Dynamical Lifetimes and Final Fates of Small Bodies: Orbit Integrations vs ÖPik Calculations

Department of Physics, Queen's University, Kingston, Ontario, K7L 3N6, Canada
Icarus (Impact Factor: 3.04). 12/1999; 142(2):509-524. DOI: 10.1006/icar.1999.6220


The dynamical lifetimes of small bodies against ejection from the Solar System or collision with the Sun or a planet are often estimated by Monte Carlo codes based on the equations of Öpik and using a method implemented by Arnold. Such algorithms assume that orbital changes are dominated by close encounters, and that successive encounters are uncorrelated. We have compared the results of an Öpik code (H. J. Melosh and W. B. Tonks, Mete-oritics28, 398 (1993)) and a fast integrator (H. F. Levison and M. J. Duncan, Icarus108, 18 (1994)) to investigate the regimes of validity of the Öpik–Arnold approach. We investigate the transfer of ecliptic comets from Neptune-crossing orbits to observable Jupiter-family comets, the dynamics of Halley-type comets, and the transport of meteorites among the terrestrial planets. In all cases, the Öpik code overestimates the median lifetime of the small bodies, although both codes show a rapid initial loss of objects followed by a slow decay. For martian impact ejecta, some of which find their way to Earth as the SNC meteorites, the Öpik code substantially overestimates lifetimes because of its neglect of secular resonances, which rapidly pump eccentricities (B. J. Gladman et al., Science 271, 1387 (1996)).

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    • "Their use of symplectic integrators improves accuracy and greatly increases the speed at which interplanetary transfer occurs in the simulations. The difference between methods is discussed in more detail in Dones et al. (1999), but in brief, the inclusion of secular effects results in gradual eccentricity increases, which causes objects initially originating from and orbiting near one planet to eventually cross the orbit of another within timescales of a few million years. At this point, the meteoroid may impact the other planet or be scattered into many possible new orbits. "
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    ABSTRACT: Abstract Material from the surface of a planet can be ejected into space by a large impact and could carry primitive life-forms with it. We performed n-body simulations of such ejecta to determine where in the Solar System rock from Earth and Mars may end up. We found that, in addition to frequent transfer of material among the terrestrial planets, transfer of material from Earth and Mars to the moons of Jupiter and Saturn is also possible, but rare. We expect that such transfers were most likely to occur during the Late Heavy Bombardment or during the ensuing 1-2 billion years. At this time, the icy moons were warmer and likely had little or no ice shell to prevent meteorites from reaching their liquid interiors. We also note significant rates of re-impact in the first million years after ejection. This could re-seed life on a planet after partial or complete sterilization by a large impact, which would aid the survival of early life during the Late Heavy Bombardment. Key Words: Panspermia-Impact-Meteorites-Titan-Europa. Astrobiology 13, 1155-1165.
    Preview · Article · Dec 2013 · Astrobiology
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    • "McSween 1976; Schröder et al. 2008). These findings, together with dynamical simulations (Gladman, 1997; Dones et al. 1999), indicate that meteorites are exchanged among the terrestrial planets of our solar system at a measurable level. Sufficiently large rocks may protect dormant microorganisms from ionizing radiation and from the hazards of the impact at landing. "
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    ABSTRACT: Abstract We examined a low-energy mechanism for the transfer of meteoroids between two planetary systems embedded in a star cluster using quasi-parabolic orbits of minimal energy. Using Monte Carlo simulations, we found that the exchange of meteoroids could have been significantly more efficient than previously estimated. Our study is relevant to astrobiology, as it addresses whether life on Earth could have been transferred to other planetary systems in the Solar System's birth cluster and whether life on Earth could have been transferred from beyond the Solar System. In the Solar System, the timescale over which solid material was delivered to the region from where it could be transferred via this mechanism likely extended to several hundred million years (as indicated by the 3.8-4.0 Ga epoch of the Late Heavy Bombardment). This timescale could have overlapped with the lifetime of the Solar birth cluster (∼100-500 Myr). Therefore, we conclude that lithopanspermia is an open possibility if life had an early start. Adopting parameters from the minimum mass solar nebula, considering a range of planetesimal size distributions derived from observations of asteroids and Kuiper Belt objects and theoretical coagulation models, and taking into account Oort Cloud formation models, we discerned that the expected number of bodies with mass>10 kg that could have been transferred between the Sun and its nearest cluster neighbor could be of the order of 10(14) to 3·10(16), with transfer timescales of tens of millions of years. We estimate that of the order of 3·10(8)·l (km) could potentially be life-bearing, where l is the depth of Earth's crust in kilometers that was ejected as the result of the early bombardment. Key Words: Extrasolar planets-Interplanetary dust-Interstellar meteorites-Lithopanspermia. Astrobiology 12, 754-774.
    Full-text · Article · Aug 2012 · Astrobiology
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    • "The probability is largest for low inclination encounters, and for encounters occurring near the projectile's pericenter and apocenter. Singularities of the encounter probability are avoided following Dones et al. (1999). For a given orbital geometry, the encounter probability is proportional to the gravitational cross section, whose radius is "
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    ABSTRACT: a b s t r a c t We model the cratering of the Moon and terrestrial planets from the present knowledge of the orbital and size distribution of asteroids and comets in the inner Solar System, in order to refine the crater chronol-ogy method. Impact occurrences, locations, velocities and incidence angles are calculated semi-analyti-cally, and scaling laws are used to convert impactor sizes into crater sizes. Our approach is generalizable to other moons or planets. The lunar cratering rate varies with both latitude and longitude: with respect to the global average, it is about 25% lower at (±65°N, 90°E) and larger by the same amount at the apex of motion (0°N, 90°W) for the present Earth–Moon separation. The measured size-frequency distributions of lunar craters are reconciled with the observed population of near-Earth objects under the assumption that craters smaller than a few kilometers in diameter form in a porous megaregolith. Vary-ing depths of this megaregolith between the mare and highlands is a plausible partial explanation for dif-ferences in previously reported measured size-frequency distributions. We give a revised analytical relationship between the number of craters and the age of a lunar surface. For the inner planets, expected size-frequency crater distributions are calculated that account for differences in impact conditions, and the age of a few key geologic units is given. We estimate the Orientale and Caloris basins to be 3.73 Ga old, and the surface of Venus to be 240 Ma old. The terrestrial cratering record is consistent with the revised chronology and a constant impact rate over the last 400 Ma. Better knowledge of the orbital dynamics, crater scaling laws and megaregolith properties are needed to confidently assess the net uncertainty of the model ages that result from the combination of numerous steps, from the observation of asteroids to the formation of craters. Our model may be inaccurate for periods prior to 3.5 Ga because of a different impactor population, or for craters smaller than a few kilometers on Mars and Mercury, due to the presence of subsurface ice and to the abundance of large secondaries, respectively. Standard parameter values allow for the first time to naturally reproduce both the size distribution and absolute number of lunar craters up to 3.5 Ga ago, and give self-consistent estimates of the planetary cratering rates relative to the Moon.
    Preview · Article · May 2011 · Icarus
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