Understanding Our Universe
3rd Edition
ISBN: 9780393614428
Author: PALEN, Stacy, Kay, Laura, Blumenthal, George (george Ray)
Publisher: W.w. Norton & Company,
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Chapter 16, Problem 22QAP
To determine
The description of each of the four different views of the cosmic microwave background.
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Cosmic Microwave Background
8. The Cosmic Microwave Background (CMB) acts as a perfect black body whose energy spectrum(energy density per unit volume per unit frequency) is given by the expression : (image attached)
38. The Cosmic Microwave Background is remarkable in many ways. Let's illustrate this by personalizing the CMB a bit.
a) Imagine that the Earth is a sphere with a radius equal to its actual equatorial radius (The radius of Earth at the equator is 3,963 miles (6,378 kilometers). If the radius of the Earth is assumed to be constant to the same level of uniformity as the temperature fluctuations of the CMB—that is, to one part in 100,000—then how high would the highest mountains be relative to the mean surface radius of the Earth?
b) Calculate the ratio of the age of the Universe when the CMB was created and the age of the Universe today (in late 2021). If a person is 20 years old, What was their age relative to their current age adopting that fraction? Give the result in hours.
Does Hubble's Law work well for galaxies in the Local Group (such as Andromeda)?
No, because dark energy is accelerating the universe's expansion over those distances.
No, because we do not know the precise value of Ho.
No, because Hubble did not know the Local Group existed when he discovered his law.
Yes, it works well for all galaxies.
No, because galaxies in the Local Group are bound gravitationally together.
Chapter 16 Solutions
Understanding Our Universe
Ch. 16.1 - Prob. 16.1CYUCh. 16.2 - Prob. 16.2CYUCh. 16.3 - Prob. 16.3CYUCh. 16.4 - Prob. 16.4CYUCh. 16.5 - Prob. 16.5CYUCh. 16.6 - Prob. 16.6CYUCh. 16 - Prob. 1QAPCh. 16 - Prob. 2QAPCh. 16 - Prob. 3QAPCh. 16 - Prob. 4QAP
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- There is still some uncertainty in the Hubble constant. (a) Current estimates range from about 19.9 km/s per million light-years to 23 km/s per million light-years. Assume that the Hubble constant has been constant since the Big Bang. What is the possible range in the ages of the universe? Use the equation in the text, T0=1H , and make sure you use consistent units. (b) Twenty years ago, estimates for the Hubble constant ranged from 50 to 100 km/s per Mps. What are the possible ages for the universe from those values? Can you rule out some of these possibilities on the basis of other evidence?arrow_forwardThe matter density in the Universe today is Pm = -27 kg m-3. What would 2.7 x 10 be the value of the density parameter, 2o, if the Hubble constant had the value Ho = 38 km/s/Mpc? Assume the Universe does not contain dark energy and choose the option below that best matches your answer. Select one: O a. 0.1 O b. 2. О с. 1. O d. 0.7 О е. 0.5arrow_forward1. The current (critical) density of our universe is pe = 10-26kg/m³. Assume the universe is filled with cubes with equal size that each contain one person of m = 100kg. What would the length of the side of such a cube have to be in order to give the correct critical density? How many hydrogen atoms would you need in a box of 1 m³ to reach the critical density? The matter we know, which consists mostly of hydrogen, constitutes only 4.8% of the current critical energy density of our universe. So how many hydrogen atoms are actually in a box of 1 m3 in our universe? Deep space is very empty and a much better vacuum than we can obtain on earth in a laboratory.arrow_forward
- What causes cosmic microwave background energy?arrow_forwardBriefly explain the young Helmholtz theory.arrow_forwardIf you find that the Hubble constant is double what we currently believe, how does this affect the calculated age of the universe? Group of answer choices It decreased it by a factor of four. It cuts it in half. It doubles it. It increases it by a factor of four.arrow_forward
