scholarly journals The structure of the co-orbital stable regions as a function of the mass ratio

2020 ◽  
Author(s):  
Luana Liberato ◽  
Othon Winter
Keyword(s):  
Solar System ◽  
Numerical Simulations ◽  
Asteroid Belt ◽  
Stable Region ◽  
Mass Ratio ◽  
Astronomical Society ◽  
Royal Astronomical Society ◽  
Astrophysical Journal ◽  
Wide Range ◽  
Orbital Region

<p>In the past years, astronomers have discovered many non-planetary structures in extrasolar systems such as a comet (Kiefer et al. 2014), an asteroid belt (Moro-Martín et al. 2008), an exoplanetary ring (Kenworthy & Mamajek 2015), and more recently the formation of an exomoon (Isella et al. 2019). But, although the search for exotrojans has not had success so far (e.g. Lillo-Box, J. et al. 2018), they must be as common as they are in the Solar System.</p> <p>Co-orbital systems were widely studied, and there are several works on stability and the formation of these structures. However, for the size and location of the stable regions, authors usually describe their results but do not provide a way to find them without numerical simulations and, in most works, the mass ratio value range is small. In the current work, we aimed to study the structure of co-orbital stable regions for a wide range of mass ratio systems and built empirical equations to describe them. It allows estimating the size and location of co-orbital stable regions from a few system’s parameters.</p> <p>In our recently published work (Liberato & Winter 2020), we have distributed thousands of massless particles in the co-orbital region of a massive secondary body adopting the planar circular restricted three-body problem. Using the N-body integrator Mercury (Chambers 1999) with the Bulirsh-Stoer integrator, we performed numerical simulations for a wide range of mass ratios (μ) for 7x10<sup>5</sup> orbital periods of the secondary body.</p> <p>We divided the results into two groups, the horseshoe and tadpole stable regions. We found that the horseshoe regions upper limit is between 9.539 × 10<sup>-4</sup>< μ < 1.192 × 10<sup>-3</sup>, which correspond to a minimum angular distance from the secondary to the separatrix between 27.239° and 27.802°. We also found that the limit to exist stability in the co-orbital region is about μ = 2.3313 × 10<sup>-2</sup>. That value is much smaller than the predicted by the linear theory, but we haven’t studied the stability for mass ratio values greater than 2.785×10<sup>-2</sup>. We have fitted polynomial functions to our results to describe the stable region parameters to represent estimates of the maximum angular and radial widths of the co-orbital stable regions for any system with 9.547 × 10<sup>-5 </sup>≤ μ ≤ 2.331 × 10<sup>-2</sup>.</p> <p> </p> <p>References:</p> <p>-Chambers J. E., 1999, Monthly Notices of the Royal Astronomical Society, 304, 793</p> <p>-Isella A., Benisty M., Teague R., Bae J., Keppler M., Facchini S., Pérez L.,2019, The Astrophysical Journal, 879, L25</p> <p>-Kenworthy M. A., Mamajek E. E., 2015, The Astrophysical Journal, 800, 126</p> <p>-Kiefer F., Lecavelier des Etangs A., Boissier J., Vidal-Madjar A., Beust H., Lagrange A. M., Hébrard G., Ferlet R., 2014, Nature, 514, 462</p> <p>-L. Liberato, O. C. Winter, The structure of the co-orbital stable regions as a function of the mass ratio, 2020, Monthly Notices of the Royal Astronomical Society, , staa1727, <a href="https://doi.org/10.1093/mnras/staa1727">https://doi.org/10.1093/mnras/staa1727</a></p> <p>-Lillo-Box, J. Barrado, D. Figueira, P. Leleu, A. Santos, N. C. Correia, A. C. M. Robutel, P. Faria, J. P. 2018, Astronomy & Astrophysics, 609, A96</p> <p>-Moro-Martín A., Wyatt M. C., Malhotra R., Trilling D. E., 2008, The Solar System Beyond Neptune, p. 465</p>

scholarly journals The structure of the co-orbital stable regions as a function of the mass ratio

2020 ◽  
Vol 496 (3) ◽  
pp. 3700-3707
Author(s):  
L Liberato ◽  
O C Winter
Keyword(s):  
Angular Distance ◽  
Stable Region ◽  
Polynomial Functions ◽  
Mass Ratio ◽  
Three Body Problem ◽  
System Parameters ◽  
Wide Range ◽  
Value Range ◽  
Three Body ◽  
Orbital Region

