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Application of the Three-Body Problem in the form of exercises
Kolář, Karel ; Šolc, Martin (advisor) ; Franc, Tomáš (referee)
The main topic of this work is the Restricted Three-Body Problem (R3BP) which is illustrated by solving several examples and by simulations in computational system Wolfram Mathematica. The aim is to offer supplemetary material for university students and it can be used also as introduction to this topic for high school students. The first part is dedidated to history of celestial mechanics and to the people who contributed to the development of the R3B Problem. The second chapter consists of simplier tasks with definitions of basic quantities and variables and revision of the undisturbed two-body problem. Subsequent chapters are concentrated to Lagrange points, Jacobi integral, Hill surfaces, tidal force, Tisserand criterion, shape and evolution of close binary stars and other partial tasks.
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Perturbed stellar motion in dense star clusters
Pavlík, Václav ; Šubr, Ladislav (advisor) ; Davies, B. Melvyn (referee) ; Portegies Zwart, Simon (referee)
Star clusters are thought to be the birthplaces of stars as well as the building blocks of galaxies. They typically consist of thousands to millions of stars bound together by self-gravity. These systems evolve on the scale of Myr to Gyr, there- fore, it is impossible for us to see any change in their global evolution even within hundreds of human lifetimes. Although the equations of motion of stars in a star cluster are simple New- tonian, it is impossible to predict precisely history of any star within them to any point in the future. Therefore, we may either compare the observations of different star clusters at different age, we may invent theoretical approaches and analytical predictions, or we must follow their evolution numerically (e.g. with direct N-body integrators) which is the main focus of my research and this thesis. First, we follow the evolution of star clusters in general while coming up with a novel method to estimate their characteristic timescale (i.e. the time of core collapse) based on global parameters. The core collapse is directly linked to the formation of hard binary stars, thus, we focus on their analysis as well. We also follow several recent observational results: (i) ALMA observations of the Serpens South star-forming region indicate that star clusters are born mass...
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Dynamics of small bodies in the Solar System: from dust particles to asteroid
Pokorný, Petr
In this thesis, we study two different topics: collisional probability between two bodies and dynamics of the sporadic meteoroids in the Solar System. Determination of the collision probabilities in the Solar System is one of the important problems in mod- ern celestial mechanics. Here, we generalize classical theories of the collisions between two bodies by Öpik, Wetherill or Greenberg by including the Kozai-Lidov oscillations, a mechanism that significantly change orbital eccentricity and inclination in the Solar System. Sporadic meteors have been studied for many decades providing a wealthy re- source of data. Here, we build dynamical steady-state models for all known populations observed in the sporadic meteoroid complex based on the latest and most precise data provided by Canadian Meteor Orbit Radar (CMOR). Our models using the latest theo- ries for cometary populations in the Solar System accurately describe observed sporadic background population. Our results are in agreement with observations provided by space probes IRAS and LDEF.
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Perturbed stellar motion in dense star clusters
Pavlík, Václav ; Šubr, Ladislav (advisor) ; Davies, B. Melvyn (referee) ; Portegies Zwart, Simon (referee)
Star clusters are thought to be the birthplaces of stars as well as the building blocks of galaxies. They typically consist of thousands to millions of stars bound together by self-gravity. These systems evolve on the scale of Myr to Gyr, there- fore, it is impossible for us to see any change in their global evolution even within hundreds of human lifetimes. Although the equations of motion of stars in a star cluster are simple New- tonian, it is impossible to predict precisely history of any star within them to any point in the future. Therefore, we may either compare the observations of different star clusters at different age, we may invent theoretical approaches and analytical predictions, or we must follow their evolution numerically (e.g. with direct N-body integrators) which is the main focus of my research and this thesis. First, we follow the evolution of star clusters in general while coming up with a novel method to estimate their characteristic timescale (i.e. the time of core collapse) based on global parameters. The core collapse is directly linked to the formation of hard binary stars, thus, we focus on their analysis as well. We also follow several recent observational results: (i) ALMA observations of the Serpens South star-forming region indicate that star clusters are born mass...
