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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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YORP effect on asteroids with heterogeneous distribution of surface thermophysical properties
Chrbolková, Kateřina ; Čapek, David (advisor) ; Ďurech, Josef (referee)
In this thesis, we study the influence of heterogeneous distribution of optical and thermal properties on asteroid surfaces onto the YORP effect. Modelling of the surface heterogeneities is done in three ways. In the first one, we create an impact crater with higher albedo regolith on a regolith-covered asteroid. In the second way, we suppose presence of higher albedo regolith on steep slopes (slope angle > 35◦ ) and in the third one, we state properties of bare rock (with different thermal parameters) in these areas. Then we evaluate the influence of torques caused by scattered or thermally emitted radiation on 200 asteroids based on different distribution of described parameters by means of statistics. We have found that the presence of heterogeneities caused by landslides on asteroid surfaces does not significantly affect the YORP effect with two exceptions: a slight inclination to decelerate the rotation in the case of landslides uncovering bare rock due to critical rotation and significant preference for deceleration in the configurations with uncovered higher albedo regolith on steep slopes. Our data suggest that the influence of heterogeneous distribution of optical properties caused by landslides on the value of typical acceleration time, so-called doubling time td, is 2 % and it does not exceed 5 % in the case...
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Modern numerical models of the YORP effect
Chrbolková, Kateřina ; Čapek, David (advisor) ; Ďurech, Josef (referee)
This thesis deals with the study of an non-gravitational effect called the YORP effect which affects the rotational state of irregularly shaped asteroids. In its first part, there is discussed the very physical nature of this phenomenon and further it demonstrates an effect similar to the YORP: the Yarkovsky effect. Second part analyzes several outstanding numerical models, which describe the YORP effect. It focuses on some aspects that no other models took in account and it also points out what approximations these models make. We have used two different nume- rical models on an asteroid shape of our own and we present it in the last part of this bachelor thesis. At the end of this paper, we compare our outputs with the findings of appropriate models. Our results agree with the cited articles in the majority of cases. We tried to analyze how the YORP effect depends on the chan- ging conductivity of the asteroids and we also found out that better resolution of shapes of asteroids leads to the convergence of the values of the YORP effect.
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Rotational dynamics of asteroids affected by thermal emission from topographic features
Ševeček, Pavel ; Brož, Miroslav (advisor) ; Henych, Tomáš (referee)
Infrared radiation emitted from an asteroid surface causes a torque that can significantly affect rotational state of the asteroid. The influence of small topographic features on this phenomenon, called the YORP effect, hasn't been studied yet in detail. In this work, we show that lateral heat diffusion in surface features of suitable sizes leads to the emergence of a local YORP effect which magnitude is comparable to the YORP effect due to the global shape. We solve a three- dimensional heat diffusion equation in a boulder and its surroundings by the finite element method using the FreeFem++ code. The contribution to the total torque is then inferred from the com- puted temperature distribution. We compare the torque for various boulder shapes and material properties. For an idealized boulder our result is consistent with an existing one-dimensional model. Topographic features may cause a spherical asteroid of radius 1 km on a circular orbit at 2.5 AU to undergo a rotational acceleration of about (2.2 ± 1.1) · 10−9 rad/day2 , which corresponds to the spin-up timescale of the order τ = (32 ± 16) Myr. We estimated a size distribution of boulders based on close-up images of (25143) Itokawa surface. Finally, we realized that topographic features of Itokawa can induce a rotational acceleration of the order 10−7...
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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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