Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 25, Problem 54Q
To determine
The value of cosmological constant by using the combined observation values.
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a) Define the term “standard candle” as used in cosmology
b). The flux is defined as f(Dlum) = L /4πD2lum , where L is the absolute luminosity and Dlum is the distance to the radiation source (you may assume z ≪ 1). Assume that we have measured the flux to be f = 7.234 10−23Wm−2 and the absolute luminosity is given by L = 3.828 1026W. Calculate the luminosity distance Dlum to the object in Mpc.
c). Calculate the distance modulus µ for the object of the previous subquestion. Show that the distance modulus µ can be written as given in image
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)
What do the results from the Wilkinson Microwave Anisotropy Probe (WMAP) observations tell cosmologists?
Chapter 25 Solutions
Universe: Stars And Galaxies
Ch. 25 - Prob. 1QCh. 25 - Prob. 2QCh. 25 - Prob. 3QCh. 25 - Prob. 4QCh. 25 - Prob. 5QCh. 25 - Prob. 6QCh. 25 - Prob. 7QCh. 25 - Prob. 8QCh. 25 - Prob. 9QCh. 25 - Prob. 10Q
Ch. 25 - Prob. 11QCh. 25 - Prob. 12QCh. 25 - Prob. 13QCh. 25 - Prob. 14QCh. 25 - Prob. 15QCh. 25 - Prob. 16QCh. 25 - Prob. 17QCh. 25 - Prob. 18QCh. 25 - Prob. 19QCh. 25 - Prob. 20QCh. 25 - Prob. 21QCh. 25 - Prob. 22QCh. 25 - Prob. 23QCh. 25 - Prob. 24QCh. 25 - Prob. 25QCh. 25 - Prob. 26QCh. 25 - Prob. 27QCh. 25 - Prob. 28QCh. 25 - Prob. 29QCh. 25 - Prob. 30QCh. 25 - Prob. 31QCh. 25 - Prob. 32QCh. 25 - Prob. 33QCh. 25 - Prob. 34QCh. 25 - Prob. 35QCh. 25 - Prob. 36QCh. 25 - Prob. 37QCh. 25 - Prob. 38QCh. 25 - Prob. 39QCh. 25 - Prob. 40QCh. 25 - Prob. 41QCh. 25 - Prob. 42QCh. 25 - Prob. 43QCh. 25 - Prob. 44QCh. 25 - Prob. 45QCh. 25 - Prob. 46QCh. 25 - Prob. 47QCh. 25 - Prob. 48QCh. 25 - Prob. 49QCh. 25 - Prob. 50QCh. 25 - Prob. 51QCh. 25 - Prob. 52QCh. 25 - Prob. 53QCh. 25 - Prob. 54QCh. 25 - Prob. 55Q
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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 thanksarrow_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_forwardSuppose the energy density of the cosmological constant is equal to the present critical density En = Ec.0 = 4870MeVm-3. What is the total energy of the cosmological constant within a sphere 1AU in radius?What is the rest energy of the Sun (Eo = Moc²)? Comparing these two numbers, do you expect the cosmological constant to have a significant effect on the motion of planets within the solar system?arrow_forward
- 1.2 1.0 0.8 0.6 Cosmic background data from COBE 0.4 0.2 0.0 0.5 10 Wavelength A in mm c) Background (CMB) undertaken by the COBE satellite. Use this diagram to estimate the current temperature of the CMB. Based on your estimate, what would the temperature of the CMB have been at a redshift of z = 5000? The left hand diagram above shows the results from observations of the Cosmic Microwave Radiated Intensity per Unit Wavelength (16° Watts/m per mm)arrow_forwardProblem 2: Black hole – the ultimate blackbody A black hole emits blackbody radiation called Hawking radiation. A black hole with mass M has a total energy of Mc², a surface area of 167G²M² /c*, and a temperature of hc³/167²KGM. a) Estimate the typical wavelength of the Hawking radiation emitted by a 1 solar mass black hole (2 × 103ºkg). Compare your answer to the size of the black hole. b) Calculate the total power radiated by a one-solar mass black hole. c) Imagine a black hole in empty space, where it emits radiation but absorbs nothing. As it loses energy, its mass must decrease; one could say "evaporates". Derive a differential equation for the mass as a function of time, and solve to obtain an expression for the lifetime of a black hole in terms of its mass.arrow_forwardc. The critical density for the Universe is given by 3H% Pcrit 8TG Calculate the ratio between the values derived for the critical density of the Universe assuming Ho = H5 Planck and Ho = H° = HSHOESarrow_forward
- 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.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_forwardCompute the critical density of the universe using the universal gravitational constant G= 6.67*10-11Nm2/kg2 and the Hubble constant of 73km/s/Mpc. B) What is the geometrical implication be if the universe has the critical density? Note: 1pc = 3.1*1016marrow_forward
- Distribution of Dark matter The most mass of our Milky Way is contained in an inner region close to the core with radius R0.Because the mass outside this inner region is almost constant, the density distribution can bewritten as following (assume a flat Milky Way with height z0):ρ(r) = (ρ0, r ≤ R00, r > R0(a) Derive an expression for the mass M(r) enclosed within the radius r.(b) Derive the expected rotational velocity of the Milky Way v(r) at a radius r.arrow_forwardThis a question on Cosmology: Suppose that you have a flat universe that has matter and dark energy with wd = -2/3 & Ωd,0 =0.7 At the time when light with z = 1 was emitted from a distant galaxy what was the ratio Ɛd /Ɛm ?arrow_forwardWith a Hubble constant of 70 km/sec/Mpc, the critical density would be 1.4 g/cc. 9 × 10-27 kg/m3. 6.23 × 10-23 g/mole. 4 × 10-36 g/cc. 3 × 10-31 g/cc.arrow_forward
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