Expert: Paul Wagner - 9/3/2004

Question
How many moons would it take to entirely fill the sky?  I heard that the number was 10,000 but round numbers like that are usually grossly inaccurate.  Hope this isn't too far afield from your center of expertise!  Thanks!

Answer
Dear Matt:

This is really a math problem...but think of it this way:

The diameter of the full moon is just about half a degree, and assuming you want to fill both the night and day skies, the sky is 360 degrees.  So it would take 720 moons just to make a single, moon-wide band around the sky. And another 719 to a similar band to cross it.  That's 1439, and we have only covered a tiny fraction of the surface of the sky. Of course, to cover those bands completely, you would need to fill in the spaces where the disks of the moon aren't touching.  


I won't do the whole homework problem for you, but here are a few clues:

The formula for the area of a sphere is 4 pi x r2. And the radius of the orbit of the moon is roughly 250,000 miles.

The area of a circle, which is what moon appears to be from earth, is pi X r2.  And the radius of the moon is about 2200 miles, so the radius is 1100.  

Can you do the math? All of this is in miles

pi x 1100 squared is 3802857

And the area of the sphere of the moon's orbit is: 785714285714

And if youdivide the two, you get:  206611

Seems like a lot of moons, huh? That's assuming you want to cover the entire sky....not just fill it with moons.

Paul wagner