How many star systems are within 50 light years of Sol?

Answer 1

That is not known exactly, since even at such a relatively short distance, many red dwarves will go undetected. You can check the Wikipedia article "List of nearest stars and brown dwarfs" for known stars up to a distance of about 16 light-years, and extrapolate. That is, just assume that a larger volume has proportionally more stars. Note that due to the difficulty of detecting red dwarves, this should give you a MORE RELIABLE figure than actually counting all the known stars up to a distance of 50 light-years (since it is likely that up to a distance of 16 light-years, the detection rate for red dwarves is higher). As a reminder, the volume of a sphere is proportional to the cube of its radius. That is, a sphere of 50 light-years has approximately 29 times as much volume as one of radius 16.3 light-years, so you would expect it to have approximately 29 times as many stars.