In reading this article about updated estimates for the number of exoplanets in the Milky Way, I am curious how to get an estimate of the mean distance between them. The Milky Way is ~50,000 light years in radius and an average of ~1000 ly in thickness, and the article estimates there to be ~500 million exoplanets in the habitable zone around their stars.
To simplify this greatly (grotesquely!), I think the galaxy can be thought of as a plane, since I want to know the method of doing this for a disc anyway, and there are so many estimates here, it shouldn't affect the results greatly. So, the area of this disc would be:
$\pi (50000ly)^2 \approx 7853981634 ly^2$
However, beyond this, to find an even distribution of 500,000,000 points, I'm not really sure how to go about that. Given this, I can later apply it to an oblate disk, but I'd like to know the general method of evenly distributing points in a circle, and possibly finding the distance between them if it's not straightforward.
Thank you in advance.