Impact and explosion crater ejecta,fragment size,and velocity

A model was developed for the mass distribution of fragments that are ejected at a given velocity for impact and explosion craters. The model is semiempirical in nature and is derived from (1) numerical calculations of cratering and the resultant mass versus ejection velocity, (2) observed ejecta blanket particle size distributions, (3) an empirical relationships between maximum ejecta fragment size and crater diameter, (4) measurements of maximum ejecta size versus ejecta velocity, and (5) an assumption on the functional form for the distribution of fragments ejected at a given velocity. This model implies that for planetary impacts into competent rock, the distribution of fragments ejected at a given velocity is broad; e.g., 68% of the mass of the ejecta at a given velocity contains fragments having a mass less than 0.1 times a mass of the largest fragment moving at that velocity. Using this model, we have calculated the largest fragment that can be ejected from asteroids, the Moon, Mars, and Earth as a function of crater diameter. The model is unfortunately dependent on the size-dependent ejection velocity limit for which only limited data are presently available from photography of high explosive-induced rock ejecta. Upon formation of a 50-km-diameter crater on an atmosphereless planet having the planetary gravity and radius of the Moon, Mars, and Earth, fragments having a maximum mean diameter of ≈30, 22, and 17 m could be launched to escape velocity in the ejecta cloud. In addition, we have calculated the internal energy of ejecta versus ejecta velocity. The internal energy of fragments having velocities exceeding the escape velocity of the moon (～2.4 km/sec) will exceed the energy required for incipient melting for solid silicates and thus, the fragments ejected from Mars and the Earth would be melted.     

Mercurian impact ejecta: Meteorites and mantle

Abstract— We have examined the fate of impact ejecta liberated from the surface of Mercury due to impacts by comets or asteroids, in order to study 1) meteorite transfer to Earth, and 2) reaccumulation of an expelled mantle in giant‐impact scenarios seeking to explain Mercury's large core. In the context of meteorite transfer during the last 30 Myr, we note that Mercury's impact ejecta leave the planet's surface much faster (on average) than other planets in the solar system because it is the only planet where impact speeds routinely range from 5 to 20 times the planet's escape speed; this causes impact ejecta to leave its surface moving many times faster than needed to escape its gravitational pull. Thus, a large fraction of Mercurian ejecta may reach heliocentric orbit with speeds sufficiently high for Earth‐crossing orbits to exist immediately after impact, resulting in larger fractions of the ejecta reaching Earth as meteorites. We calculate the delivery rate to Earth on a time scale of 30 Myr (typical of stony meteorites from the asteroid belt) and show that several percent of the high‐speed ejecta reach Earth (a factor of 2–3 less than typical launches from Mars); this is one to two orders of magnitude more efficient than previous estimates. Similar quantities of material reach Venus. These calculations also yield measurements of the re‐accretion time scale of material ejected from Mercury in a putative giant impact (assuming gravity is dominant). For Mercurian ejecta escaping the gravitational reach of the planet with excess speeds equal to Mercury's escape speed, about one third of ejecta reaccretes in as little as 2 Myr. Thus collisional stripping of a silicate proto‐Mercurian mantle can only work effectively if the liberated mantle material remains in small enough particles that radiation forces can drag them into the Sun on time scale of a few million years, or Mercury would simply re‐accrete the material.     

Electrolysis in space and fate of Phaethon

A new process of the energy accumulation in icy bodies (e.g., planetary satellites, cometary nuclei) is advanced which is applicable for space conditions: namely, the volumetric electrolysis of the ice containing foreign inclusions. The electrolysis takes place when the electric current, generated by virtue of the body's movement in the external magnetic field (planetary magnetospheres, the solar wind field, etc.) flows through the body.The cosmogonical concept which treats the Sun-Jupiter system as a limiting case of a close binary star, together with the known data on mass, composition and space distribution of asteroids, allows one to assume the initial existence between Mars and Jupiter of a Moon-like planet enriched with ices and allied by its parameters to the Galilean satellites (mainly Ganymede and Callisto). If this planet was affected by the ancient solar wind with during 10⁹ yr, it could have accumulated the energy sufficient for its explosion.The process considered seems able to explain, from a unified point of view, a large number of phenomena — such as the burst activity of comets, a considerable hydrogen excess in their tails, a noticeable long-period comet perihelia orientation toward the solar apex, the existence of asteroidal families and the separation of asteroids by their chemical composition into two main groups, the Tunguska event, etc.     