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Yarkovsky and YORP Effects in Dynamics of Small Bodies of the Solar System
Žižka, Jindřich ; Vokrouhlický, David (advisor) ; Čapek, David (referee) ; Neslušan, Luboš (referee)
In this thesis, we study the influence of non-gravitational perturbations induced by the Yarkovsky/YORP effect and solar radiation pressure (SRP) on the orbital evolution of selected asteroids, asteroid families and pairs. These perturbations are of great importance if one wants to perform precise and long-term propagation of meter-sized and kilometer-sized bodies. Although they have found many applications in the Solar System, here, we particularly investigated how they influence the orbit of near-Earth asteroid (99942) Apophis and what is their role in the age determination of asteroid families and pairs. Our numerical simulations showed that the perturbations of Apophis' orbit caused by the SRP are orders of magnitude smaller than those produced by the Yarkovsky effect. The age determination of asteroid families and pairs was another pillar of this work. Over the past decade it turned out that the Yarkovsky effect must be taken into account for backward propagation of pair/family members. We modified the current method for estimating the age of asteroid pairs to be suitable for weakly convergent cases and discovered 7 young pairs with similar-sized components, which is in contradiction with the current theory of pair formation. In addition, we focused on an interesting pair of asteroids -...
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Dynamics of small bodies in the Solar System: from dust particles to asteroid
Pokorný, Petr ; Vokrouhlický, David (advisor) ; Borovička, Jiří (referee) ; Wiegert, Paul (referee)
In this thesis, we study two different topics: collisional probability between two bodies and dynamics of the sporadic meteoroids in the Solar System. Determination of the collision probabilities in the Solar System is one of the important problems in mod- ern celestial mechanics. Here, we generalize classical theories of the collisions between two bodies by Öpik, Wetherill or Greenberg by including the Kozai-Lidov oscillations, a mechanism that significantly change orbital eccentricity and inclination in the Solar System. Sporadic meteors have been studied for many decades providing a wealthy re- source of data. Here, we build dynamical steady-state models for all known populations observed in the sporadic meteoroid complex based on the latest and most precise data provided by Canadian Meteor Orbit Radar (CMOR). Our models using the latest theo- ries for cometary populations in the Solar System accurately describe observed sporadic background population. Our results are in agreement with observations provided by space probes IRAS and LDEF.
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Dynamics of small bodies in the Solar System: from dust particles to asteroid
Pokorný, Petr
In this thesis, we study two different topics: collisional probability between two bodies and dynamics of the sporadic meteoroids in the Solar System. Determination of the collision probabilities in the Solar System is one of the important problems in mod- ern celestial mechanics. Here, we generalize classical theories of the collisions between two bodies by Öpik, Wetherill or Greenberg by including the Kozai-Lidov oscillations, a mechanism that significantly change orbital eccentricity and inclination in the Solar System. Sporadic meteors have been studied for many decades providing a wealthy re- source of data. Here, we build dynamical steady-state models for all known populations observed in the sporadic meteoroid complex based on the latest and most precise data provided by Canadian Meteor Orbit Radar (CMOR). Our models using the latest theo- ries for cometary populations in the Solar System accurately describe observed sporadic background population. Our results are in agreement with observations provided by space probes IRAS and LDEF.
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Application of the Three-Body Problem in the form of exercises
Kolář, Karel ; Šolc, Martin (advisor) ; Franc, Tomáš (referee)
The main topic of this work is the Restricted Three-Body Problem (R3BP) which is illustrated by solving several examples and by simulations in computational system Wolfram Mathematica. The aim is to offer supplemetary material for university students and it can be used also as introduction to this topic for high school students. The first part is dedidated to history of celestial mechanics and to the people who contributed to the development of the R3B Problem. The second chapter consists of simplier tasks with definitions of basic quantities and variables and revision of the undisturbed two-body problem. Subsequent chapters are concentrated to Lagrange points, Jacobi integral, Hill surfaces, tidal force, Tisserand criterion, shape and evolution of close binary stars and other partial tasks.
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