Lunar-forming collisions with pre-impact rotation

Prior models of lunar-forming impacts assume that both the impactor and the target protoearth were not rotating prior to the Moon-forming event. However, planet formation models suggest that such objects would have been rotating rapidly during the late stages of terrestrial accretion. In this paper I explore the effects of pre-impact rotation on impact outcomes through more than 100 hydrodynamical simulations that consider a range of impactor masses, impact angles and impact speeds. Pre-impact rotation, particularly in the target protoearth, can substantially alter collisional outcomes and leads to a more diverse set of final planet-disk systems than seen previously. However, the subset of these impacts that are also lunar-forming candidates—i.e. that produce a sufficiently massive and iron-depleted protolunar disk—have properties similar to those determined for collisions of non-rotating objects [Canup, R.M., Asphaug, E., 2001. Nature 412, 708-712; Canup, R.M., 2004a. Icarus 168, 433-456]. With or without pre-impact rotation, a lunar-forming impact requires an impact angle near 45 degrees, together with a low impact velocity that is not more than 10% larger than the Earth's escape velocity, and produces a disk containing up to about two lunar masses that is composed predominantly of material originating from the impactor. The most significant differences in the successful cases involving pre-impact spin occur for impacts into a retrograde rotating protoearth, which allow for larger impactors (containing up to 20% of Earth's mass) and provide an improved match with the current Earth-Moon system angular momentum compared to prior results. The most difficult state to reconcile with the Moon is that of a rapidly spinning, low-obliquity protoearth before the giant impact, as these cases produce disks that are not massive enough to yield the Moon.     

A hit-and-run giant impact scenario

The formation of the Moon from the debris of a slow and grazing giant impact of a Mars-sized impactor on the proto-Earth (Cameron and Ward [1976]. Lunar Planet. Sci. Conf.; Canup and Asphaug [2001]. Nature 412, 708) is widely accepted today. We present an alternative scenario with a hit-and-run collision (Asphaug [2010]. Chem. Erde 70, 199) with a fractionally increased impact velocity and a steeper impact angle.     

Co-accretion of the Earth-Moon system after the giant impact: reduction of the total angular momentum by lunar impact ejecta

Though the Moon is considered to have been formed by the so-called giant impact, the mass of the Earth immediately after the impact is still controversial. If the Moon was formed during the Earth's accretion, a subsequent accretion of residual heliocentric planetesimals onto the protoearth and the protomoon must have occurred. In this co-accretion stage, a significant amount of lunar-impact-ejecta would be ejected to circumterrestrial orbits, since the mean impact velocity of the planetesimals with the protomoon is much larger than the escape velocity of the protomoon. Orbital calculations of test particles ejected from the protomoon, whose semimajor axis is smaller than that of the present Moon, reveal that most of the particles escaping from the protomoon also escape from the Hill sphere of the protoearth and reduce the planetocentric angular momentum of the primordial Earth-Moon system. Using the results of the ejecta simulations, we investigate the evolution of the mass ratio and the total angular momentum (Earth's spin angular momentum + Moon's orbital angular momentum) of the Earth-Moon system during the co-accretion. We find that the mass of the protomoon is almost constant or rather decreases and the total angular momentum decreases significantly, if the random velocity of planetesimals is as large as the escape velocity of the protoearth. On the other hand, if the random velocity is the half of the escape velocity of the protoearth, the mass ratio is kept to be almost as large as the present value and the decrease of the total angular momentum is not so significant. Comparing with the results of giant impact simulations, we find that the mass of the protoearth immediately after the Moon-forming impact was 0.7-0.8 times the present value if the impactor-to-target mass ratio was 3:7, whereas the giant impact occurred almost in the end of the Earth's accretion if the impactor-to-target mass ratio was 1:9.     

