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The Hungaria Asteroids: Close encounters and impacts with terrestrial planets
Abstract and Figures
The Hungaria asteroid family (Named after (434) Hungaria), which consists of
more than 5000 members with semi-major axes between 1.78 and 2.03 AU and have inclinations of the order of 20°, is regarded as one source for Near-Earth Asteroids (NEAs).
They are mainly perturbed by Jupiter and Mars, and are ejected because of mean motion
and secular resonances with these planets and then become Mars-crossers; later they may
even cross the orbits of Earth and Venus. We are interested to analyze the close encounters
and possible impacts with these planets. For 200 selected objects which are on the edge
of the group we integrated their orbits over 100 million years in a simplified model of the
planetary system (Mars to Saturn) subject to only gravitational forces. We picked out a sam-
ple of 11 objects (each with 50 clones) with large variations in semi-major axis and some
of them achieve high inclinations and eccentricities in connection with mean motion and
secular resonances which then leads to relatively high velocity impacts on Venus, Earth and
Mars. We report all close encounters and impacts with the terrestrial planets and statistically
determine the mean life and the orbital distribution of the NEAs of these Hungarias.
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... Each clone was integrated over the time span of 10 Myr into the future using the Lie integrator (Bancelin, Hestroffer & Thuillot, 2012;Eggl & Dvorak, 2010;Hanslmeier & Dvorak, 1984) with an accuracy parameter set to 10 13 . The code was upgraded by a subroutine designed to compute encounter velocity, deflection of the orbit, impact angle, impact velocity after an impact is identified (see Galiazzo, Bazso & Dvorak (2014)). Orbits were taken from the HORIZONS Web-Interface 2 at Epoch 2453724.5 JDTBT (Epoch Julian Date, Barycentric Dynamical Time). ...
... In case condition (a) is valid, but not (b) we consider the body to burn up as a meteor. For each detected planetary impact, we derived the impact velocity, and impact angle (Galiazzo, Bazsó & Dvorak, 2013a;Galiazzo, Bazso & Dvorak, 2014). Where necessary, we took into consideration the atmospheric effect as modeled by Collins, Melosh & Marcus (2005). ...
... Concerning the probability of an impact, we assume the average impact probability per body per Gyr (Table 2) and we compare the probability of impacts to that of the Hungarias (the Hungaria family is one of the principal main belt sources of NEAs (Bottke et al., 2002;Galiazzo, Bazsó & Dvorak, 2013a;Galiazzo, Bazso & Dvorak, 2014)) and to observed planetary crossers with H < 17 (OPC17). The average impact probability per 1 Gyr is: ...
Background
Asteroids colliding with planets vary in composition and taxonomical type. Among Near‐Earth Asteroids (NEAs) are the V‐types, basaltic asteroids that are classified via spectroscopic observations.
Materials and Methods
we performed numerical simulations and statistical analysis of close encounters and impacts between V‐type NEAs and the terrestrial planets over the next 10 Myr. We study the probability of V‐ type NEAs colliding with Earth, Mars and Venus, as well as the Moon. We perform a correlational analysis of possible craters produced by V‐type NEAs, using available catalogs for terrestrial impact craters.
Results
The results suggest that V‐type NEAs can have many close encounters below 1 LD and even some of them impacts with all the terrestrial planets, the Earth in particular. There are four candidate craters on Earth that were likely caused by V‐type NEAs.
Conclusion
At least 70% of the V‐type NEAs can have close encounters with the terrestrial planets (and 58% with the Moon) . They can collide with all the terrestrial planets. In particular for the Earth the average rate is one every ∼12 Myr. The two craters with the highest probability of being generated by an impact with a basaltic impactor are: the Strangways crater (24 km diameter) in Australia and the Nicholson crater (12.5 km diameter) in Canada.