ABSTRACT Although the search for extrasolar co-orbital bodies has not had success so far, it is believed that they must be as common as they are in the Solar system. Co-orbital systems have been widely studied, and there are several works on stability and even on formation. However, for the size and location of the stable regions, authors usually describe their results but do not provide a way to find them without numerical simulations, and, in most cases, the mass ratio value range is small. In this work, we study the structure of co-orbital stable regions for a wide range of mass ratio systems and build empirical equations to describe them. It allows estimating the size and location of co-orbital stable regions from a few system parameters. Thousands of massless particles were distributed in the co-orbital region of a massive secondary body and numerically simulated for a wide range of mass ratios (μ) adopting the planar circular restricted three-body problem. The results show that the upper limit of horseshoe regions is between 9.539 × 10−4 < μ < 1.192 × 10−3, which corresponds to a minimum angular distance from the secondary body to the separatrix of between 27.239º and 27.802º. We also found that the limit to existence of stability in the co-orbital region is about μ = 2.3313 × 10−2, much smaller than the value predicted by the linear theory. Polynomial functions to describe the stable region parameters were found, and they represent estimates of the angular and radial widths of the co-orbital stable regions for any system with 9.547 × 10−5 ≤ μ ≤ 2.331 × 10−2.

scholarly journals A scattered Uranus and Neptune, and implications for the asteroid belt

2004 ◽  
Vol 202 ◽  
pp. 241-243
Author(s):  
Edward W. Thommes ◽  
Martin J. Duncan ◽  
Harold F. Levison ◽  
John E. Chambers
Keyword(s):  
Solar System ◽  
Numerical Simulations ◽  
Initial Conditions ◽  
Asteroid Belt ◽  
Outer Solar System ◽  
Wide Range ◽  
Gas Giant ◽  
Gas Accretion ◽  
High Degree

It has been proposed that Uranus and Neptune originated interior to ∽ 10 AU, as potential gas giant cores which were scattered outward when Jupiter won the race to reach runaway gas accretion. We present further numerical simulations of this scenario, which show that it reproduces the present configuration of the outer Solar System with a high degree of success for a wide range of initial conditions. Also, we show that this mechanism may have simultaneously ejected planets from the asteroid belt.

Preface

1974 ◽  
Vol 336 (1604) ◽  
pp. 3-4
Keyword(s):  
Solar System ◽  
Physical System ◽  
Royal Society ◽  
Physical Science ◽  
Planetary Science ◽  
The Sun ◽  
Astronomical Society ◽  
Royal Astronomical Society ◽  
Long Course ◽  
Nicolaus Copernicus

On 1973 January 25 the Royal Society with the support of the Royal Astronomical Society celebrated the quincentenary of the birth of Nicolaus Copernicus by a symposium on planetary science followed by a reception. The work of Copernicus opened the way to sensible studies of the Sun and planets as a physical system and, down the long course of history, this has led directly to the emergence of almost the whole of modern physical science. As the symposium lectures (chapters 2-5 of this volume) abundantly demonstrate, however, at this present time there is a greater and more productive interest in the physics of the Solar System itself than there has been, it could well be claimed, since the work of Newton which, through that of Kepler, depended so essentially upon the work of Copernicus.

A composite luminous and dark flight model allowing strewn field prediction

2021 ◽  
Author(s):  
Maria Gritsevich ◽  
Jarmo Moilanen
Keyword(s):  
Monte Carlo Model ◽  
Planetary Science ◽  
Astronomical Society ◽  
Royal Astronomical Society ◽  
Astrophysical Journal ◽  
Successful Recovery ◽  
The Matrix ◽  
Meteorite Fall ◽  
Adequate Representation ◽  
Set Up

