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Recent findings in astrophysics suggest that the observable Universe can be modeled as a sphere of radius $R=13.7 \times 10^{\circ}$ light-years with an average mass density of about $1 \times 10^{-26} \mathrm{kg} / \mathrm{m}^{3}$ , where only about 4$\%$ of the Universe's total mass is due to "ordinary" matter (such as protons, neutrons, and electrons). Use this information to estimate the total mass of ordinary matter in the observable Universe. (1 light-year =9.46 \times $10^{15} \mathrm{m.}$ .

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$4 \times 10^{51} k g$

Physics 101 Mechanics

Chapter 1

Introduction, Measurement, Estimating

Physics Basics

Cornell University

University of Michigan - Ann Arbor

University of Winnipeg

Lectures

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So we want the total mass of ordinary matter. There is sexually as black matter, but we're not. We're not going to do with that. We're only trying to associate. Uh, we only tried to estimate the total amount of ordinary matter in the observed in the observable universe. Now here, Um uh, ordinary matter is considered a proton electron or neutron. So here we can say that we're going to approximate the universe as a sphere so we can say a spherical universe. And the mass would be equal to, Of course, the density times the volume. Ah, they're giving us the density of the universe. So this would be one times 10 to the negative 26th kilograms per meters cubed again. This is so low because most of the universe is not made up of ordinary matter. Most of it is a complete void. And then we're going to multiply it by the volume of a sphere. So 4/3 pi times the radius of the universal 4/3 pie and then the radius of the universe's 13.7, uh, times 10 to the ninth light years. So that's how in this case this would be the radius of the universe. And then we're going Thio, multiply this, uh, by the number of meters in a light year. So 9.46 times 10 to the 15th. My apologies. It's Let's actually, um, put this lower. My apologies. New line. 13.7 times 10 to the ninth light years again multiplied by 9.446 times 10 to the 15th meters for every one light year. And then we're going to cube this entire term, and then we're going to multiply it by 0.4 And so we find that the mass is going to be equal to 3.65 times 10 to the 51st kilograms. So this would be the mass of all of the ordinary matter again, ordinary matter in the universe. That is the end of the solution. Thank you for watching

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