Reading:

Roos chapter 1 (excluding section 1.2), attached.

Problems:

1. In class, we claimed that the dominant physical mechanism explaining Olbers' paradox is the fact that starlight propagates at finite speed, from stars with a finite lifetime. Show that this effect radically reduces the flux of starlight onto the earth, by calculating the flux under the following brutal approximation: the stars have existed with the same density $n$, and shined with the same luminosity $L$, since the beginning of the universe, approximately $10^{10}$ years ago. Before that, they did not exist -- $n$ was zero. Express your answer as a factor times the brightness of the sun, and evaluate that factor given the cosmological values $n \approx 10^{10}/ {\rm Mpc}^3, R_\odot = 10^{-7} {\rm pc}$.

2. The Virgo cluster exhibits a Doppler shift with redshift $z = 4 \times 10^{-3}$. Calculate the recessional velocity of the Virgo cluster, relative to us. How far away is the Virgo cluster from us (in light years), if it obeys Hubble's law?