The global budget of impact-derived sediments on Venus

The observed record of impact craters on the surface of the planet Venus can be used to calculate the contribution of fine materials generated by impact processes to the global sedimentary cycle. Using various methods for the extending the population of impact craters with diameters larger than 8 km observed on the northern 25% of the Venus to the entire surface area of the planet, we have estimated how materials ejected from the integrated record of impact cratering over the past 0.5 to 1.0 æ might have been globally distributed. Relationships for computing the fraction of ejected materials from impact craters in a given size range originally developed for the Moon (and for terrestrial nuclear explosion cratering experiments) were scaled for Venus conditions, and the ejecta fragments with sizes less than 30 m were considered to represent those with the greatest potential for global transport and eventual fallout. A similar set of calculations were carried out using the observed terrestrial cratering record, corrected for the missing population of small craters and oceanic impacts that have either been eroded or are unobserved (due to water cover). Our calculations suggest that both Venus and the Earth should have experienced approximately 6000 impact events over the past 0.5 to 1 æ (in the size range from 1 km to about 180 km). The cumulative global thickness of impact-derived fine materials that could have produced from this record of impacts in this time period is most likely between 1–2 mm for Venus, and certainly no more than 6 mm (assuming an enhanced population of large 150–200 km scale impact events). For Earth, the global cumulative thickness is most likely 0.2 to 0.3 mm, and certainly no more than 2 to 3 mm. The cumulative volume of impact ejecta (independent of particle size) for Venus generated over the past 1 æ, when spread out over the global surface area to form a uniform layer, would fall between 2 and 12 meters, although 99% of this material would be deposited in the near rim ejecta blanket (from 1 to 2.3 crater radii from the rim crest), and only 0.02% would be available for global transport as dust-sized particles. Thus, our conclusion is that Venus, as with the Earth, cannot have formed a substantial impact-derived regolith layer over the past billion years of its history as is typical for smaller silicate planets such as the Moon and Mercury. This conclusion suggests that there must be other extant mechanisms for sediment formation and redistribution in the Venus environment, on the basis of Venera Lander surface panoramas which demonstrate the occurrence of local sediment accumulations.'Geology and Tectonics of Venus', special issue edited by Alexander T. Basilevsky (USSR Acad. of Sci. Moscow), James W. Head (Brown University, Providence), Gordon H. Pettengill (MIT, Cambridge, Massachusetts) and R. S. Saunders (J.P.L., Pasadena).     

Martian and terrestrial paleoclimatology: Relevance of solar variability

Evidence for past Martian rivers is perhaps the most puzzling and inconsistent present planetary problem, conflicting as it does with current conditions on the planet. This paper emphasizes the similar puzzling evidence that the Earth, as well as Mars, was warmer in the past. Neutrino evidence raises the suggestion that the sun was also “warmer” in the past. A hypothetical cause reconciling all effects is episodic change in solar luminosity on a time-scale of a few hundred million years. This paper outlines requirements and consequences of such a working hypothesis, with pro and con arguments. It is important to try to prove or disprove this hypothesis because it has radical implications for current science. For example, it suggests (1) climates of all the planets have been markedly altered simultaneously by solar changes, sometimes catastrophically; (2) solar changes have been a dominant “forcing function” driving biological speculation and evolution on Earth; (3) the concept of geologic uniformitarianism is somewhat modified by cosmic variables; (4) evolution of water-utilizing intelligent creatures near other stars may be less likely than has been thought, due to catastrophic planetary climate reactions to change in stellar luminosity.     

Populating the asteroid belt from two parent source regions due to the migration of giant planets—“The Grand Tack”

Abstract– The asteroid belt is found today in a dramatically different state than that immediately following its formation. It is estimated that it has been depleted in total mass by a factor of at least 1000 since its formation, and that the asteroids’ orbits evolved from having near‐zero eccentricity and inclination to the complex distributions we find today. The asteroid belt also hosts a wide range of compositions, with the inner regions dominated by S‐type and other water‐poor asteroids and the outer regions dominated by C‐type and other primitive asteroids. We discuss a model of early inner solar system evolution whereby the gas‐driven migration of Jupiter and Saturn brings them inwards to 1.5 AU, truncating the disk of planetesimals in the terrestrial planet region, before migrating outwards toward their current locations. This model, informally titled “The Grand Tack,” examines the planetary dynamics of the solar system bodies during the final million years of the gaseous solar nebula lifetime—a few million years (Myr) after the formation of the first solids, but 20–80 Myr before the final accretion of Earth, and approximately 400–600 Myr before the Late Heavy Bombardment of the inner solar system. The Grand Tack attempts to solve some outstanding problems for terrestrial planet formation, by reproducing the size of Mars, but also has important implications for the asteroid population. The migration of Jupiter causes a very early depletion of the asteroid belt region, and this region is then repopulated from two distinct source regions, one inside the formation region of Jupiter and one between and beyond the giant planets. The scattered material reforms the asteroid belt, producing a population the appropriate mass, orbits, and with overlapping distributions of material from each parent source region.     

