Foundations of Astronomy (MindTap Course List)
14th Edition
ISBN: 9781337399920
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Textbook Question
Chapter 4, Problem 18RQ
How does Kepler’s first law of planetary motion overthrow one of the basic beliefs of classical astronomy? How about Kepler’s second law?
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Statistical thermodynamics. The number of imaginary replicas of a system of N particlesa) cannot be greater than Avogadro's numberb) must always be greater than Avogadro's number.c) has no relation to Avogadro's number.
Lab-Based Section
Use the following information to answer the lab based scenario.
A student performed an experiment in an attempt to determine the index of refraction of glass.
The student used a laser and a protractor to measure a variety of angles of incidence and
refraction through a semi-circular glass prism. The design of the experiment and the student's
results are shown below.
Angle of
Incidence (°)
Angle of
Refraction (º)
20
11
30
19
40
26
50
31
60
36
70
38
2a) By hand (i.e., without using computer software), create a linear graph on graph paper
using the student's data. Note: You will have to manipulate the data in order to achieve a
linear function.
2b) Graphically determine the index of refraction of the semi-circular glass prism, rounding your
answer to the nearest hundredth.
Chapter 4 Solutions
Foundations of Astronomy (MindTap Course List)
Ch. 4 - Prob. 1RQCh. 4 - Why did early human cultures observe astronomical...Ch. 4 - Prob. 3RQCh. 4 - Name one example each of a famous politician,...Ch. 4 - Why did Plato propose that all heavenly motion was...Ch. 4 - On what did Plato base his knowledge? Was it...Ch. 4 - Which two-dimensional (2D) and three-dimensional...Ch. 4 - Are the spheres of Eudoxus a scientific model? If...Ch. 4 - In Ptolemys model, how do the epicycles of Mercury...Ch. 4 - Describe in detail the motions of the planets...
Ch. 4 - In Ptolemys model, which of the followingepicycle,...Ch. 4 - Why did Copernicus have to keep small epicycles in...Ch. 4 - Was the belief held by ancient astronomers that...Ch. 4 - When Tycho observed the new star of 1572, he could...Ch. 4 - Assume the night is clear and the Moons phase is...Ch. 4 - Does Tychos model of the Universe explain the...Ch. 4 - Name an empirical law. Why is it considered...Ch. 4 - How does Keplers first law of planetary motion...Ch. 4 - When Mercury is at aphelion (farthest from the...Ch. 4 - Prob. 20RQCh. 4 - What is P for Earth? What is a for Earth? Do these...Ch. 4 - Based Figure 4-13c, do planets with larger a take...Ch. 4 - How did the Alfonsine Tables, the Prutenic Tables,...Ch. 4 - Explain how each of Galileos telescopic...Ch. 4 - How did discovery of the Galilean moons disprove...Ch. 4 - Prob. 26RQCh. 4 - How Do We Know? Describe the differences between a...Ch. 4 - Draw and label a diagram of the western horizon...Ch. 4 - If you lived on Mars, which planets would exhibit...Ch. 4 - How long does it take for one retrograde cycle of...Ch. 4 - If a planet has an average distance from the Sun...Ch. 4 - If a space probe is sent into an orbit around the...Ch. 4 - Uranus orbits the Sun with a period of 84.0 years....Ch. 4 - An object takes 29.5 years to orbit the Sun. What...Ch. 4 - One planet is three times farther from the Sun...Ch. 4 - Galileos telescope showed him that Venus has a...Ch. 4 - Which is the phase of Venus when it is closest?...Ch. 4 - Galileos telescopes were not of high quality by...Ch. 4 - Arrange the following in order of increasing...Ch. 4 - Arrange the following in order of increasing...Ch. 4 - Prob. 1LTLCh. 4 - Study Figures 4-11 and 4-16 and describe the...Ch. 4 - What three astronomical objects are represented...Ch. 4 - Use the figure below to explain how the Ptolemaic...
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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…arrow_forwardSECTION 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]arrow_forwardPage 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)…arrow_forward
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