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How Big is the Sky?

Week of February 24, 1997
The sky appears to us as a sphere surrounding the Earth, so we use angular measures to figure out distances on the sky. For example, a circle is divided into 360 degrees, with each degree further divided into 60 arcminutes, and each arcminute divided into 60 arcseconds (so there are 3600 arcseconds in a degree). These measurements are based on a time, which is why we use 'minutes' and 'seconds', but to avoid confusion with real time measurement we put the word 'arc' in front to remind us we are dealing with arcs. So you can say, 'Those two stars are 4 degrees, or 240 arcminutes, or 14,400 arcseconds apart on the sky'.

The sky is 360 degrees around. But the sky has area! Area is measured in square units, like a floor area is measured in square meters. How many square degrees are there in the sky?

Warning: a small amount of math follows!

Well, we know two things: one is that the the circumference of a circle is 360 degrees, and is defined as 2 x pi x radius (pi is a number that equals about 3.1415) and the other is that the surface area of a sphere is 4 x pi x (radius)^2.


   2 x pi x radius=360 degrees
  one radius=360 / (2 x pi)=about 57.3 degrees
(57.2958 to be more precise). Simply plug that into the second equation to get

   4 x pi x 57.3^2=41253 square degrees. 
So there you have it! There are over 40 thousand square degrees in the sky. The sky is pretty big. For comparison, the Moon is only a half degree across. That gives it an area of only 0.2 square degrees. The Moon is small!

Next week, we'll see how the stars are distributed across the sky, using the numbers we just derived.

©2008 Phil Plait. All Rights Reserved.

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