# Finding the number of stars n light-years from the sun

The nearby stars seem homogenously spaced out enough to give a general "stellar density."
Does there exist some kind of mathematical expression that can determine the number of stars n light-years from the sun?
Or—
Is there a rough value for this supposed stellar density idea? (Ex: 0.3 stars per cubic light-year.)

• Likely you need some strong assumption. Locally it works. – Alchimista Dec 17 '17 at 11:02

## 1 Answer

Wikipedia, quoting Erik Gregersen. The Milky Way and beyond. gives a local value of 0.004 stars per cubic light year, or 0.14 stars per cubic parsec.

So within n light years you would expect $0.004\times 4\pi n^3/3\approx 0.016n^3$ stars.

This predicts the nearest star to be about 4 light-years away, consistent with observation.