Jupiter – friend or foe? I: The asteroids

Horner, Jonathan; Jones, Barrie W.

doi:10.1017/s1473550408004187

Cited by 88 publications

(71 citation statements)

References 17 publications

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“…We note a great deal of similarity between this method of calculating average impact probabilities and the technique of simulating actual impact probabilities from orbit integrations by "super-sizing" the terrestrial planets (Horner & Jones 2008;Horner et al 2009). The idea is the same, and these authors noted that no unforeseen drawbacks had been found in detailed tests.…”

Section: The Hill Sphere Methodsmentioning

confidence: 99%

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Monte Carlo methods to calculate impact probabilities

Rickman

Wiśniowski

Wajer

et al. 2014

A&A

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Context. Unraveling the events that took place in the solar system during the period known as the late heavy bombardment requires the interpretation of the cratered surfaces of the Moon and terrestrial planets. This, in turn, requires good estimates of the statistical impact probabilities for different source populations of projectiles, a subject that has received relatively little attention, since the works of Öpik (1951, Proc. R. Irish Acad. Sect. A, 54, 165) and Wetherill (1967, J. Geophys. Res., 72, 2429. Aims. We aim to work around the limitations of the Öpik and Wetherill formulae, which are caused by singularities due to zero denominators under special circumstances. Using modern computers, it is possible to make good estimates of impact probabilities by means of Monte Carlo simulations, and in this work, we explore the available options. Methods. We describe three basic methods to derive the average impact probability for a projectile with a given semi-major axis, eccentricity, and inclination with respect to a target planet on an elliptic orbit. One is a numerical averaging of the Wetherill formula; the next is a Monte Carlo super-sizing method using the target's Hill sphere. The third uses extensive minimum orbit intersection distance (MOID) calculations for a Monte Carlo sampling of potentially impacting orbits, along with calculations of the relevant interval for the timing of the encounter allowing collision. Numerical experiments are carried out for an intercomparison of the methods and to scrutinize their behavior near the singularities (zero relative inclination and equal perihelion distances). Results. We find an excellent agreement between all methods in the general case, while there appear large differences in the immediate vicinity of the singularities. With respect to the MOID method, which is the only one that does not involve simplifying assumptions and approximations, the Wetherill averaging impact probability departs by diverging toward infinity, while the Hill sphere method results in a severely underestimated probability. We provide a discussion of the reasons for these differences, and we finally present the results of the MOID method in the form of probability maps for the Earth and Mars on their current orbits. These maps show a relatively flat probability distribution, except for the occurrence of two ridges found at small inclinations and for coinciding projectile/target perihelion distances. Conclusions. Our results verify the standard formulae in the general case, away from the singularities. In fact, severe shortcomings are limited to the immediate vicinity of those extreme orbits. On the other hand, the new Monte Carlo methods can be used without excessive consumption of computer time, and the MOID method avoids the problems associated with the other methods.

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Section: The Hill Sphere Methodsmentioning

confidence: 99%

“…Thus, like the abovementioned super-sizing technique (Horner & Jones 2008), it has to be used with care, even though it works well in almost all situations. Returning now to Fig.…”

Section: Checks Of Consistency Between the Methodsmentioning

confidence: 99%

Monte Carlo methods to calculate impact probabilities

Rickman

Wiśniowski

Wajer

et al. 2014

A&A

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“…Horneck et al 2016); (ii) the formation and maintenance of an atmosphere that enables the presence of liquid water (Grenfell et al 2010); (iii) the existence of a magnetic field that could protect the surface from high-energy particles (Lundin et al 2007); (iv) climate stabilization, possibly via the presence of a large moon (Laskar et al 1993); (v) environmental diversity and climate-stabilizing feedbacks, for example due to the presence of plate tectonics which favours the carbonate-silicate cycle (e.g. Korenaga 2011;Höning & Spohn 2016); (vi) planetary protection from impacts due to the presence of gas giants (Horner & Jones 2008); and (vii) the properties of the central star (Beech 2011). It should be noted that complex molecules such as proteins have a limited range of temperature over which they are stable.…”