The origin of the moon and the single-impact hypothesis I

Recently the single-impact hypothesis for forming the Moon has gained some favorable attention. We present in this paper a series of three-dimensional numerical simulations of an impact between the protoearth and an object about 0.1 of its mass. For computational convenience both objects were assumed to be composed of granite. We studied the effects on the outcome of the collision of varying the impact parameter, the initial internal energy, and the relative velocity. The results show that if the impact parameter is large enough so that the center of the impactor approximately grazes the limb of the protoearth, the impactor is not completely destroyed; part of it forms a clump in a large elliptical orbit about the Earth. This clump does not collide with the Earth, since the effects, first, of vapor pressure gradients during the impact, and later, of angular momentum transfer due to the rotation of the deformed Earth, have modified the ballistic trajectory. However, since the orbit of the clump comes close to the Earth (within the Roche limit) the clump will be destroyed and spread out to form a disk around the Earth. The amount of angular momentum in the Earth-Moon system thus obtained tends to fall short of the observed amount; this deficiency would be eliminated if the mass of the impactor were somewhat greater than the one assumed here. The scenario for making the Moon from a single-impact event is supported by these simulations.     

The fate of primordial lunar Trojans

Multiple large impact basins on the lunar nearside formed in a relatively-short interval around 3.8-3.9 Gyr ago, in what is known as the Lunar Cataclysm (LC; also known as Late Heavy Bombardment). It is widely thought that this impact bombardment has affected the whole Solar System or at least all the inner planets. But with non-lunar evidence for the cataclysm being relatively weak, a geocentric cause of the Lunar Cataclysm cannot yet be completely ruled out [Ryder, G., 1990. Eos 71, 313, 322-323]. In principle, late destabilization of an additional Earth satellite could result in its tidal disruption during a close lunar encounter (cf. [Asphaug, E., Agnor, C.B., Williams, Q., 2006. Nature 439, 155-160]). If the lost satellite had D>500 km, the resulting debris can form multiple impact basins in a relatively short time, possibly explaining the LC. Canup et al. [Canup, R.M., Levison, H.F., Stewart, G.R., 1999. Astron. J. 117, 603-620] have shown that any additional satellites of Earth formed together with (and external to) the Moon would be unable to survive the rapid initial tidally-driven expansion of lunar orbit. Here we explore the fate of objects trapped in the lunar Trojan points, and find that small lunar Trojans can survive the Moon's orbital evolution until they and the Moon reach 38 Earth radii, at which point they are destabilized by a strong solar resonance. However, the dynamics of Trojans containing enough mass to cause the LC (diameters >150 km) is more complex; we find that such objects do not survive the passage through a weaker solar resonance at 27 Earth radii. This distance was very likely reached by the Moon long before the LC, which seems to rule out the disruption of lunar Trojans as a cause of the LC.     

Atmospheric angular momentum variations of Earth, Mars and Venus at seasonal time scales

Atmospheric angular momentum variations of a planet are associated with the global atmospheric mass redistribution and the wind variability. The exchange of angular momentum between the fluid layers and the solid planet is the main cause for the variations of the planetary rotation at seasonal time scales. In the present study, we investigate the angular momentum variations of the Earth, Mars and Venus, using geodetic observations, output of state-of-the-art global circulation models as well as assimilated data. We discuss the similarities and differences in angular momentum variations, planetary rotation and angular momentum exchange for the three terrestrial planets. We show that the atmospheric angular momentum variations for Mars and Earth are mainly annual and semi-annual whereas they are expected to be “diurnal” on Venus. The wind terms have the largest contributions to the LOD changes of the Earth and Venus whereas the matter term is dominant on Mars due to the CO₂ sublimation/condensation. The corresponding LOD variations (ΔLOD) have similar amplitudes on Mars and Earth but are much larger on Venus, though more difficult to observe.     

Survival of a proto-atmosphere through the stage of giant impacts: the mechanical aspects

When a giant impact occurs, atmosphere loss may occur due to global ground motion excited by a strong shock wave traveling in the planetary interior. Here, the relations between the ground motion and the amount of the lost atmosphere are systematically investigated through calculations of a spherically one-dimensional atmospheric motion for various initial atmospheric conditions. The fraction of the lost atmosphere to the total mass of the atmosphere is found to be controlled only by the ground velocity and, insensitive to the initial atmospheric conditions. Unlike the previous studies (Ahrens, 1990, Origin of the Earth, H.E. Newson, J.H. Jones (Eds.), pp. 211-227; Ahrens, 1993, Annu. Rev. Earth Planet. Sci. 21, 525-555; Chen and Ahrens, 1997, Phys. Earth Planet. Inter. 100, 21-26); the estimated loss fraction for the giant impact is only 20%. Significant escape occurs only when the ground velocity is close to the escape velocity. Thus, most of the atmosphere should survive the giant impact. The cause of the difference from previous estimates is discussed from energetic and dynamic points of view. Moreover, if our estimates are applied to the atmosphere of the impactor planet, a significant fraction of it is carried to the target planet. Survival of the proto-atmosphere has very important effects on the origin and evolution of the terrestrial planets' volatile budget.     