... Because these asteroids could not have dynamically evolved from the Vesta family region to their present orbits in ∼1 g.y., they are presumably fragments excavated from (4) Vesta's basaltic crust by an earlier impact. Note 9 -Other asteroid families whose long-term dynamics has been studied in detail, listed here in the alphabetical order, are the Adeona family (affected in e P and i P by the 8:3 resonance at 2.705 AU, Carruba et al., 2003), Agnia family (inside the z 1 resonance; Vokrouhlický et al., 2006c), Astrid family (near the border of the 5:2 resonance; Vokrouhlický et al., 2006b), Eunomia family (Carruba et al., 2007b), Euphrosyne family (located in a region with many resonances, including g − g 6 = 0, near the inner border of the 2:1 resonance; Carruba et al., 2014), Erigone family (cut in the middle by the z 2 resonance; Vokrouhlický et al., 2006b), Gefion family (affected by various resonances near 2.75 AU, Carruba et al., 2003, Hilda and Schubart families in the 3:2 resonance with Jupiter (Brož and Vokrouhlický, 2008), Hungaria family (perturbed by 2g − g 5 − g 6 = 0 and other secular resonances below 1.93 AU; Warner et al. (2009), Milani et al. (2010, also see Galiazzo et al. (2013Galiazzo et al. ( , 2014 for the contribution of Hungarias to the E-type NEAs andĆuk et al. (2014) for their suggested relation to the aubrite meteorites), Hygiea family (Carruba, 2013;Carruba et al., 2014), Massalia family (the part with a P > 2.42 AU disturbed by the 1:2 resonance with Mars, Vokrouhlický et al., 2006b), Merxia family (spread by the 3J-1S-1 three-body resonance at a P = 2.75 AU; Vokrouhlický et al., 2006b), Padua family (Carruba, 2009a), Pallas family , Phocaea family (Carruba, 2009b), Sylvia family ((87) Sylvia has two satellites, possibly related to the impact that produced the Sylvia family, Vokrouhlický et al., 2010), and Tina family (Carruba and Morbidelli, 2011). Note 10http://sbn.psi.edu/pds/resource/nesvornyfam.html ...
Asteroids formed in a dynamically quiescent disk but their orbits became gravitationally stirred enough by Jupiter to lead to high-speed collisions. As a result, many dozen large asteroids have been disrupted by impacts over the age of the solar system, producing groups of fragments known as asteroid families. Here we explain how the asteroid families are identified, review their current inventory, and discuss how they can be used to get insights into long-term dynamics of main-belt asteroids. Electronic tables of the membership for 122 notable families are reported on the Planetary Data System node. See related chapters in this volume for the significance of asteroid families for studies of physics of large-scale collisions, collisional history of the main belt, source regions of the near-Earth asteroids, meteorites and dust particles, and space weathering.
... Because these asteroids could not have dynamically evolved from the Vesta family region to their present orbits in ∼1 g.y., they are presumably fragments excavated from (4) Vesta's basaltic crust by an earlier impact. Note 9 -Other asteroid families whose long-term dynamics has been studied in detail, listed here in the alphabetical order, are the Adeona family (affected in e P and i P by the 8:3 resonance at 2.705 AU, Carruba et al., 2003), Agnia family (inside the z 1 resonance; Vokrouhlický et al., 2006c), Astrid family (near the border of the 5:2 resonance; Vokrouhlický et al., 2006b), Eunomia family (Carruba et al., 2007b), Euphrosyne family (located in a region with many resonances, including g − g 6 = 0, near the inner border of the 2:1 resonance; Carruba et al., 2014), Erigone family (cut in the middle by the z 2 resonance; Vokrouhlický et al., 2006b), Gefion family (affected by various resonances near 2.75 AU, Carruba et al., 2003, Hilda and Schubart families in the 3:2 resonance with Jupiter (Brož and Vokrouhlický, 2008), Hungaria family (perturbed by 2g − g 5 − g 6 = 0 and other secular resonances below 1.93 AU; Warner et al. (2009), Milani et al. (2010, also see Galiazzo et al. (2013Galiazzo et al. ( , 2014 for the contribution of Hungarias to the E-type NEAs andĆuk et al. (2014) for their suggested relation to the aubrite meteorites), Hygiea family (Carruba, 2013;Carruba et al., 2014), Massalia family (the part with a P > 2.42 AU disturbed by the 1:2 resonance with Mars, Vokrouhlický et al., 2006b), Merxia family (spread by the 3J-1S-1 three-body resonance at a P = 2.75 AU; Vokrouhlický et al., 2006b), Padua family (Carruba, 2009a), Pallas family , Phocaea family (Carruba, 2009b), Sylvia family ((87) Sylvia has two satellites, possibly related to the impact that produced the Sylvia family, Vokrouhlický et al., 2010), and Tina family (Carruba and Morbidelli, 2011). Note 10http://sbn.psi.edu/pds/resource/nesvornyfam.html ...
Asteroids formed in a dynamically quiescent disk but their orbits became
gravitationally stirred enough by Jupiter to lead to high-speed collisions. As
a result, many dozen large asteroids have been disrupted by impacts over the
age of the Solar System, producing groups of fragments known as asteroid
families. Here we explain how the asteroid families are identified, review
their current inventory, and discuss how they can be used to get insights into
long-term dynamics of main belt asteroids. Electronic tables of the membership
for 122 notable families are reported on the Planetary Data System node.
