Chapter 82, The Fate of the Universe Video Solutions, Pathways to Astronomy

Problem 1

The critical density depends on the value of Hubble's constant $H$ If $H$ turns out to be $65 \mathrm{km} / \mathrm{sec}$ per $\mathrm{Mpc}$, calculate how much the critical density changes compared to $H=71 \mathrm{km} / \mathrm{sec}$ per Mpc.

Pronoy Sinha

Numerade Educator

02:02

Problem 2

The following equations can help us begin to understand why the Local Group is predicted to survive the effects of dark energy, but more distant galaxies are expected to be pulled away:
a. Using the values of mass and size in the text, what is $\Omega_{\mathrm{M}}$ for the Local Group? Note that in the text, this is calculated out to the distance of neighboring groups.
b. Instead calculate the density inside of the central 1-Mpc radius region of the Local Group (where nearly all of the group's mass resides. How does this density compare to critical density?

Salamat Ali

Numerade Educator

02:05

Problem 3

Dark energy retains a constant density even as the universe expands. Today it has a value of $\Omega_{\mathrm{DE}}=0.7 .$ Matter, by contrast, grows more dilute as space expands, so its density would have been larger in the past by a factor that depends on the redshift, as $(z+1)^{3}$. At what redshift would dark energy and matter (currently $\Omega_{\mathrm{M}}=0.3$ ) have had the same density?

Farhanul Hasan

Numerade Educator

01:15

Problem 4

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? How many 1 -mm-wavelength microwave photons would this correspond to in each liter?

Narayan Hari

Numerade Educator

04:39

Problem 5

If the Solar System were at the critical density, what would be its total mass? (Assume that the Solar System is spherical with a radius of 40 AU.) How many joules of energy does this correspond to? How many Joules of dark energy are there within this volume?

Bettina Hanlon

Numerade Educator