Section: Habitabilitymentioning

confidence: 99%

The habitability of a stagnant-lid Earth

Tosi

Godolt

Stracke

et al. 2017

A&A

128

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Context. Plate tectonics is considered a fundamental component for the habitability of the Earth. Yet whether it is a recurrent feature of terrestrial bodies orbiting other stars or unique to the Earth is unknown. The stagnant lid may rather be the most common tectonic expression on such bodies. Aims. To understand whether a stagnant-lid planet can be habitable, i.e. host liquid water at its surface, we model the thermal evolution of the mantle, volcanic outgassing of H 2 O and CO 2 , and resulting climate of an Earth-like planet lacking plate tectonics. Methods. We used a 1D model of parameterized convection to simulate the evolution of melt generation and the build-up of an atmosphere of H 2 O and CO 2 over 4.5 Gyr. We then employed a 1D radiative-convective atmosphere model to calculate the global mean atmospheric temperature and the boundaries of the habitable zone (HZ).Results. The evolution of the interior is characterized by the initial production of a large amount of partial melt accompanied by a rapid outgassing of H 2 O and CO 2 . The maximal partial pressure of H 2 O is limited to a few tens of bars by the high solubility of water in basaltic melts. The low solubility of CO 2 instead causes most of the carbon to be outgassed, with partial pressures that vary from 1 bar or less if reducing conditions are assumed for the mantle to 100-200 bar for oxidizing conditions. At 1 au, the obtained temperatures generally allow for liquid water on the surface nearly over the entire evolution. While the outer edge of the HZ is mostly influenced by the amount of outgassed CO 2 , the inner edge presents a more complex behaviour that is dependent on the partial pressures of both gases. Conclusions. At 1 au, the stagnant-lid planet considered would be regarded as habitable. The width of the HZ at the end of the evolution, albeit influenced by the amount of outgassed CO 2 , can vary in a non-monotonic way depending on the extent of the outgassed H 2 O reservoir. Our results suggest that stagnant-lid planets can be habitable over geological timescales and that joint modelling of interior evolution, volcanic outgassing, and accompanying climate is necessary to robustly characterize planetary habitability.

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“…The bulk of that structure is the direct result of perturbations from Jupiter, and, to a lesser extent, Saturn. Jupiter also acts to control the flux of small bodies to the inner solar system, acting to perturb asteroids and comets onto Earth-crossing orbits (e.g., Laakso et al 2006;Horner & Jones 2008. Jupiter also hosts a large population of Trojan asteroids (Fornasier et al 2007;Vinogradova & Chernetenko 2015) and irregular satellites, both of which are thought to have been captured during the giant planet's migration (e.g., Sheppard & Jewitt 2003;Morbidelli et al 2005;Jewitt & Haghighipour 2007;Lykawka & Horner 2010).…”

Section: Introductionmentioning

confidence: 99%

The Anglo-Australian Planet Search Xxiv: The Frequency of Jupiter Analogs

Wittenmyer

Butler

Tinney

et al. 2016

ApJ

132

109

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We present updated simulations of the detectability of Jupiter analogs by the 17-year Anglo-Australian Planet Search. The occurrence rate of Jupiter-like planets that have remained near their formation locations beyond the ice line is a critical datum necessary to constrain the details of planet formation. It is also vital in our quest to fully understand how common (or rare) planetary systems like our own are in the Galaxy. From a sample of 202 solartype stars, and correcting for imperfect detectability on a star-by-star basis, we derive a frequency of 6.2 1.6 2.8 -+ % for giant planets in orbits from 3 to 7 au. When a consistent definition of "Jupiter analog" is used, our results are in agreement with those from other legacy radial-velocity surveys.

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Jupiter – friend or foe? I: The asteroids

Cited by 88 publications

References 17 publications

Monte Carlo methods to calculate impact probabilities

Monte Carlo methods to calculate impact probabilities

The habitability of a stagnant-lid Earth

The Anglo-Australian Planet Search Xxiv: The Frequency of Jupiter Analogs

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