Does the Moon Have a Metallic Core?: Constraints from Giant Impact Modeling and Siderophile Elements

The issue of whether the Moon has a small metallic core is reexamined in light of new information: improved dynamical modeling, new constraints on core size, and high temperature and pressure metal-silicate partition coefficients. Addressed specifically is the question of whether the Moon's siderophile element budget can be explained by derivation of the Moon from a differentiated impactor or proto-Earth (stage 1), followed by formation of a small metallic core within the Moon (stage 2). If the Moon is made of mantle material from either a “hot” impactor or a “warm” impactor or proto-Earth, a small metallic core (0.7 to 2 mass%) is predicted. If the Moon is made from mantle material from a “hot” proto-Earth, the lunar mantle would be more depleted in W or Re than is observed. Scenarios in which the Moon is made from impactor or proto-Earth mantle material that has equilibrated with metal at low pressures and temperatures (“cold” scenarios) would yield a much larger metallic core than observed. Finally, the greater depletions of Ni, Mo, and Re in the Moon (relative to the Earth) can be explained by low PT and reduced metal-silicate equilibrium in an impactor without later core formation in the Moon (i.e., no stage 2), but depletions of Co, Ga, and W cannot. Altogether, geochemically unlikely or geophysically inadequate non-metallic core alternatives, substantial geophysical evidence for a metallic core, and the successful models presented here for siderophile element depletions all favor the presence of a small lunar metallic core. Previous geochemical objections to an impactor origin of the Moon are eliminated because siderophile element concentrations in the lunar mantle are consistent with separation of a small core from a bulk Moon derived from impactor mantle material.     

Possible potentially threatening co‐orbiting material of asteroid 2000EE104 identified through interplanetary magnetic field disturbances

Near‐Earth objects (NEOs) with diameters of <300 m are difficult to detect from the Earth with radar or optical telescopes unless and until they approach closely. If they are on collisional courses with the Earth, there is little that can be done to mitigate the considerable damage. Although destructive collisions in space are rare for 1 km diameter bodies and above, once hit by a sizeable impactor, such a NEO can develop a relatively dense cloud of co‐orbiting material in which destructive collisions are relatively frequent. The gas and nanoscale dust released in the destructive collisions can be detected remotely by downstream spacecraft equipped with magnetometers. In this paper, we use such magnetic disturbances to identify regions of near‐Earth space in which high densities of small objects are present. We find that asteroid (138175) 2000EE104 currently may have a cloud of potentially threatening co‐orbiting material. Due to the scattered co‐orbitals, there can be a finite impact probability whenever the Earth approaches the orbit of asteroid 2000EE104, regardless of the position of the asteroid itself.     

An Estimate of the Long-term Tendency of Tidal Evolution of Earth-lunar System

According to the conservation principle of angular momentum, we calculate in this paper the revolution period and the distance between the Earth and the Moon in the equilibrium state of the tidal evolution in the Earth-Moon system. The difference of energy between the current state and the equilibrium state is used to compute the time needed to fulfil the equilibrium state. Then the long-term variations of the Earth-Moon distance and of the Earth rotation rate are further estimated.     

Early tides: Response to Varga et al.

