Line of sight and star density question.

[Illuminati]

This is blatant homework help that I don't know how to approach. Any hints would be appreciated.

Suppose you are in an infinitely large old universe in which the average density of stars is n = 10⁹ Mpc^-3 and the average stellar radius is equal to the sun's radius is R = 7*10⁸. How far, on average, could you see in any direction before your line of sight strikes a star?

 

[gneill]

Look up "mean free path".

 

[Ken G]

Also, be careful of the units here-- if the density is in terms of Mpc^-3, then you want the cross sectional area of the Sun in units of Mpc² to avoid having to convert units during your calculation. wolframalpha.com tells me that the answer for the Sun is 2 times 10^-38 Mpc². How can you combine that with the density to get a distance, which will be the mean free path you want? (It would require a pretty darn big universe to hit a star-- for one thing, the universe would need to be almost 10¹⁹ times older than it actually is, right?)

 

[Matterwave]

You can use dimensional analysis to get something out of this, and then see if it makes sense to you. 1/L^3 and L^2 can be combined how to get L?

This won't get you any constants or other unit-less things though, but maybe it will help you see the problem more clearly.