📝 Original Info
- Title: Dynamics of the Universe in Problems
- ArXiv ID: 0904.0382
- Date: 2014-06-10
- Authors: Researchers from original ArXiv paper
📝 Abstract
To our best knowledge, there are no problem books on cosmology yet, that would include its spectacular recent achievements. We believe there is a strong need for such now, when cosmology is swiftly becoming a strict and vast science, and the book would be extremely useful for the youth pouring in this area of research. Indeed, the only way to rise over the popular level in any science is to master its alphabet, that is, to learn to solve problems. Of course, most of modern textbooks on cosmology include problems. However, a reader, exhausted by high theory, may often be thwarted by the lack of time and strength to solve them. Might it be worth sometimes to change the tactics and just throw those who wish to learn to swim into the water? We present an updated version of the "Dynamics of the Universe in Problems" We have the following new sections, 'Gravitational Waves', "Interactions in the Dark Sector", "Horizons" and "Quantum Cosmology" . A number of new problems have been added to almost every section. The total number of problems exceeds fifteen hundred. Solutions to all the problems can be found at www.universeinproblems.com
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To our best knowledge, there are no problem books on cosmology yet, that would include its spectacular recent achievements. We believe there is a strong need for such now, when cosmology is swiftly becoming a strict and vast science, and the book would be extremely useful for the youth pouring in this area of research. Indeed, the only way to rise over the popular level in any science is to master its alphabet, that is, to learn to solve problems. Of course, most of modern textbooks on cosmology include problems. However, a reader, exhausted by high theory, may often be thwarted by the lack of time and strength to solve them. Might it be worth sometimes to change the tactics and just throw those who wish to learn to swim into the water? We present an updated version of the “Dynamics of the Universe in Problems” We have the following new sections, ‘Gravitational Waves’, “Interactions in the Dark Sector”, “Horizons” and “Quantum Cosmology” . A number of new problems have been added to
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To our best knowledge, there are no problem books on cosmology yet, that would include its spectacular recent achievements. We believe there is a strong need for such now, when cosmology is swiftly becoming a strict and vast science, and the book would be extremely useful for the youth pouring in this area of research. Indeed, the only way to rise over the popular level in any science is to master its alphabet, that is, to learn to solve problems.
Of course, most of modern textbooks on cosmology include problems. However, a reader, exhausted by high theory, may often be thwarted by the lack of time and strength to solve them. Might it be worth sometimes to change the tactics and just throw those who wish to learn to swim into the water?
We present an updated version of the “Dynamics of the Universe in Problems” We have the following new sections , ‘Gravitational Waves’, “Interactions in the Dark Sector”, “Horizons” and “Quantum Cosmology” . A number of new problems have been added to almost every section. The total number of problems exceeds fifteen hundred. Solutions to all the problems can be found at Dynamics of the Universe in Problems 9. In 1982 Doppler predicted the effect of change in the percieved frequency of oscillations when there is relative motion of emitter and detector. Doppler assumed that this effect can cause the difference in the color of stars: a star moving towards the Earth seems “bluer”, while the one moving away “reddens”. Explain why the Doppler effect cannot substantially change the color of a star.
- In the beginning of the XXth century J.F. Hartmann, a German astronomer, was studying the spectra of double stars. The wavelengths of their spectral lines shifted periodically due to their relative motion, with the period equal to the orbital one.
In the spectra of some of the binaries he also noticed there were absorption lines with wavelengths that did not change with time. What discovery did Hartmann make due to this observation?
Originally the interstellar gas was discovered by its absorption of spectral lines of calcium. Does that mean that calcium is the dominating component of the interstellar medium?
One of the creators of the Theory of Relativity, Henry Poincare, when speaking in 1904 (!) of the fact that the speed of light c enters all the equations of electromagnetism, compared the situation with the Ptolemy’s geocentric theory of epicycles, in which the Earth’s year enters all the relations for the relative motion of celestial bodies. Poincare expressed hope that a future Copernicus would rid electrodynamics of c. Recall other examples of blunders of geniuses.
1.2 Quantities large and small 13. From what distance will one astronomical unit length have visible size of one angular second?
What is the angular dimension of our Galaxy for an observer in the Andromeda galaxy, if the distance to it is about 700kpc? Compare it with the angular size of the Sun viewed from the Earth. 15. A glance on the night sky makes the impression of invariability of the Universe. Why do the stars seem to us practically static? 16. * A supernova outburst in the Andromeda galaxy has been observed on Earth. Estimate the time since the star’s explosion. 17. A galaxy at distance R from us at the moment of observation recedes with velocity V . At what distance was it situated at the moment of emission of the observed light?
Suppose that we have concentrated the whole cosmic history (14 billion years) in one day. Display the main events in the history of the Universe using the logarithmic time scale. Start from the Planck’s time to avoid singularities. 19. According to the Big Bang model the initial ratio of the uranium isotopes’ abundances was U 235 /U 238 ≈ 1.65, while the presently observed one is U 235 /U 238 ≈ 0.0072. Taking into account that the half-value periods of the isotopes are equal to t 1/2 (U 235 ) = 1.03 • 10 9 years and t 1/2 (U 238 ) = 6.67 • 10 9 years, determine the age of the Universe. 20. Estimate the mass M G of Milky Way and the number of stars in it, if the Sun is an avarage star of mass M ⊙ , situated almost at the edge of our Galaxy and it orbits its center with the period T ⊙ = 250 millions years at the distance R G = 30 thousands light years.
Estimate the density of luminous matter in the Universe assuming that the Milky Way containing ∼ 10 11 stars of solar type is a typical galaxy, and average intergalactic distance is of order of L = 1Mpc.
Assume that the space is infinite and on average uniformly filled with matter. Estimate the distance from our observable part of the Universe to the part of the Universe with identical distribution of galaxies and the same Earth.
Show that in the hydrogen atom the ratio of electrical forces to gravitational ones is close to the ratio of the size of the Universe to the size of an electron (this fact was first noted by P.Dirac).
Express the Bohr radius through the fine structure constant and
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