Tidal cycling has been causally implicated at the origin of life, but the speed of early tides has not been established. The rotation period of the Earth is the dominant parameter, and a length of day (LOD) of under 6 h at 3.9 Ga was inferred by regression from present values [Lathe, R. 2004. Icarus 168, 18-22]. However, this would imply critical lunar proximity at that time; in their commentary Varga et al. instead argue for a more distant Moon, proposing LOD=16.8 h. The debate is accentuated because regression from current values requires an Earth-Moon juxtaposition at around 2 Ga, for which there is no evidence. A smooth retreat from a Moon-forming impact at 4.5 Ga is also irreconcilable with the weight of paleotidal evidence. An inflection in the lunar recession curve is required to reconcile current and recent Earth-Moon values with a 4.5 Ga origin, requiring a change in tidal friction during the evolution of the Earth-Moon system. Depending on whether this took place at ∼2-2.5 Ga before present, or more recently (∼0.8-0.2 Ga), LOD values are estimated at between 12 and 16 h, suggesting a compromise figure of LOD=∼14 h, with tides every ∼7 h, at 3.9 Ga.     

The atmospheric influence, size and possible asteroidal nature of the July 2009 Jupiter impactor

Near-infrared and mid-infrared observations of the site of the 2009 July 19 impact of an unknown object with Jupiter were obtained within days of the event. The observations were used to assess the properties of a particulate debris field, elevated temperatures, and the extent of ammonia gas redistributed from the troposphere into Jupiter’s stratosphere. The impact strongly influenced the atmosphere in a central region, as well as having weaker effects in a separate field to its west, similar to the Comet Shoemaker-Levy 9 (SL9) impact sites in 1994. Temperatures were elevated by as much as 6 K at pressures of about 50-70 mbar in Jupiter’s lower stratosphere near the center of the impact site, but no changes above the noise level (1 K) were observed in the upper stratosphere at atmospheric pressures less than ∼1 mbar. The impact transported at least ∼2 × 10¹⁵ g of gas from the troposphere to the stratosphere, an amount less than derived for the SL9 C fragment impact. From thermal heating and mass-transport considerations, the diameter of the impactor was roughly in the range of 200-500 m, assuming a mean density of 2.5 g/cm³. Models with temperature perturbations and ammonia redistribution alone are unable to fit the observed thermal emission; non-gray emission from particulate emission is needed. Mid-infrared spectroscopy of material delivered by the impacting body implies that, in addition to a silicate component, it contains a strong signature that is consistent with silica, distinguishing it from SL9, which contained no evidence for silica. Because no comet has a significant abundance of silica, this result is more consistent with a “rocky” or “asteroidal” origin for the impactor than an “icy” or “cometary” one. This is surprising because the only objects generally considered likely to collide with Jupiter and its satellites are Jupiter-Family Comets, whose populations appear to be orders of magnitude larger than the Jupiter-encountering asteroids. Nonetheless, our conclusion that there is good evidence for at least a major asteroidal component of the impactor composition is also consistent both with constraints on the geometry of the impactor and with results of contemporaneous Hubble Space Telescope observations. If the impact was not simply a statistical fluke, then our conclusion that the impactor contained more rocky material than was the case for the desiccated Comet SL9 implies a larger population of Jupiter-crossing asteroidal bodies than previously estimated, an asteroidal component within the Jupiter-Family Comet population, or compositional differentiation within these bodies.     

Mass dispersal and angular momentum transfer during collisions between rubble-pile asteroids

We perform N-body simulations of impacts between initially non-rotating rubble-pile asteroids, and investigate mass dispersal and angular momentum transfer during such collisions. We find that the fraction of the dispersed mass (Mdisp) is approximately proportional to , where Qimp is the impact kinetic energy; the power index α is about unity when the impactor is much smaller than the target, and 0.5?α<1 for impacts with a larger impactor. Mdisp is found to be smaller for more dissipative impacts with small values of the restitution coefficient of the constituent particles. We also find that the efficiency of transfer of orbital angular momentum to the rotation of the largest remnant depends on the degree of disruption. In the case of disruptive oblique impacts where the mass of the largest remnant is about half of the target mass, most of the orbital angular momentum is carried away by the escaping fragments and the efficiency becomes very low (<0.05), while the largest remnant acquires a significant amount of spin angular momentum in moderately disruptive impacts. These results suggest that collisions likely played an important role in rotational evolution of small asteroids, in addition to the recoil force of thermal re-radiation.     