<p>As of today, instrumentally observed meteorite falls account for only 37 recovered meteorite cases, with derived Solar System orbit, out of 65098 registered meteorite names. To bridge this knowledge gap, a number of fireball networks have been set up around the globe. These networks regularly obtain thousands of records of well-observed meteor phenomena, some of which may be classified as a likely meteorite fall (Sansom et al. 2019). A successful recovery of a meteorite from the fireball event often requires that the science team can be promptly directed to a well-defined search area. Here we present a neat Monte Carlo model, which comprises adequate representation of the processes occurring during the luminous trajectory coupled together with the dark flight (Moilanen et al. 2021). In particular, the model accounts for fragmentation and every generated fragment may be followed on its individual trajectory. Yet, the algorithm accounts only for the mass constrained by the observed deceleration, so that the model does not overestimate the total mass of the fragments on the ground (and this mass may also be retrieved as zero). We demonstrate application of the model using historical examples of well-documented meteorite falls, which illustrate a good match to the actual strewn field with the recovered meteorites, both, in terms of fragments’ masses and their spatial distribution on the ground. Moreover, during its development, the model has already assisted in several successful meteorite recoveries including Annama, Botswana (asteroid 2018 LA), and Ozerki (Trigo-Rodríguez et al. 2015, Lyytinen and Gritsevich 2016, Maksimova et al. 2020, Jenniskens et al. 2021).</p><p>References</p><p>Jenniskens P. et al. (2021). Asteroid 2018 LA, impact, recovery and origin on Vesta. Submitted to Science.</p><p>Lyytinen E., Gritsevich M. (2016). Implications of the atmospheric density profile in the processing of fireball observations. Planetary and Space Science, 120, 35-42 http://dx.doi.org/10.1016/j.pss.2015.10.012</p><p>Maksimova A.A., Petrova E.V., Chukin A.V., Karabanalov M.S., Felner I., Gritsevich M., Oshtrakh M.I. (2020). Characterization of the matrix and fusion crust of the recent meteorite fall Ozerki L6. Meteoritics and Planetary Science 55(1), 231–244, https://doi.org/10.1111/maps.13423 </p><p>Moilanen J., Gritsevich M., Lyytinen E. (2021). Determination of strewn fields for meteorite falls. Monthly Notices of the Royal Astronomical Society, in revision.</p><p>Sansom E.K., Gritsevich M., Devillepoix H.A.R., Jansen-Sturgeon T., Shober P., Bland P.A., Towner M.C., Cupák M., Howie R.M., Hartig B.A.D. (2019). Determining fireball fates using the α-β criterion. The Astrophysical Journal 885, 115, https://doi.org/10.3847/1538-4357/ab4516</p><p>Trigo-Rodríguez J.M., Lyytinen E., Gritsevich M., Moreno-Ibáñez M., Bottke W.F., Williams I., Lupovka V., Dmitriev V., Kohout T., Grokhovsky V. (2015). Orbit and dynamic origin of the recently recovered Annama’s H5 chondrite. Monthly Notices of the Royal Astronomical Society, 449 (2): 2119-2127, http://dx.doi.org/10.1093/mnras/stv378</p>

On the origin of the solar system

1944 ◽  
Vol 40 (3) ◽  
pp. 256-258 ◽  
Author(s):  
F. Hoyle
Keyword(s):  
Solar System ◽  
Total Mass ◽  
Binary Systems ◽  
Planetary Systems ◽  
Stellar Mass ◽  
Mass Ratio ◽  
Solar Mass ◽  
Essential Requirement ◽  
Wide Range

3. The essential requirement that the nova must satisfy in the above theory is that the total mass in the form of diffuse gaseous material must be of the order of 1/10 the solar mass, which requirement seems to be consistent with the observations of novae. Thus, although the theory applies explicitly to novae that break into two pieces of stellar mass having a gaseous filament drawn out between them (the pieces may have a mass ratio as great as 5/1), it seems clear that the discussion could be adjusted to include the case of novae following other models.The process described above can be applied to the formation of non-solar planets. The mass of available planetary material depends upon such factors as the mass of the nova and its separation from the companion before outburst. It is to be expected that variations in these factors can lead to planetary masses that vary over a fairly wide range. It follows that since an appreciable fraction of the stars of mass comparable or greater than the solar mass are known to be members of binary systems, the number of planetary systems must be at least of the same order as the number of novae that have occurred in this class of star.

Panel discussion: does chemical evidence give diagnostic tests for the credibility of physical models of the origin of the Solar System?

