21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 22, Problem 39QP
To determine
The scale factor of universe.
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Recent findings in astrophysics suggest that the observable universe can be modeled as a sphere of radius R=13.7x109 light-years=13.0 x 1025m with an average total mass density of about 1x10-26 kg/m3 Only about 4% of total mass is due to “ordinary” matter (such as protons, neutrons, and electrons). Estimate how much ordinary matter (in kg) there is in the observable universe. (For the light-year, see Problem 19.)
Suppose that the universe were full of spherical objects, each of mass m and radius r . If the objects were distributed uniformly throughout the universe, what number density (#/m3) of spherical objects would be required to make the density equal to the critical density of our Universe?
Values:
m = 4 kg
r = 0.0407 m
Answer must be in scientific notation and include zero decimal places (1 sig fig --- e.g., 1234 should be written as 1*10^3)
What would be your estimate for the age of the universe if you measured Hubbleʹs constant to be 33 km/s/Mly? You can assume that the expansion rate has remained unchanged during the history of the universe.
Chapter 22 Solutions
21st Century Astronomy
Ch. 22.1 - Prob. 22.1CYUCh. 22.2 - Prob. 22.2CYUCh. 22.3 - Prob. 22.3CYUCh. 22.4 - Prob. 22.4CYUCh. 22.5 - Prob. 22.5CYUCh. 22 - Prob. 1QPCh. 22 - Prob. 2QPCh. 22 - Prob. 3QPCh. 22 - Prob. 4QPCh. 22 - Prob. 5QP
Ch. 22 - Prob. 6QPCh. 22 - Prob. 7QPCh. 22 - Prob. 8QPCh. 22 - Prob. 9QPCh. 22 - Prob. 10QPCh. 22 - Prob. 11QPCh. 22 - Prob. 12QPCh. 22 - Prob. 13QPCh. 22 - Prob. 14QPCh. 22 - Prob. 15QPCh. 22 - Prob. 16QPCh. 22 - Prob. 17QPCh. 22 - Prob. 18QPCh. 22 - Prob. 19QPCh. 22 - Prob. 20QPCh. 22 - Prob. 21QPCh. 22 - Prob. 22QPCh. 22 - Prob. 24QPCh. 22 - Prob. 28QPCh. 22 - Prob. 29QPCh. 22 - Prob. 31QPCh. 22 - Prob. 32QPCh. 22 - Prob. 33QPCh. 22 - Prob. 34QPCh. 22 - Prob. 35QPCh. 22 - Prob. 36QPCh. 22 - Prob. 37QPCh. 22 - Prob. 38QPCh. 22 - Prob. 39QPCh. 22 - Prob. 40QPCh. 22 - Prob. 41QPCh. 22 - Prob. 42QPCh. 22 - Prob. 43QPCh. 22 - Prob. 44QPCh. 22 - Prob. 45QP
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- The geometry of spacetime in the Universe on large scales is determined by the mean energy density of the matter in the Universe, ρ. The critical density of the Universe is denoted by ρ0 and can be used to define the parameter Ω0 = ρ/ρ0. Describe the geometry of space when: (i) Ω0 < 1; (ii) Ω0 = 1; (iii) Ω0 > 1. Explain how measurements of the angular sizes of the hot- and cold-spots in the CMB projected on the sky can inform us about the geometry of spacetime in our Universe. What do measurements of these angular sizes by the WMAP and PLANCK satellites tell us about the value of Ω0?arrow_forwardI asked the following question and was given the attached solution: Suppose that the universe were full of spherical objects, each of mass m and radius r . If the objects were distributed uniformly throughout the universe, what number density (#/m3) of spherical objects would be required to make the density equal to the critical density of our Universe? Values: m = 4 kg r = 0.0407 m Answer must be in scientific notation and include zero decimal places (1 sig fig --- e.g., 1234 should be written as 1*10^3) I don't follow the work and I got the wrong answer, so please help and show your work as I do not follow along easily thanksarrow_forwardThe visible section of the Universe is a sphere centered on the bridge of your nose, with radius 13.7 billion light-years. (a) Explain why the visible Universe is getting larger, with its radius increasing by one light-year in every year. (b) Find the rate at which the volume of the visible section of the Universe is increasing.arrow_forward
- If the current mass of the universe consists of 75% protons and 25% 4He, what is the current ratio of protons to neutrons?arrow_forwardmathematician Archimedes, responding to a claim that the number of grains of sand was infinite, calculated that the number of grains of sand needed to fill the universe was on the order of 1063. Our understanding of the size of the universe has changed since then, and we now know that the observable universe alone is a sphere with a radius of 1026 m. Estimating the size of a grain of sand, A) Approximately how many grains of sand would fill the observable universe? B) How many times larger or smaller is this number than Archimedes' result?arrow_forwardThe Universe is approximately 13.8 Billion years old. What is the volume of the visible universe in m3?arrow_forward
- The matter density in the Universe today is ?m=2.7×10−27kgm−3. What would be the value of the density parameter, Ω0, if the Hubble constant had the value H0 = 38 km/s/Mpc?arrow_forwardProblem 6. The average density p of the Universe today is 3 x 10-27kgm-³. -3 1. Find this density in (a) gcm-³ (b) M.Mpc-³ (c) m₂cm-³ 2. Find the mass within a sphere of radius (a) R. (b) 1 AU (c) 10 Mpcarrow_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
- Pretend that galaxies are spaced evenly, 7.0 Mpc apart, and the average mass of a galaxy is 1.0 ✕ 1011 M. What is the average density (in kg/m3) of matter in the universe? (Note: The volume of a sphere is 4/3pieR^3 and the mass of the sun is 2.0 ✕ 1030 kg.) ______ kg/m^3 Which model universe does this density value support? A: open B: flat C: closedarrow_forwardThe mass of the neutrino plays an important role in the universe. Suppose the mass of two neutrinos in the universe is 4.8×10-³5 kg and the current Hubble’s constant is 72 km/s/Mpc. The critical density of the universe is five times the average density of the universe. Estimate the number of neutrons present per cubic meter in the universe. (a) 2.1×10⁹ (b) 4.1×10² (c) 1.1x10° (d) 8.1×107arrow_forwardIn the deep space between galaxies, the number density of atoms is as low as 106 atoms/m3, and the temperature is a frigid 2.7 K. a)What is the pressure, in pascals, in the region between galaxies? b)What volume, in cubic meters, is occupied by 1.5 mol of gas? c)If this volume is a cube, what is the length of one of its edges, in kilometers?arrow_forward
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