Supplemental satellites and lunisolar precession

Summary Two earth orbiting satellites with the same semimajor axes and eccentricities, but supplemental inclinations, define a direction — the bisector of their nodal lines — which is free from the secular motion due to the oblateness of the earth (Ciufolini 1986). We show that the inclination and the longitude of the node refer to the direction of the angular momentum of the earth. Because of the lunisolar precession and nutation, the longitude of the bisector so defined changes in a way dependent on the orientation of the angular momentum. If the relativistic Lense-Thirring precession is assumed, its measurement with two supplemental satellites will give information about the precessional and nutational constants.Research supported by the Piano Spazïale Nazionale of Italy.     

High-resolution simulations of the impacts of asteroids into the venusian atmosphere III: further 3D models

We report on high-resolution three-dimensional calculations of oblique impacts into planetary atmospheres, specifically the atmosphere of Venus, extending the results of Korycansky et al. (2000, Icarus 146, 387-403; 2002, Icarus 157, 1-23). We have made calculations for impacts at 0°, 45°, and 60° from the vertical, different impactor velocities (10, 20, and 40 km s⁻¹), and different impactor masses and orientations. We present results for porous impactors using a simple model of porosity. We have investigated the sensitivity to initial conditions of the calculations [as a follow-up to the results found in Korycansky et al. (2002)] and resolution effects. For use in cratering calculations, we fit simple functions to the numerical results for mass and momentum that penetrate to a given altitude (column mass) and investigate the behavior of the fit coefficients as functions of impactor parameters such as mass, velocity, and impact angle. Generally speaking, the mass and momentum (and hence resulting crater diameters) depend primarily on impactor mass and mass of atmosphere encountered and weakly or not at all on other parameters such as impactor velocity, impact angle, or porosity. The column mass to which the last portion of the impactor penetrates is approximately equal to the mass of impactor at the top of the atmosphere before the impact takes place. Finally, we present the beginnings of a simplified but physically based model for the impactor and its fragments to reproduce the mass and momentum fluxes as a function of height during the impact.     

On the shapes and spins of “rubble pile” asteroids

We examine the shape of a “rubble pile” asteroid as it slowly gains angular momentum by YORP torque, to the point where “landsliding” occurs. We find that it evolves to a “top” shape with constant angle of repose from the equator up to mid-latitude, closely resembling the shapes of several nearly critically spinning asteroids imaged by radar, most notably (66391) 1999 KW4 [Ostro, S.J., Margot, J.-L., Benner, L.A.M., Giorgini, J.D., Scheeres, D.J., Fahnestock, E.G., Broschart, S.B., Bellerose, J., Nolan, M.C., Magri, C., Pravec, P., Scheirich, P., Rose, R., Jurgens, R.F., De Jong, E.M., Suzuki, S., 2006. Science 314, 1276-1280]. Similar calculations for non-spinning extremely prolate or oblate “rubble piles” show that even loose rubble can sustain shapes far from fluid equilibrium, thus inferences based on fluid equilibrium are generally useless for inferring bulk properties such as density of small bodies. We also investigate the tidal effects of a binary system with a “top shape” primary spinning at near the critical limit for stability. We find that very close to the stability limit, the tide from the secondary can actually levitate loose debris from the surface and re-deposit it, in a process we call “tidal saltation.” In the process, angular momentum is transferred from the primary spin to the satellite orbit, thus maintaining the equilibrium of near-critical spin as YORP continues to add angular momentum to the system. We note that this process is in fact dynamically related to the process of “shepherding” of narrow rings by neighboring satellites.     

Chemical composition of the Earth after the giant impact

The giant impact hypothesis for the origin of the Moon has been widely accepted. One of the most important features of this hypothesis is that the impactor's metallic core was incorporated in the Earth after impact. If the mass of the impactor is 0.82 × 10²⁷ g, the mass of the impactor core was estimated to be 0.19 × 10²⁷ g, which is about 1/10 of present Earth's core. Liu (1982) derived the bulk composition of the Earth from CI chondrites, and concluded that the Fe content of his model appears to be low in comparison with the present Earth, which, however, can be rationalized by the addition of impactor core into the proto-Earth developed by Liu (1982). If the impactor's mantle contains 14 wt% FeO as suggested, the mass ratio of impactor/proto-Earth should not exceed 0.22. The same ratio is not likely to exceed 0.30, if a giant blowoff did not occur during impact.     

