudinal mosaics of Jupiter’s atmosphere at several wavelengths. We also utilized image pairs derived from these observations to generate full-longitudinal maps of wind vectors and atmospheric kinetic energy within Jupiter’s troposphere. We computed power spectra of the image mosaics and kinetic energy maps using spherical harmonic analysis. Power spectra of Jupiter’s cloud patterns imaged at certain wavelengths resemble theoretical spectra of two-dimensional turbulence, with power-law slopes near −5/3 and −3 at low and high wavenumbers, respectively. The slopes of the kinetic energy power spectrum are also near −5/3 at low wavenumbers. At high wavenumbers, however, the spectral slopes are relatively flatter than the theoretical prediction of −3. In addition, the image mosaic and kinetic energy power spectra differ with respect to the location of the transition in slopes. The transition in slope is near planetary wavenumber 70 for the kinetic energy spectra, but is typically above 200 for the image mosaic spectra. Our results also show the importance of calculating spectral slopes from full 2D velocity maps rather than 1D zonal mean velocity profiles, since at large wavenumbers the spectra differ significantly, though at low wavenumbers, the 1D zonal and full 2D kinetic energy spectra are practically indistinguishable. Furthermore, the difference between the image and kinetic energy spectra suggests some caution in the interpretation of power spectrum results solely from image mosaics and its significance for the underlying dynamics. Finally, we also report prominent variations in kinetic energy within the equatorial jet stream that appear to be associated with the 5 μm hotspots. Other eddies are present within the flow collar of the Great Red Spot, suggesting caution when interpreting snapshots of the flow inside these features as representative of a time-averaged state.     

Campo del Cielo modeling and comparison with observations: II. Funnels and craters

The Campo del Cielo impact structure exhibits several penetration funnels and impact craters. Here, we model the formation of these funnels with pre-impact conditions consistent with the results of meteoroid entry models. We study vertical impacts to find the dependence of funnel geometry (depth, diameter) on impact velocity and target porosity. At velocities above 1 km s⁻¹, we observe strong deformation of the projectile and transformation of funnels into regular impact craters. We also use 3-D impact models to study oblique impacts and find that in the case of impact angles <25° to the horizon, the projectile bounces off the target. Instead of a funnel, an elongated groove forms, while the fragmented projectile escapes and moves farther downrange. At steeper impact angles, funnels form with the projectile at its tip. Early interpretations of the Campo del Cielo impact angle at 9–10° were based on (i) an oversimplified atmospheric model allowing “correct” strewn field elongation and (ii) the results of excavation in which the sloping boundary between breccia-like materials and infilling loess was interpreted as a true crater floor and its slope was equated to the impact angle. As our models show, the projectile trajectory within the target is not a straight line, and the angle to horizon changes from a steep one at the impact point to zero and then to a negative value (the projectile is moving upward). We also model two impact craters (Hoyo de la Cañada and Laguna Negra) created by high-velocity fragments to demonstrate the projectile remnants ricochet in the downrange direction.     

Large kinetic power in FRII radio jets

We investigate the total kinetic powers (L _j) and ages (t _age) of powerful jets of four FR II radio sources (Cygnus A, 3C 223, 3C 284, and 3C 219) by the detail comparison of the dynamical model of expanding cocoons with observed ones. It is found that these sources have quite large kinetic powers with the ratio of L _j to the Eddington luminosity (L _Edd) resides in 0.02<L _j/L _Edd<10. Reflecting the large kinetic powers, we also find that the total energy stored in the cocoon (E _c) exceed the energy derived from the minimum energy condition (E _min): 2<E _c/E _min<160. This implies that a large amount of kinetic power is carried by invisible components such as thermal leptons (electron and positron) and/or protons.