21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 22, Problem 20QP
To determine
The limitations of Hubble time.
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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.
According 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.
Explain how the Hubble constant, H0, can be used to make an estimate for the age of the Universe. Use the value of H0 = 0.07×103 kms-1/Mpc to estimate the Universe’s age. Comment on the significance of your answer.
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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- How would I calculate the age of the universe in billions of years from the Hubble constant (73.48 +/- 1.66 km/s/Mpc)? I know I need to use basic unit conversion but I’m not sure which numbers to use.arrow_forwardAssume the observable Universe is charge neutral, and that it contains n nuclei (hydrogen plus helium nuclei, ignoring other elements). Take the helium mass fraction as 1/4. How many electrons are there in the observable Universe? Enter your answer in scientific notation with one decimal place. Values: n = 1*10^80arrow_forwardWhat is the estimated age of the Universe (in years) if the Hubble constant is 60 km/s/Mpc?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_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 235 million light-years receding from us at a velocity, v. If the Hubble constant is 20.5 km/s per million light-years, what is its velocity? (Enter the magnitude in km/s.) _________ km/sarrow_forwardAssume the observable Universe is charge neutral, and that it contains n nuclei (hydrogen plus helium nuclei, ignoring other elements). Take the helium mass fraction as 1/4. How many electrons are there in the observable Universe? Enter your answer in scientific notation with one decimal place. Value: n = 4*1080arrow_forward
- If a galaxy is 8.9 Mpc away from Earth and recedes at 497 km/s, what is H. (in km/s/Mpc)? km/s/Mрс What is the Hubble time (in yr)? years How old (in yr) would the universe be, assuming space-time is flat and the expansion of the universe has not been accelerating? years How would acceleration change your answer? If the expansion of the Universe has been accelerating, the Universe could be substantially younger than the value entered above. If the expansion of the Universe has been accelerating, the Universe could be substantially older than the value entered above.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_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 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_forward
- Assuming that the Hubble constant is, in fact, constant over the age of the universe, what is the Hubble look-back time (effectively the age of the universe in this case) if the Hubble constant is measured to be 50 km/s/Mpc (Please give your answer in units of billions of years; i.e. 10 billion years should be answered as 10)? Keep in mind that this is not the observed measurement of the Hubble constant (70 km/s/Mpc) and is only a value given for this problem. That said, it is not incredibly different so you should expect your answer to still be on the scale of billions of years.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_forwardIf a galaxy is 8.8 Mpc away from Earth and recedes at 498 km/s, what is H0 (in km/s/Mpc)? _______ km/s/Mpc What is the Hubble time (in yr)? _______ yr How would acceleration change your answer? A: If the expansion of the Universe has been accelerating, the Universe could be substantially younger than the value entered above. B: If the expansion of the Universe has been accelerating, the Universe could be substantially older than the value entered above.arrow_forward
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