A former asteroidal planet as the origin of comets

The idea of a missing planet between Mars and Jupiter has been with us since the formulation of the Titius-Bode law. The discovery of the asteroid belt in that location led to speculation about a planetary breakup event. Both ideas remained conjectures until Ovenden's finding in 1972, from which it could be derived that the mass of the missing planet was about 90 Earth masses and that its breakup was astronomically recent. Apparently much of that mass was blown out of the solar system during the disruption of the planet. Because of the action of planetary perturbations, only two types of orbits of surviving fragments could remain at present-asteroid orbits and once-around very-long-period elliptical orbits. Objects in the latter type of orbit are known to exist-the very-long-period comets. A large number of these are on elliptical trajectories with periods of revolution of 5 million years; yet they are known to have made no more than one revolution in an orbit passing close to the Sun. By direct calculation it is possible to predict the distribution of the orbital elements of objects moving on long-period ellipses which might have originated in a breakup event in the asteroid belt 5 million years ago. The comet orbits have the predicted distribution in every case where a measure is possible. Some of the distribution anomalies, such as a bias in the directions of perihelion passage, are statistically strong and would be difficult to explain in any other uncontrived way. In addition, a relative deficiency of orbits with perihelia less than 1 AU indicates that the comets must have had small perihelion distances since their origin, rather than that they have been perturbed into small perihelion orbits from a distant “cloud” of comets by means of stellar encounters. The comet orbital data lead to the conclusion that all comets originated in a breakup event in the asteroid belt (5.5±0.6) × 10⁶ years ago. Asteroid and meteoritic evidence can now be interpreted in a way which not only is supportive but also provides fresh insights into understanding their physical, chemical, and dynamical properties. Particularily noteworthy are the young cosmic-ray exposure ages of meteorites, evidence of a previous high-temperature/pressure environment and of chemical differentiation of the parent body, and compositional similarities among comets, asteroids, and meteorites. Certain “explosion signatures” in asteroid orbital element distributions are likewise indicative. Tektites may also have originated in the same event; but if so, there are important implications regarding the absolute accuracy of certain geological dating methods. Little is known about possible planetary breakup mechanisms of the requisite type, though some speculations are offered. In any case, the asteroid belt is an existing fact; and the arguments presented here that a large planet did disintegrate 5 million years ago must be judged on their merits, even in the absence of a suitable theory of planetary explosions.     

Some recent work on the orbital theory of asteroids

This is a brief report on three theoretical projects about asteroids. The results presented here were recently obtained at the Astronomisches Rechen-Institut in Heidelberg, and it is planned to publish them in astronomy and Astrophysics in detail. The first project is a continuation of former work on asteroids with a mean motion commensurable to that of Jupiter (compare Schubart, 1968). In the two other cases the problem consists in the best possible determination of the value of a planetary mass in units of solar mass.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 27–September 2, 1972.     

Evolutionary tracks of the terrestrial planets

On the basis of the model proposed by Matsui and Abe, we will show that two major factors — distance from the Sun and the efficiency of retention of accretional energy — control the early evolution of the terrestrial planets. A diagram of accretional energy versus the optical depth of a proto-atmosphere provides a means to follow the evolutionary track of surface temperature of the terrestrial planets and an explanation for why the third planet in our solar system is an aqua-planet.     

Formation of a ‘magma ocean’ on the terrestrial planets due to the blanketing effect of an impact-induced atmosphere

We show that the surface of a planet growing by planetesimal impact is heated over the melting temperature of the surface materials due to the blanketing effect of an impact induced H₂O atmosphere with the present H₂O abundance of the Earth even when the accretion time is as long as 10⁸ years. Hence, a magma ocean covering the entire surface was formed on the Earth and Moon and other terrestrial planets during their formations.     

