[BAFacts are short, tweetable astronomy/space facts that I post every day. On some occasions, they wind up needing a bit of a mathematical explanation. The math is pretty easy, and it adds a lot of coolness, which I'm passing on to you! You're welcome.]

Todays BAFact: The Sun is 12 trillion times brighter than the faintest star you can see with your naked eye.

In yesterdays BAFact, I showed how the Sun is about 400,000 times brighter than the full Moon and I showed my math. Thats an amazing brightness difference, but while I was writing it I had to wonder: how much brighter is the Sun than the faintest star you can see?

The faintest stars visible to the naked eye have a magnitude of about 6. This depends on lots of stuff, like how dark the sky is, how good your eyesight is, and so on. Some people with excellent vision can see stars down to magnitude 7, and there are reports of a few extraordinary people who can see even fainter. But on a dark night, the average person can just barely see 6th magnitude stars.

Lets use that number then. All we have to do is plug that into the equation I gave yesterday (and remembering that the Sun has a magnitude of -26.7):

Brightness ratio = 2.512(6 (-26.7)) = 2.51232.7 = 12 trillion

Yegads! Thats 12,000,000,000,000 times brighter!

Now, to be fair, thats not really the brightness range your eyes can detect. You cant look right at the Sun easily or comfortably; its simply too bright. So the range of brightness your eye can see is probably smaller.

We can put a lower limit on it easily enough using the Moon. The Moon is the second brightest object in the sky, and we know we can look at that easily enough, so lets do that math (the Moons magnitude is -12.7 when its full):

Brightness ratio = 2.512(6 (-12.7)) = 2.51218.7 = 30 million

See the original post:

BAFact Math: The Sun is 12 *trillion* times brighter than the faintest star you can see | Bad Astronomy