The well-investigated size-frequency distributions (SFD) for lunar craters can be used to estimate the SFD for projectiles that formed craters both on terrestrial planets and on asteroids. Our results suggest these distributions may have been relative stable over the past 4 G.y. The derived projectile SFD is found to have a shape that is similar to the SFD of main-belt asteroids as compared with the astronomical observations (Spacewatch asteroid data, Palomar-Leiden survey, IRAS data) and in situ images obtained by space missions. This result suggests that asteroids (or, more generally, collisionally evolved bodies) are the main component of the family of impactors striking the terrestrial planets.
An analysis based on the wavelet transform has been performed in order
to identify families in the proper elements space of asteroids. This
multi-scale analysis has been made on a set of 4100 proper element
computed by a new second order fourth-degree secular perturbation theory
(Milani and Knezevic 1990). A metric has been defined in the proper
element space in order to give a dynamical definition of families. This
metric is related to the incremental velocity needed for orbital change
after the ejection from a fragmented parent body. A degree of
significance has been established from the same analysis on a
quasi-random distribution, matching the large scale structure of the
real distribution. The influence of the metric has been tested as well
as the sensitivity of families to small variations of the proper
elements within the accuracy of the theory. A cross comparison has been
made between these results and the families obtained from the same data
by another method (Zappala et al. 1990). A good agreement between these
two different methods has been established not only for the well known
populous families, but also for the little ones the existence of which
seemed before to depend on the method used.
The method of Lie series is used to construct a solution for the elliptic restricted three body problem. In a synodic pulsating coordinate system, the Lie operator for the motion of the third infinitesimal body is derived as function of coordinates, velocities and true anomaly of the primaries. The terms of the Lie series for the solution are then calculated with recurrence formulae which enable a rapid successive calculation of any desired number of terms. This procedure gives a very useful analytical form for the series and allows a quick calculation of the orbit.
To use the information about impact craters on terrestrial planets for study of planetary geology and geophysics, one should combine a wide set of processes and parameters. The chapter presents a review of impact cratering processes, estimates of average impact velocities, and impact probability for terrestrial planets. Basics of the impact crater scaling is discussed to present to date level of confidence in problems, where one needs to correlate measured size of an impact crater and mass and size of a body, created the impact structure. Scaling laws for large impact crates are discussed in comparison with results of the direct numerical modeling of impact cratering. The accumulation rate for impact craters on terrestrial planets is believed to be constant (within a factor of 2) during the last ∼3 Ga of the solar system history. Measuring the number of accumulated craters of a given size in the area of interest, one can estimate relative age of the visible surface, provided the older surfaces accumulate larger number of craters. In connection with this technique measured size-frequency distribution of impact craters is discussed, including the now widely disputable topic of secondary cratering, preventing the simple interpretation of cratering record for small craters.
The average density of craters in the 4- to 10-km diameter range was determined for 23 geologic-geomorphic units of Mars. The determinations, based on Mariner-9 images and the 1:25,000,000 geologic map of Scott and Carr (1977), relied on digitized, same-scale versions of the imagery and the geologic map. Crater densities have been suggested as indicators of the age of the Martian geologic formations. On the basis of this suggestion, a ranking from youngest to oldest formation was devised: Tharsis volcanic material, smooth plains, rolling plains, plains, ridged plains, hilly and cratered material, and cratered plateaus.
The aim of this work is the construction of a fast integration method
for differential equations (DE), especially the equations of the motion
of celestial bodies. Although a number of integration schemes are
available none of them seem to be adequate for treating n-body systems
with variable masses, which arise in some cosmogonic problems of the
early solar system. As a first step we are now able to present a
high-speed numerical integration scheme of the classical n-body system.
The basic idea of solving differential equations with Lie-series is due
to Grobner (1967) but, unfortunately, he did not elaborate on this
method and stopped after some numerically unsatisfactory results. We
could simplify the calculation of the Lie-terms and derived finally a
recurrence formula for the Lie-terms. Whereas Grobner tried to solve the
two-body and three (n-body)problem by two different approaches we
solved, at first, in an optimal way the 2-body- problem. Then we were
able to derive in a quite similar way the solutions of the 3-body and
n-body system. Our integration method for planetary motions has two
major advantages: First, it is a relatively fast method (about the
factor 3-10 faster in comparison with the n-body program by
Schubart-Stumpff, which is commonly used by Astronomers). Second,
because larger step lengths can be used, roundoff errors are smaller
(e.g. step length 135 d for Jupiter).