Origin and evolution of the atmospheres of early Venus,Earth and Mars

We review the origin and evolution of the atmospheres of Earth, Venus and Mars from the time when their accreting bodies were released from the protoplanetary disk a few million years after the origin of the Sun. If the accreting planetary cores reached masses \(\ge 0.5 M_\mathrm{Earth}\) before the gas in the disk disappeared, primordial atmospheres consisting mainly of H\(_2\) form around the young planetary body, contrary to late-stage planet formation, where terrestrial planets accrete material after the nebula phase of the disk. The differences between these two scenarios are explored by investigating non-radiogenic atmospheric noble gas isotope anomalies observed on the three terrestrial planets. The role of the young Sun’s more efficient EUV radiation and of the plasma environment into the escape of early atmospheres is also addressed. We discuss the catastrophic outgassing of volatiles and the formation and cooling of steam atmospheres after the solidification of magma oceans and we describe the geochemical evidence for additional delivery of volatile-rich chondritic materials during the main stages of terrestrial planet formation. The evolution scenario of early Earth is then compared with the atmospheric evolution of planets where no active plate tectonics emerged like on Venus and Mars. We look at the diversity between early Earth, Venus and Mars, which is found to be related to their differing geochemical, geodynamical and geophysical conditions, including plate tectonics, crust and mantle oxidation processes and their involvement in degassing processes of secondary \(\hbox {N}_2\) atmospheres. The buildup of atmospheric \(\hbox {N}_2\), \(\hbox {O}_2\), and the role of greenhouse gases such as \(\hbox {CO}_2\) and \(\hbox {CH}_4\) to counter the Faint Young Sun Paradox (FYSP), when the earliest life forms on Earth originated until the Great Oxidation Event \(\approx \) 2.3 Gyr ago, are addressed. This review concludes with a discussion on the implications of understanding Earth’s geophysical and related atmospheric evolution in relation to the discovery of potential habitable terrestrial exoplanets.     

Higher-order stability of the restricted problem and the solar system

A generalization is expressed of the Poisson theorem referring to the invariance of the planetary semi-major axes using the restricted problem model. In particular, it is shown that first and second approximation in terms of a change in the initial states of planets describing closed motions in the solar system remain invariant in modulus after any number of revolutions. But third-order terms contain secular parts and, thus, they undergo a secular change in their orbital motion. Such change would be apparent after ^-2 Jovian years, where is a constant and is the maximum initial deviation of each planet from its reference orbit.     

On the feasibility of studying the exospheres of Earth-like exoplanets by Lyman-<Emphasis Type="Italic">α</Emphasis> monitoring

Observations of the Earth’s exosphere have unveiled an extended envelope of hydrogen reaching further than 10 Earth radii composed of atoms orbiting around the Earth. This large envelope increases significantly the opacity of the Earth to Lyman α (Lyα) photons coming from the Sun, to the point of making feasible the detection of the Earth’s transit signature from 1.35 pc if pointing with an 8 meter primary mirror space telescope through a clean line of sight (N _H <?10¹⁷ cm^??2), as we show. In this work, we evaluate the potential detectability of Earth analogs orbiting around nearby M-type stars by monitoring the variability of the Lyα flux variability. We show that, in spite of the interstellar, heliospheric and astrospheric absorption, the transit signature in M5 V type stars would be detectable with a dedicated Lyα flux monitor implemented in a 4–8 m class space telescope. Such monitoring programs would enable measuring the robustness of planetary atmospheres under heavy space weather conditions like those produced by M-type stars. A 2-m class telescope, such as the World Space Observatory, would suffice to detect an Earth-like planet orbiting around Proxima Centauri, if there was such a planet or nearby M5 type stars.     

The distribution of mass in the planetary system and solar nebula

A model solar nebula is constructed by adding the solar complement of light elements to each planet, using recent models of planetary compositions. Uncertainties in this approach are estimated. The computed surface density varies approximately asr ^–3/2. Mercury, Mars and the asteroid belt are anomalously low in mass, but processes exist which would preferentially remove matter from these regions. Planetary masses and compositions are generally consistent with a monotonic density distribution in the primordial solar nebula.     

Glaciopanspermia: Seeding the terrestrial planets with life?

The question whether life originated on Earth or elsewhere in the solar system has no obvious answer, since Earth was sterilized by the Moon-forming impact and possibly also during the LHB, about 700 Ma after the formation of the solar system. Seeding by lithopanspermia has to be considered. Possible sources of life include Earth itself, Mars, Venus (if it had a more benign climate than today) and icy bodies of the solar system. The first step of lithopanspermia is the ejection of fragments of the surface into space, which requires achieving at least escape velocity. As the velocity distribution of impact ejecta falls off steeply, attention is drawn to bodies with lower escape velocities. Ceres has had, or still has, an ocean more than 100 km deep, with hydrothermal activity at its rocky core. The possible presence of life, its relative closeness to the terrestrial planets and Ceres' low escape velocity of 510 m/s suggest that Ceres could well be a parent body for life in the solar system.Icy impact ejecta - hence glaciopanspermia - from Ceres will be subject to evaporation of volatiles. Spores may be loosened by evaporation and enter the atmospheres of the terrestrial planets as micrometeorites.The seeding of the terrestrial planets from Ceres would result in (1) detection of life in the crustal layers of Ceres; (2) a commonality of Cerean life with Terran and possible Martian and Venusian life and (3) biomarkers of Cerean life, which might be found in the ice at the Moon's poles and on the surface of other main belt asteroids.     

