Chapter 26

What is the greatest distance at which a galaxy survey sensitive to objects as faint as 20 th magnitude could detect a galaxy as bright as the Milky Way (absolute magnitude- 20 )?

Assuming that the entire universe is uniformly filled with Sun-like stars with a density of 5 billion stars per cubic megaparsec (corresponding to 50 billion stars per galaxy and critical mass density), calculate how far out into space one would have to look, on average, before the line of sight intersects a star.

Eight galaxies are located at the corners of a cube. The present distance from each galaxy to its nearest neighbor is \(10 \mathrm{Mpc},\) and the entire cube is expanding according to Hubble's law, with \(H_{0}=70 \mathrm{km} / \mathrm{s} / \mathrm{Mpc}\). Calculate the recession velocity of one corner of the cube relative to the opposite corner.

For a Hubble constant of \(70 \mathrm{km} / \mathrm{s} / \mathrm{Mpc}\), the critical density is \(9 \times 10^{-23} \mathrm{kg} / \mathrm{m}^{3} .\) (a) How much mass does this correspond to within a volume of 1 cubic astronomical unit? (b) How large a cube would be required to enclose 1 Earth mass of material?