Explorations: An Introduction to Astronomy (Arny), 7th Edition

Chapter 18: Cosmology

Problems

1
Until recently, experimental results for the Hubble constant ranged from about 50 to 100 km/sec/Mpc. Calculate the age of the Universe for both of these extremes. Do you see any potential conflicts with other astronomical observations if H had been either of these numbers?
2
The temperature of Universe at recombination was about 3000 K. If the ratio of the temperature of the background radiation at recombination to the temperature of the CMB radiation today is equal to the ratio of the wavelength of light today to the wavelength of the background radiation at recombination, how many times wider is the Universe today than it was at recombination? Remember that as the Universe expands, it stretches the light.
3
Using the same logic as in the previous question, how many times wider is the Universe today than it was when the average temperature was 3 × 109 K, sometime between 1 and 3 minutes old? If you shrank the Milky Way's disk by that factor, would it fit inside the Solar System?
4
If the change in the previous problem is the change in diameter, how many times larger is the volume of the Universe today than when the temperature was 3 × 109 K?
5
The temperature of the Universe at recombination was about 3000 K. Use Wien's law to calculate the peak wavelength of the radiation at that temperature. Which spectral type of star has this surface temperature?
6
One second after the Big Bang, the density of the universe was about 0.1 kg/L. How big a volume of the universe contained as much mass as the Solar System?
7
When the Universe was extremely young, it increased in size "exponentially" until it was 1025 times larger than it began. How many times would the Universe have to double in size to grow this much larger than it started? (If you are unfamiliar with logarithms, you can estimate this by testing different powers of 2 on a calculator by trial and error.)
8
If dark energy in the universe currently is about 73% of the critical density, then how many joules of energy are there in each liter of space? (Use the critical density given in the chapter to find a mass in kg, then use E = mc2.) How many 1-mm-wavelength microwave photons would this correspond to in each liter? (The energy of a photon is discussed in section 4.2.)
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