- The CMB contains roughly 400 million photons per m3. The energy of each photon depends on its wavelength. Calculate the typical wavelength of a CMB photon. Hint: The CMB is blackbody radiation at a temperature of 2.73 K. According to Wien’s law, the peak wave length in nanometers is given by max=3106T . Calculate the wavelength at which the CMB is a maximum and, to make the units consistent, convert this wavelength from nanometers to meters.arrow_forwardIt is possible to derive the age of the universe given the value of the Hubble constant and the distance to a galaxy, again with the assumption that the value of the Hubble constant has not changed since the Big Bang. Consider a galaxy at a distance of 400 million light-years receding from us at a velocity, v. If the Hubble constant is 20 km/s per million light-years, what is its velocity? How long ago was that galaxy right next door to our own Galaxy if it has always been receding at its present rate? Express your answer in years. Since the universe began when all galaxies were very close together, this number is a rough estimate for the age of the universe.arrow_forwardGiven that only about 5% of the galaxies visible in the Hubble Deep Field are bright enough for astronomers to study spectroscopically, they need to make the most of the other 95%. One technique is to use their colors and apparent brightnesses to try to roughly estimate their redshift. How do you think the inaccuracy of this redshift estimation technique (compared to actually measuring the redshift from a spectrum) might affect our ability to make maps of large-scale structures such as the filaments and voids shown in Figure 28.21? Figure 28.21 Sloan Digital Sky Survey Map of the Large-Scale Structure of the Universe. This image shows slices from the SDSS map. The point at the center corresponds to the Milky Way and might say “You Are Here!” Points on the map moving outward from the center are farther away. The distance to the galaxies is indicated by their redshifts (following Hubble’s law), shown on the horizontal line going right from the center. The redshift z=/ , where is the difference between the observed wavelength and the wavelength emitted by a nonmoving source in the laboratory. Hour angle on the sky is shown around the circumference of the circular graph. The colors of the galaxies indicate the ages of their stars, with the redder color showing galaxies that are made of older stars. The outer circle is at a distance of two billion light-years from us. Note that red (older stars) galaxies are more strongly clustered than blue galaxies (young stars). The unmapped areas are where our view of the universe is obstructed by dust in our own Galaxy. (credit: modification of work by M. Blanton and the Sloan Digital Sky Survey)arrow_forward
- (a) Calculate The approximate age of the universe from the average value of the Hubble constant, To do this, calculate the time it would take to travel 1 Mly at a constant expansion rate of 20 km/s. (b) If deceleration is taken into account, would the actual age of the universe be greater or less than that found here? Explain.arrow_forwardWhy is it difficult to determine where cosmic rays come from?arrow_forwardCalculate the velocity, the distance, and the look-back time of the most distant galaxies in Figure 28.21 using the Hubble constant given in this text and the redshift given in the diagram. Remember the Doppler formula for velocity (v=c) and the Hubble law ( v=Hd , where d is the distance to a galaxy). For these low velocities, you can neglect relativistic effects. Figure 28.21 Sloan Digital Sky Survey Map of the Large-Scale Structure of the Universe. This image shows slices from the SDSS map. The point at the center corresponds to the Milky Way and might say “You Are Here!” Points on the map moving outward from the center are farther away. The distance to the galaxies is indicated by their redshifts (following Hubble’s law), shown on the horizontal line going right from the center. The redshift z=/ , where is the difference between the observed wavelength and the wavelength emitted by a nonmoving source in the laboratory. Hour angle on the sky is shown around the circumference of the circular graph. The colors of the galaxies indicate the ages of their stars, with the redder color showing galaxies that are made of older stars. The outer circle is at a distance of two billion light-years from us. Note that red (older stars) galaxies are more strongly clustered than blue galaxies (young stars). The unmapped areas are where our view of the universe is obstructed by dust in our own Galaxy. (credit: modification of work by M. Blanton and the Sloan Digital Sky Survey)arrow_forward
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