Table of Contents
Table of Contents
“Exercises of Relativity and Astrophysics”
INTRODUCTION
SPECIAL RELATIVITY
GENERAL RELATIVITY
COSMOLOGY
ASTROPHYSICS
“Exercises of Relativity and Astrophysics”
“Exercises of Relativity and Astrophysics”
SIMONE MALACRIDA
In this book, exercises are carried out regarding the following physics topics:
theory of special and general relativity
relativistic cosmology
astronomy and astrophysics
Simone Malacrida (1977)
Engineer and writer, has worked on research, finance, energy policy and industrial plants.
ANALYTICAL INDEX
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INTRODUCTION _ _
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I – SPECIAL RELATIVITY
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
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II – GENERAL RELATIVITY
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 10
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III - COSMOLOGY
Exercise1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
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IV - ASTROPHYSICS
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise8
INTRODUCTION
INTRODUCTION
In this workbook some exemplifying problems are carried out about the special and general theory of relativity, cosmology, astronomy and astrophysics, ranging throughout the physics of the macrocosm.
These disciplines are generally addressed at university level in advanced physics courses (courses of general relativity and/or astronomical and astrophysics).
For this reason, they are aimed only at those who already have an advanced understanding of both university-level mathematical analysis problems and the physical theories necessary to understand the proposed exercises.
I
SPECIAL RELATIVITY
SPECIAL RELATIVITY
Exercise 1
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Given three inertial frames of reference as in the figure:
Find the length of the segment:
In the system below.
Write the relative speed u in the middle and top systems.
Find, as a function of the speed, the length of the segment:
In the system above.
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Given L the length of the segments, in the system below there is a contraction by the Lorentz factor:
The speed is given by:
Finally, the segments will have this speed dependency:
Exercise 2
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Given a system consisting of two equal bodies of mass m connected through a spring, we consider the two bodies initially stationary with a given potential energy U.
Determine the energy value of the system in the initial state.
Then the spring snaps and the two bodies are launched with the same speed but in opposite directions.
Determine the energy value of the system in the final state.
Determine the final velocity of the two bodies as a function of m and U.
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The relativistic energy of a system is given by the sum of the internal energy and the kinetic energy of the center of mass.
The internal energy in turn is given by the sum of the potential energy, the kinetic energy of the bodies and the energy constituting the two bodies.
In formulas:
In our case, in the initial state the kinetic energy of the center of mass is zero as well as the kinetic energies of the bodies therefore the energy of the system is:
Impressum
Verlag: BookRix GmbH & Co. KG
Tag der Veröffentlichung: 24.04.2023
ISBN: 978-3-7554-4029-1
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