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Rovnice vedení tepla ve fyzice planetek a meteoroidů
Pohl, Leoš ; Brož, Miroslav (advisor) ; Vokrouhlický, David (referee)
Non-gravitational forces caused by thermal emission of photons can significantly change orbits and spin states of asteroids in the long term. A solution of the Heat Conduction Equation (HCE) in an asteroid is necessary to evaluate the forces. Finite Difference Methods (FDMs) are implemented in a Fortran numerical HCE solver to calculate a temperature distribution within a system of 1-dimensional slabs which approximate the asteroid. We compare the methods w.r.t. convergence, accuracy and computational efficiency. The numerical results are compared with a simplified steady-state analytical solution. We calculate the non-gravitational accelerations and resulting semimajor axis drift from the numerical results. The implemented FDMs are shown to be convergent with denser grids and the best method has been selected. The analytical solution provides a good first-guess estimate of the temperature amplitude. The drift in semimajor axis of the tested asteroids, which is due to the non-gravitational forces, is in order-of-magnitude agreement with more accurate models and observational data.
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Numerical analysis of the Hills mechanism
Čížek, Kryštof ; Haas, Jaroslav (advisor) ; Brož, Miroslav (referee)
Interaction of three bodies is generally quite chaotic and a problem difficult to solve. Case in which binary star approaches third, heavier body is a special configuration of this problem and was investigated by J. G. Hills in his articles. In such interaction, either absolute breakup of the system to three independent bodies, survival of the binary star, or replacement of one component of the binary by the heavier body would occur - an exchange collision. If the replacement is to happen, the exchanged body is ejected away from the system with high velocity and such effect we call Hills mechanism. In such case the binary star usually has higher binding energy and is much more resistant if such situation were to occur again. However, Hills' results are not sufficient e.g. for effects within the core of our galaxy. Using numerical integration we modelled approximations of binary stars to a third, heavier body, thanks to which we could verify Hills' results and expand on them with initial conditions which are more suited to situations occuring within the core of our galaxy.
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Velké pozdní bombardování v různých místech sluneční soustavy
Zajaček, Michal ; Brož, Miroslav (advisor) ; Ďurech, Josef (referee)
In this work, we study the Late Heavy Bombardment (LHB) in the Solar System which took place from 4.1 to 3.8 billion years ago, and represents a period of intense collisions whose traces are observed on the Moon and other bodies mainly in the form of craters or impact melts. The first part of the thesis is a review on the LHB with the focus on observational evidence and recent dynamical models. In the second part, we test a particular dynamical model of the LHB using the observed cratering records on various Solar-System bodies, which was not done previously to such an extent. For this purpose, we use the symplectic integrator SyMBA, the collisional code Boulder, and various projectile-crater scaling laws. We discuss the sources of uncertainties of the observations as well as that of the models. Furthermore, we use our results to constrain the size-frequency distribution of the primordial cometary population.
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Dynamical processes in Jupiter's and Saturn's ring systems
Řehák, Matyáš ; Brož, Miroslav (advisor) ; Hanuš, Josef (referee)
The main subject of this thesis is a review of dynamical processes acting in Jupiter's and Saturn's rings. The thesis is divided into three chapters. Observed orbital and physical characteristics of the rings are described in the first one. In Chapter 2, we discuss physical processes forming the rings. Tidal disruptions, mutual collisions of ring particles, meteoroid bombardment and ballistic transport are among them. Various electromagnetic effects are analyzed too - e.g. the Poynting-Robertson effect, the Lorentz resonaces, plasma drag and radiation pressure. Yet another types of phenomena are resonant gravitational influence of satellites, shepherding moons and also collective dynamics of ring particles which results in formation of spiral waves. Finally, there is a review of theories concerning the origin of Saturn's rings in Chapter 3. We can distinguish three types of models - a disruption of a moon, a disruption of an external body and a formation from protolunar matter. At present, a tidal disruption of large differentiated moon seems to be the most probable theory.
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Simulations of asteroid collisions using a hybrid SPH/N-body approach
Ševeček, Pavel ; Brož, Miroslav (advisor) ; Kobayashi, Hiroshi (referee) ; Schäfer, Christoph M. (referee)
Understanding asteroid collisions is a key part of Solar System science. To in- terpret observations of more than 100 asteroid families, various numerical sim- ulations are used. In this work, we prefer the smoothed particle hydrodynamics (SPH), which allows a detailed description of impact mechanics, shock wave propagation, fragmentation of the target, ejection, or reaccumulation controlled by self-gravity and secondary collisions. Since the respective time scale may reach the orbital time scale, the SPH is often complemented by efficient N-body integrators and collisional handlers. In the review part of the thesis, we describe details of numerical methods and their implementation in the new OpenSPH code. We also thoroughly test the code, using analytical solutions and labora- tory experiments as references, and discuss its stability and convergence with respect to spatial resolution. In the refereed papers, included in the thesis, we focus on collisions with targets of particular sizes (D = 10 and 100 km). We explore the dependence of outcomes on the target size, the projectile size, the impact speed, the impact angle, and most importantly, the initial spin rate. We demonstrate that rotation significantly decreases the effective strength of the targets and increases the ejected mass. We self-consistently...
