Question

To get an idea of how empty deep space is on the average, perform the following calculations:
(a) Find the volume our Sun would occupy if it had an average density equal to the critical density of $10^{-26}\textrm{ kg/m}^3$ thought necessary to halt the expansion of the universe.
(b) Find the radius of a sphere of this volume in light years.
(c) What would this radius be if the density were that of
luminous matter, which is approximately 5% that of the
critical density?
(d) Compare the radius found in part (c) with the 4-ly average separation of stars in the arms of the Milky Way.

- $2\times 10^{56}\textrm{ m}^3$
- $4\times 10^{2}\textrm{ ly}$
- $1\times 10^{3}\textrm{ ly}$
- The radius would be greater than the average stellar separation in the Milky Way by a factor of 300.

Solution Video