Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 29, Problem 23E
Suppose the Hubble constant were not 22 but 33 km/s per million light-years. Then what would the critical density be?
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I 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
thanks
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 = 10 kg
r = 0.0399 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)
(a) Calculate the approximate age of the universe from the average value of the Hubble constant, H0 = 20km/s ⋅ Mly . 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.
Chapter 29 Solutions
Astronomy
Ch. 29 - What are the basic observations about the universe...Ch. 29 - Describe some possible futures for the universe...Ch. 29 - What does the term Hubble time mean in cosmology,...Ch. 29 - Which formed first: hydrogen nuclei or hydrogen...Ch. 29 - Describe at least two characteristics of the...Ch. 29 - Describe two properties of the universe that are...Ch. 29 - Why do astronomers believe there must be dark...Ch. 29 - What is dark energy and what evidence do...Ch. 29 - Thinking about the ideas of space and time in...Ch. 29 - Astronomers have found that there is more helium...
Ch. 29 - Describe the anthropic principle. What are some...Ch. 29 - Describe the evidence that the expansion of the...Ch. 29 - What is the most useful probe of the early...Ch. 29 - What are the advantages and disadvantages of using...Ch. 29 - Would acceleration of the universe occur if it...Ch. 29 - Suppose the universe expands forever. Describe...Ch. 29 - Some theorists expected that observations would...Ch. 29 - There are a variety of ways of estimating the ages...Ch. 29 - Since the time of Copernicus, each revolution in...Ch. 29 - The anthropic principle suggests that in some...Ch. 29 - Penzias and Wilson’s discovery of the Cosmic...Ch. 29 - Construct a timeline for the universe and indicate...Ch. 29 - Suppose the Hubble constant were not 22 but 33...Ch. 29 - Assume that the average galaxy contains...Ch. 29 - The CMB contains roughly 400 million photons per...Ch. 29 - Following up on Exercise 29.27 calculate the...Ch. 29 - Continuing the thinking in Exercise 29.27 and...Ch. 29 - Continuing the thinking in the last three...Ch. 29 - There is still some uncertainty in the Hubble...Ch. 29 - It is possible to derive the age of the universe...
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- 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.arrow_forwardAccording to the version of the Big Bang Theory without a Cosmological Constant (and without Dark Energy of any kind), what would be the maximum possible age of the universe in Gyr (Gigayears, meaning billions of years) if the Hubble Constant had the following values? Another way of asking the question would be: What is the Hubble Time in Gyr, given the following values of H0? H0 = 50 km/s/Mpc H0 = 75 km/s/Mpc H0 = 100 km/s/Mpc answer to two significant figures.arrow_forward(a) Calculate the approximate age of the universe from the average value of the Hubble constant, H0 = 20km/s ⋅ Mly . To do this, calculate the time itwould 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_forward
- 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.)arrow_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_forwardThe 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_forward
- Using our example from the previous unit, let's try to determine the Hubble time for this example universe. You were given that a good representative galaxy receded at a speed of 4000 km/s and was found to be 20 Mpc away. With that in mind, what would the age of that universe be in years (aka what is that universe's Hubble time)? Go ahead and take the number of kilometers per Mpc to be approximately 3.1*10^19 km/Mpc. While this problem may look scary at first, this is really just bringing you full circle to one of the unit conversion problems you encountered at the beginning of this course.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_forwardIf the universe had a density equal to its estimated critical density of 9= 10-30 g/cm3, and if it were composed entirely of one-solar-mass stars (mass 2.0 x1030 kg) distributed uniformly across the universe, what would be the distance between stars? Compare your result with the density of stars in the neighborhood of the sun and comment on the result.arrow_forward
- mathematician 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_forwardTo get an idea of how empty deep space is on the average, perform the following calculations: (a) Find the volume our Sun would occupy if it had an average density equal to the critical density of 10-26 kg / m3 thought necessary to halt the expansion of the universe. (b) Find the radius of a sphere of this volume in light years. (c) What would this radius be if the density were that of luminous matter, which is approximately 5% that of the critical density? (d) Compare the radius found in part (c) with the 4-ly average separation of stars in the arms of the Milky Way.arrow_forwardCompute a numerical value (in units of protons/m3) for the critical density of our Universe. Howdoes it compare to the density of hydrogen gas at standard temperature and pressure?arrow_forward
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