How large must the universe be to avoid Olbers' paradox at 1 star per parsec?

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J.Welder12
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Homework Statement


Suppose all stars had the same radius as the Sun, and they were distributed throughout the universe with the same density as we have nearby- about 1 star per cubic parsec. Approximatly how bigh in parsecs and light years would the universe have to be in order to avoid Oblers Paradox?


Homework Equations


Think of light as a particle- how far does the photon have to go until it hits another particle?



The Attempt at a Solution


photon- particle relation xr= 1/an
tr= 1/anc
κ= nσr/ρ where (n/ρ) is the number of atoms per unit mass and κ= total cross section per unit mass
 
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Discussion

The universe must be as large as necessary for the photon to hit another particle before it reaches the edge of the universe. Therefore, the size in parsecs and light years would depend on the total cross section per unit mass and the number of atoms per unit mass.