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- Homework Statement
- Summary: The highest concentration of asteroids is in a doughnut shaped region between the Kirkwood gaps at radii of 2.06AU and 3.27AU from the Sun. There are an estimated 10^9 asteroids of radius 100m or larger. What's the average distance between asteroids?

- Relevant Equations
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What I did was find the total area of the space between the Kirkwood gaps and the area occupied by the asteroids (assuming they all had a 100m radius). I subtracted the two to get the area that is empty in that region. To find the average empty area between asteroids I divided this by the estimated number of asteroids. I don't know how to convert this area into a distance. I tried assuming the area was a square and just finding the lenght of the side or the diagonal of the square, which definetely feels like a big assumption to make, but this results in a much too low number. (The solution is approximately 400 000km)

I'm at a loss as to what to do so any help would be appreciated.

I'm at a loss as to what to do so any help would be appreciated.