High-resolution simulations of the final assembly of Earth-like planets I. Terrestrial accretion and dynamics

The final stage in the formation of terrestrial planets consists of the accumulation of ∼1000-km “planetary embryos” and a swarm of billions of 1-10 km “planetesimals.” During this process, water-rich material is accreted by the terrestrial planets via impacts of water-rich bodies from beyond roughly 2.5 AU. We present results from five high-resolution dynamical simulations. These start from 1000-2000 embryos and planetesimals, roughly 5-10 times more particles than in previous simulations. Each simulation formed 2-4 terrestrial planets with masses between 0.4 and 2.6 Earth masses. The eccentricities of most planets were ∼0.05, lower than in previous simulations, but still higher than for Venus, Earth and Mars. Each planet accreted at least the Earth's current water budget. We demonstrate several new aspects of the accretion process: (1) The feeding zones of terrestrial planets change in time, widening and moving outward. Even in the presence of Jupiter, water-rich material from beyond 2.5 AU is not accreted for several millions of years. (2) Even in the absence of secular resonances, the asteroid belt is cleared of >99% of its original mass by self-scattering of bodies into resonances with Jupiter. (3) If planetary embryos form relatively slowly, then the formation of embryos in the asteroid belt may have been stunted by the presence of Jupiter. (4) Self-interacting planetesimals feel dynamical friction from other small bodies, which has important effects on the eccentricity evolution and outcome of a simulation.     

Formation of the prelunar accretion disk

According to the single-impact hypothesis for forming the Moon, the angular momentum needed for the present Earth-Moon system can be imparted to the proto-Earth by a collision with a body having one-tenth of the mass or more. The collision must vaporize a large amount of rock which must stay in the form of vapor after expanding in density by a factor of several, so that pressure gradients can accelerate significant amounts of the matter into orbital motion about the proto-Earth. A successful theory must put considerably more than a lunar mass into orbit, having considerably more angular momentum than is needed to assemble a lunar mass in orbit at 3 Earth radii. Such a collision has been simulated by a particular form of a particle-in-cell representation of hydrodynamics and 78 cases have been run representing variations in a variety of parameters. A significant fraction of the cases were successful in creating a satisfactory prelunar accretion disk. A fairly common characteristic of these cases was the presence of an excess velocity in the collision (above that of a parabolic orbit), implying that the projectile involved in the collision existed in an Earth-crossing orbit of significant ellipticity. A majority of the mass of the prelunar accretion disk is contributed by the projectile.     

On YORP-induced spin deformations of asteroids

The alteration of the spin states of small Solar-System bodies by the YORP thermal effect has recently become a plausible and, for some, the favorite candidate for the formation of binary asteroids. The idea is that if an asteroid is slowly spun up to a state where some strength measure is exceeded; it can no longer remain rigid and adjusts to a new configuration. Such a process might involve global fission, global shape changes without fission, or gradual surface mass loss with subsequent mass re-accumulations forming a secondary body.Here I analyze the changes in the shape, spin, and state during slowly increasing angular momentum of rubble-pile, self-gravitating, homogeneous ellipsoidal bodies undergoing homogeneous motions. I use, as appropriate for rubble-pile asteroids, the strength models of granular materials with zero tensile strength (cohesionless but arbitrary dilatancy); those are characterized by the “angle of friction” material constant. There are distinct limit spins depending on that angle of friction and the shape, which were previously presented [Holsapple, K.A., 2001. Icarus 154, 432-448; Holsapple, K.A., 2004. Icarus 172, 272-303]. Here the deformations and state changes when the angular momentum is slowly increased from that of a limit spin state are determined, to study the YORP processes. When a body is at its limit spin and the angular momentum increases further, the body deforms in a unique way along definite paths in the ellipsoidal shape space: it evolves as an elongating shape with an increasing rotational inertia, which in most cases produces a decreasing spin. I give exact analytical solutions for those shape and spin histories, as well as the histories of the mass density, angular momentum and energy. Comparison to other approaches is made.