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Orbital and collisional dynamics of small bodies
Rozehnal, Jakub ; Brož, Miroslav (advisor) ; Granvik, Mikael (referee) ; Delbo, Marco (referee)
This work is devoted to a study of dynamical and collisional processes, governing populations of small bodies in the Solar System. It pays special attention to asteroid families and Jupiter Trojans. Librating around L4 and L5 Lagrangian points of the Sun-Jupiter-asteroid system, these asteroids are believed to be captured from the trans- Neptunian region during a giant planet system instability about 4 Gy ago. We discovered (back in 2011) there is only one significant collisional family among Trojans, associated with C-type asteroid (3548) Eurybates, i.e., one of the targets for the upcoming 'Lucy' mission. Detailed analysis of new proper resonant orbital elements, colours and albedos, together with statistical significance computations, allowed us to find five more collisional families: Hektor, (9799), Arkesilaos, Ennomos, and (247341). The discovery of the first D-type family associated with (624) Hektor was the most surprising, because it is the most primitive taxonomic type. Using long-term dynamical simulations of synthetic families, evolving by chaotic diffusion, we estimated the ages of the Eurybates and Hektor families, approximately (2.5±1.5) Gy for both. We also studied impact processes by means of the smoothed-particle hydrodynamics (SPH). We simulated cratering events on (624) Hektor, the origin...
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Interactions of migrating giant planets and small solar-system bodies
Chrenko, Ondřej ; Brož, Miroslav (advisor)
Changes of semimajor axes of giant planets, which took place 4 billion years ago and evolved the Solar System towards its present state, affected various populations of minor Solar-System bodies. One of these populations was a group of dynamically stable asteroids in the 2:1 mean-motion resonance with Jupiter which reside in two islands of the phase space, denoted A and B, and exhibit lifetimes comparable to the age of the Solar System. The origin of stable asteroids has not been explained so far. Our main goal is to create a viable hypothesis of their origin. We update the resonant population and its physical properties on the basis of up-to-date observational data. Using an N-body model with seven giant planets and the Yarkovsky effect included, we demonstrate that the depletion of island A is faster compared to island B. We then investigate: (i) survivability of primordial resonant asteroids and (ii) capture of the population during planetary migration, using a recently described scenario with an escaping fifth giant planet and a jumping-Jupiter instability. We employ simulations with prescribed migration, smooth late migration and we statistically evaluate the results using dynamical maps. We also model collisions during the last 4 billion years. We conclude that the long-lived group was created by a...
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Orbital and internal dynamics of terrestrial planets
Walterová, Michaela ; Běhounková, Marie (advisor) ; Efroimsky, Michael (referee) ; Brož, Miroslav (referee)
Title: Orbital and internal dynamics of terrestrial planets Author: Michaela Walterová Department: Department of Geophysics Supervisor: RNDr. Marie Běhounková, Ph.D., Department of Geophysics Abstract: Close-in exoplanets are subjected to intense tidal interaction with the host star and their secular evolution is strongly affected by the resulting tidal dissipation. The tidal dissipation not only provides an additional heat source for the planet's internal dynamics but it also contributes to the evolution of the planet's spin rate and orbital elements. At the same time, the tidal dissipation itself is also determined by the planet's thermal state and by the spin-orbital parameters. The evolutions of the orbit and of the interior are, therefore, intrinsically linked. In this work, we combine analytical and numerical techniques to gain insight into the interconnection between the internal properties and the orbital evolution, with special focus on the role of tides. After a general study of parametric dependencies of the tidal heating and tidal locking, we present a semi-analytical model assessing the coupled tidally-induced thermal-orbital evolution in systems consisting of a host star and one or two planets. Specifically, we study the thermal-orbital evolution in three systems inspired by existing low-mass...
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Early phases of formation and evolution of planetary systems
Chrenko, Ondřej ; Brož, Miroslav (advisor) ; Kley, Wilhelm (referee) ; Morbidelli, Alessandro (referee)
We study orbital evolution of multiple Earth-mass protoplanets in their natal protoplanetary disk. Our aim is to explore the interplay between migration of protoplanets driven by the disk gravity, their growth by pebble accretion, and accretion heating which affects gas in their neighbourhood. Radiation hydrodynamic (RHD) simulations in 2D and 3D are used to model the problem. We find that the heating torque, i.e. the torque exerted by asymmetric hot underdense gas near accreting protoplanets, significantly changes the migration. Specifically, it excites orbital eccentricities of migrating protoplanets, thus preventing their capture in chains of mean-motion resonances. The protoplanets then undergo numerous close encounters and form giant planet cores by mutual collisions. Additionally, if inclinations also become excited, we describe a new mechanism that can form binary planets by means of consecutive two-body and three-body encounters, with the assistance of the disk gravity. Finally, our 3D RHD simulations reveal a complex distortion of the gas flow near an accreting protoplanet, driven by baroclinic perturbations and convection. For specific temperature-dependent opacities of the disk, an instability is triggered which redistributes gas around the protoplanet and leads to an oscillatory migration,...
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