1st Edition

ISBN: 9781938168284

Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff

Publisher: OpenStax

Concept explainers

We may see thousands of stars in the dark sky. Our universe consists of billions of stars. Stars may appear tiny to us but they are huge balls of gasses. Sun is a star of average size. Some stars are even a thousand times larger than the sun. The stars d…

Red Shift

It is an astronomical phenomenon. In this phenomenon, increase in wavelength with corresponding decrease in photon energy and frequency of radiation of light. It is the displacement of spectrum of any kind of astronomical object to the longer wavelengths…

Textbook Question

Chapter 28, Problem 20E

Using the information from Example 28.1, if galaxies are distributed homogeneously, how many times more of them would you expect to count on your second survey?

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Chapter 28, Problem 19E

Chapter 28, Problem 21E

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Question B3 Consider the following FLRW spacetime: t2 ds² = -dt² + (dx² + dy²+ dz²), t2 where t is a constant. a) State whether this universe is spatially open, closed or flat. [2 marks] b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function of time t, starting at t = 0. [3 marks] c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect to galaxy A. d) The Friedmann equations are 2 k 8πG а 4πG + a² (p+3p). 3 a 3 [5 marks] Use these equations to determine the energy density p(t) and the pressure p(t) for the FLRW spacetime specified at the top of the page. [5 marks] e) Given the result of question B3.d, state whether the FLRW universe in question is (i) radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv) none of the previous. Justify your answer. f) [5 marks] A conformally…

SECTION B Answer ONLY TWO questions in Section B [Expect to use one single-sided A4 page for each Section-B sub question.] Question B1 Consider the line element where w is a constant. ds²=-dt²+e2wt dx², a) Determine the components of the metric and of the inverse metric. [2 marks] b) Determine the Christoffel symbols. [See the Appendix of this document.] [10 marks] c) Write down the geodesic equations. [5 marks] d) Show that e2wt it is a constant of geodesic motion. [4 marks] e) Solve the geodesic equations for null geodesics. [4 marks]

Page 2 SECTION A Answer ALL questions in Section A [Expect to use one single-sided A4 page for each Section-A sub question.] Question A1 SPA6308 (2024) Consider Minkowski spacetime in Cartesian coordinates th = (t, x, y, z), such that ds² = dt² + dx² + dy² + dz². (a) Consider the vector with components V" = (1,-1,0,0). Determine V and V. V. (b) Consider now the coordinate system x' (u, v, y, z) such that u =t-x, v=t+x. [2 marks] Write down the line element, the metric, the Christoffel symbols and the Riemann curvature tensor in the new coordinates. [See the Appendix of this document.] [5 marks] (c) Determine V", that is, write the object in question A1.a in the coordinate system x'. Verify explicitly that V. V is invariant under the coordinate transformation. Question A2 [5 marks] Suppose that A, is a covector field, and consider the object Fv=AAμ. (a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a coordinate transformation. [5 marks] (b)…

Chapter 28 Solutions

Astronomy

Ch. 28 - How are distant (young) galaxies different from...Ch. 28 - What is the evidence that star formation began...Ch. 28 - Describe the evolution of an elliptical galaxy....Ch. 28 - Explain what we mean when we call the universe...Ch. 28 - Describe the organization of galaxies into...Ch. 28 - What is the evidence that a large fraction of the...Ch. 28 - When astronomers make maps of the structure of the...Ch. 28 - How does the presence of an active galactic...Ch. 28 - Describe how you might use the color of a galaxy...Ch. 28 - Suppose a galaxy formed stars for a few million...

Ch. 28 - Given the ideas presented here about how galaxies...Ch. 28 - Can an elliptical galaxy evolve into a spiral?...Ch. 28 - If we see a double image of a quasar produced by a...Ch. 28 - The left panel of Figure 27.1 shows a cluster of...Ch. 28 - Suppose you are standing in the center of a large,...Ch. 28 - Astronomers have been making maps by observing a...Ch. 28 - Human civilization is about 10,000 years old as...Ch. 28 - Given that only about 5% of the galaxies visible...Ch. 28 - Using the information from Example 28.1, how much...Ch. 28 - Using the information from Example 28.1, if...Ch. 28 - Using the information from Example 28.1, how much...Ch. 28 - Galaxies are found in the “walls” of huge voids;...Ch. 28 - Calculate the velocity, the distance, and the...Ch. 28 - Assume that dark matter is uniformly distributed...Ch. 28 - The simulated box of galaxy filaments and...Ch. 28 - The first objects to collapse gravitationally...

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