How Can We See Stars in the Night Sky When They Are So Far Away?

Answer:

Even though the stars that we see in the night sky are all very far away, we can see them not by actually being able to resolve their sizes, but by measuring the light that they produce.  The light from a star is sent out in all directions, and is largely unimpeded in its path from the star to us, as on average there is very little matter to block the star’s light between the star and us.

To get an idea as to how far away we could see our own Sun if we ventured out into space, we can use the measured brightness of our Sun using a brightness scale that reflects how our eyes respond to changes in brightness.  That star brightness scale is called the “magnitude scale”, and on that scale a star’s brightness as it appears to our eyes, which is called the “apparent magnitude” (m), is defined as:

where F is a measure of the amount of light from the star (called the “flux”) and d is the distance to the star.  We also need a standardized measure of the star’s brightness called the “absolute magnitude” (M), which is a star’s apparent magnitude at a distance of 10 parsecs:

If we take the difference of the apparent and absolute magnitudes of a star we get something called the “distance modulus” (m-M):

Now, using our Sun’s known absolute magnitude (M = 4.83) and assuming that the average person can see stars down to an apparent magnitude of about m = 6, we can plug these two values into the distance modulus equation above to find that the distance that our Sun would just barely be detectable to the human eye is about d = 17.1 parsecs, or about 56 light years.