Unbound planets

Current protostellar theory has determined a lower limit to the mass of a pre-stellar gas cloud fragment of ~0.01 M. This suggests that isolated interstellar bodies in the mass range ~10 M_-710_-2 M must have originated within a planetary system. Two possible mechanisms whereby planets are lost from their parental systems to interstellar space are discussed and the abundance and distribution of such unbound planets within the Galaxy is examined. It is found that, except within the central regions of the Galaxy, unbound planets are expected to be scarce. In the solar neighbourhood for instance, the number density ratio of unbound planets to stars is estimated to range between extremes of ~4 × 10^–4–3 × 10^–2 with a most probable value of ~6 x 10^–3. The faint possibility that the hypothetical Planet X might be of extra-solar origin is also discussed.     

Dynamics of dust in a plasma sheath and injection of dust into the plasma sheath above Moon and asteroidal surfaces

We have examined single dust particle dynamics in a plasma sheath near the surface of solid bodies in space, considering conditions which resemble those of planetary system bodies, when photoelectric effect can be neglected. The forces on the dust particles are assumed to be from the electric field in the sheath and from gravitation only. As the dust particles will charge negatively in the sheath, these forces will act in opposite directions and may balance.The charge delay of a moving dust particle is responsible for many of the interesting dynamical properties, and we show that for a stationary plasma, dust motion is unstable to about one Debye length out from the surface of the solid body. This part of the sheath will therefore be devoid of dust particles as they will either fall down, escape completely from the solid body or collect and make damped oscillations at stable positions in the outer part of the sheath. With increasing plasma bulk speed towards the surface, the inner unstable part of the sheath will decrease in thickness.The sources for the dust in the sheath are assumed to be mainly ejecta from meteorites and micrometeorites, but may also, for the smallest solid bodies, be from electrostatic levitation of very small dust particles. We have for different sizes of solid bodies calculated the sizes of ejecta that can be floated in the sheath. For the solar wind plasma, the suspended dust particles range from less than 1 m for the Moon to about 80 m for an asteroid with radius 1 km. These particles create a dust atmosphere.The results in this paper hold when the dust particle density is so low that the charges on the dust particles do not contribute significantly to the total space charge; a higher density will lead to a modification of the sheath.Our calculations show that ejecta below a certain size will be accelerated in the sheath and totally escape from the body even if they have near zero initial vertical velocity, while ejecta above this size will need a much larger velocity to escape. This is especially significant for the small solid bodies (radius of order km and less) which will therefore act as important sources of micronsized dust. This could be of significance for the dust production and the size distribution of dust in planetary ring systems.     

Light Deflection Near the Sun's Limb: Refraction by the Solar Atmosphere

Light refraction by the Sun's atmosphere is calculated.As detected from the Earth, the refraction can deflect a light ray emitted from the Sun's limb by 13 or a starlight ray grazing the solar limb by 26, an effect 15 times larger than the gravitational deflection.     

Paleocratering of the Moon: Review of post-Apollo data

As a result of the dating of lunar samples, we are in a position to utilize the lunar surface as a recorder of environmental conditions in the Earth-Moon neighborhood in the past. Plots of crater density vs rock age at different lunar landing sites can be used to date unexplored lunar provinces. These plots also demonstrate evolution in the population of planetesimals that struck the Moon. Prior to 4.1 aeons ago, the cratering rate on the Moon was at least 10³ times the present rate, and the rate declined with a half-life less than 8×10⁷ yr. During the interval from 4.1 to 3.2 aeons ago, the number of planetesimals showed an exponential decay with a half-life about 3×10⁸ yr, corresponding to sweep-up of particles from solar orbits somewhat similar to those of Apollo asteroids. A more nearly constant cratering rate applied in the last three aeons. These data indicate that the Moon displays at least the final stages of an ancient accretion process; they also set certain conditions on possible capture processes relating to the Moon's origin. Pre-Apollo expectations that the Moon would provide a Rosetta Stone for interpreting solar system history and planet formation thus appear justified.Paper given at Philadelphia meeting of American Association for Advancement of Science, December, 1971.     

Carbon suboxide and the genetic code

Carbon suboxide (C₃O₂) polymers formed in the primitive atmosphere would have produced an organic compound soup of high concentration on the Earth. Various vestiges of C₃O₂ are found in the present genetic scheme, which might suggest that the living system had formed from the polymer soup.