1988 ◽  
Vol 325 (1587) ◽  
pp. 631-641
Keyword(s):  
Solar System ◽  
Panel Discussion ◽  
Physical Models ◽  
Asteroid Belt ◽  
Early Solar System ◽  
Irregular Satellites ◽  
Resisting Medium ◽  
Eccentric Orbits ◽  
Wide Range ◽  
Cometary Material

M. M. Woolfson. Under the conditions of the capture theory, planets were originally formed in highly eccentric orbits which were close to, but not exactly coplanar. A resisting medium rounded off these orbits but, because it produced a non-central gravitational force on the planets, it also caused their orbits to precess. Differential precession gave intersecting orbits from time to time and it is possible to compute characteristic times for major interactions between pairs of planets. It turns out that these are similar to the rounding-off times and it can be concluded that some major event in the early Solar System was more likely than not. In 1977 Dormand and I postulated a planetary collision in the asteroid-belt region. Such a model readily explains the known characteristics of asteroids and meteorites, especially as a wide range of thermal regimes was present during the collision event. Other Solar System features that could be explained in a very straightforward way included the terrestrial planets, irregular satellites, e.g. the Moon and Triton, and the origin of cometary material.

scholarly journals Organic matter and water from asteroid Itokawa

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Q. H. S. Chan ◽  
A. Stephant ◽  
I. A. Franchi ◽  
X. Zhao ◽  
R. Brunetto ◽  
...  
Keyword(s):  
Organic Matter ◽  
Solar System ◽  
Parent Body ◽  
Asteroid Belt ◽  
True Nature ◽  
Water Ice ◽  
Nanocrystalline Graphite ◽  
Terrestrial Water ◽  
Solar System Bodies ◽  
Small Dust

AbstractUnderstanding the true nature of extra-terrestrial water and organic matter that were present at the birth of our solar system, and their subsequent evolution, necessitates the study of pristine astromaterials. In this study, we have studied both the water and organic contents from a dust particle recovered from the surface of near-Earth asteroid 25143 Itokawa by the Hayabusa mission, which was the first mission that brought pristine asteroidal materials to Earth’s astromaterial collection. The organic matter is presented as both nanocrystalline graphite and disordered polyaromatic carbon with high D/H and 15N/14N ratios (δD =  + 4868 ± 2288‰; δ15N =  + 344 ± 20‰) signifying an explicit extra-terrestrial origin. The contrasting organic feature (graphitic and disordered) substantiates the rubble-pile asteroid model of Itokawa, and offers support for material mixing in the asteroid belt that occurred in scales from small dust infall to catastrophic impacts of large asteroidal parent bodies. Our analysis of Itokawa water indicates that the asteroid has incorporated D-poor water ice at the abundance on par with inner solar system bodies. The asteroid was metamorphosed and dehydrated on the formerly large asteroid, and was subsequently evolved via late-stage hydration, modified by D-enriched exogenous organics and water derived from a carbonaceous parent body.

scholarly journals The Impact of Initial Conditions in N-Body Simulations of Debris Discs

2015 ◽  
Vol 32 ◽  
Author(s):  
E. Thilliez ◽  
S. T. Maddison
Keyword(s):  
Numerical Simulations ◽  
Initial Conditions ◽  
Parent Body ◽  
Dust Trapping ◽  
Physical Context ◽  
Disc Width ◽  
Wide Range ◽  
Belt Width ◽  
New Generation ◽  
The Impact

AbstractNumerical simulations are a crucial tool to understand the relationship between debris discs and planetary companions. As debris disc observations are now reaching unprecedented levels of precision over a wide range of wavelengths, an appropriate level of accuracy and consistency is required in numerical simulations to confidently interpret this new generation of observations. However, simulations throughout the literature have been conducted with various initial conditions often with little or no justification. In this paper, we aim to study the dependence on the initial conditions of N-body simulations modelling the interaction between a massive and eccentric planet on an exterior debris disc. To achieve this, we first classify three broad approaches used in the literature and provide some physical context for when each category should be used. We then run a series of N-body simulations, that include radiation forces acting on small grains, with varying initial conditions across the three categories. We test the influence of the initial parent body belt width, eccentricity, and alignment with the planet on the resulting debris disc structure and compare the final peak emission location, disc width and offset of synthetic disc images produced with a radiative transfer code. We also track the evolution of the forced eccentricity of the dust grains induced by the planet, as well as resonance dust trapping. We find that an initially broad parent body belt always results in a broader debris disc than an initially narrow parent body belt. While simulations with a parent body belt with low initial eccentricity (e ~ 0) and high initial eccentricity (0 < e < 0.3) resulted in similar broad discs, we find that purely secular forced initial conditions, where the initial disc eccentricity is set to the forced value and the disc is aligned with the planet, always result in a narrower disc. We conclude that broad debris discs can be modelled by using either a dynamically cold or dynamically warm parent belt, while in contrast eccentric narrow debris rings are reproduced using a secularly forced parent body belt.

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