The estimated age of the universe by Hubble’s law.

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Chapter 16, Problem 6QAP

To determine

The estimated age of the universe by Hubble’s law.

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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.)

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.

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?