The history, probability, and physical and biological effects of asteroid and comet impacts on the earth are surveyed. Astronomical-survey data on earth-crossing asteroids and comets are presented and compared with theoretical models of impact cratering, geological-survey data on extant craters, and observations of lunar cratering to calculate the present and geological-time frequency distribution of the kinetic energy of colliding bodies. Data from historic-collision observations and prehistoric-collision geological studies are used to classify small craters from iron meteorites, large young craters, ancient Phanerozoic impact structures, and large Precambrian impact structures. The transient effects of projectiles of 5-km or larger diameter on global climate are considered capable of causing the extinction of species in some environments, and dozens of such impacts are estimated to have occurred during the Phanerozoic. Precambrian life was probably subjected to the effects of several 20-30-km projectiles and a higher overall collision rate.
Abstract— The Vredefort structure in South Africa was created by a meteorite impact about two billion years ago. Since that time, the crater has been deeply eroded; so to estimate its original size, researchers have had to rely heavily upon comparison to other terrestrial impact structures. Recent estimates of the original crater diameter range from 160 km to as much as 400 km. In this study, we combined the capabilities of both hydrocode and finite-element modeling, using the former to predict where the pressure of an impact-generated shock wave would have been high enough to form planar deformation features (PDFs) and shatter cones and the latter to follow the subsequent displacement of these shock isobars during the collapse of the crater. We established constraints on the sizes of the projectile and the transient crater (and, thus, on the size of the final crater) by comparing the observed locations of PDFs around Vredefort to the results of our simulations of impacts by projectiles of various sizes. These simulations indicate that a rocky projectile with a diameter of ∼10 km, impacting vertically at a velocity of 20 km/s generates shock pressures that are consistent with the distribution of PDFs around Vredefort. These projectile parameters correspond to a transient crater ∼80 km in diameter or a final crater ∼120–160 km in diameter. Allowing for uncertainties in our modeling procedures, we consider final craters 120 to 200 km in diameter to be consistent with the observed locations of PDFs at Vredefort. The shock pressure contour corresponding to the formation of shatter cones is almost horizontal near the surface, making the locations of these features less useful constraints on the crater size. However, they may provide a constraint on the amount of erosion that has occurred since the impact.
Abstract— We have developed a Web-based program for quickly estimating the regional environmental consequences of a comet or asteroid impact on Earth (http:www.lpl.arizona.eduimpacteffects). This paper details the observations, assumptions and equations upon which the program is based. It describes our approach to quantifying the principal impact processes that might affect the people, buildings, and landscape in the vicinity of an impact event and discusses the uncertainty in our predictions. The program requires six inputs: impactor diameter, impactor density, impact velocity before atmospheric entry, impact angle, the distance from the impact at which the environmental effects are to be calculated, and the target type (sedimentary rock, crystalline rock, or a water layer above rock). The program includes novel algorithms for estimating the fate of the impactor during atmospheric traverse, the thermal radiation emitted by the impact-generated vapor plume (fireball), and the intensity of seismic shaking. The program also approximates various dimensions of the impact crater and ejecta deposit, as well as estimating the severity of the air blast in both crater-forming and airburst impacts. We illustrate the utility of our program by examining the predicted environmental consequences across the United States of hypothetical impact scenarios occurring in Los Angeles. We find that the most wide-reaching environmental consequence is seismic shaking: both ejecta deposit thickness and air-blast pressure decay much more rapidly with distance than with seismic ground motion. Close to the impact site the most devastating effect is from thermal radiation; however, the curvature of the Earth implies that distant localities are shielded from direct thermal radiation because the fireball is below the horizon.
As the tree of numerical methods used to solve ordinary differential equations develops more and more branches, it may, despite
great literature, become hard to find out which properties should be aimed for, given certain problems in celestial mechanics.
With this chapter the authors intend to give an introduction to common, symplectic, and non-symplectic algorithms used to
numerically solve the basic Newtonian gravitational N-body problem in dynamical astronomy. Six methods are being presented, including a Cash–Karp Runge–Kutta, Radau15, Lie Series,
Bulirsch-Stoer, Candy, and a symplectic Hybrid integrator of Mon. Not.R. Astro. Soc. 304: 793–799,?]. Their main properties, as for example, the handling of conserved quantities, will be discussed on the basis
of the Kepler problem.