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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.
Question by OpenStax is licensed under CC BY 4.0.
  1. $2\times 10^{56}\textrm{ m}^3$
  2. $4\times 10^{2}\textrm{ ly}$
  3. $1\times 10^{3}\textrm{ ly}$
  4. The radius would be greater than the average stellar separation in the Milky Way by a factor of 300.
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OpenStax College Physics for AP® Courses Solution, Chapter 34, Problem 30 (Problems & Exercises) (4:14)

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