Draw a circle and mark the exact centre. You'll notice that if you draw two lines that cut a
wedge into the circle, starting at the middle and going to the edge as if you were cutting a
slice of pie, there will be an angle between those two lines.

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If you were to cut three hundred and sixty equal slices from this pie, each slice would have
an angle of one degree—again, regardless of how big the pie is; similarly, any size of pie can
be cut into four equal pieces, and the pieces are called quarters.
Now, whenever you look at two stars and you want to know how far apart they are on your
sky, you can measure the angle between them and say how many degrees it is. Imagine that
the two stars are sitting on a hoop, and you're at the centre of the hoop. Measuring their
separation in degrees is like measuring how far around the circle you have to go to get from
one to the other.
If you need more precise measurements, each degree can be divided into sixty arcminutes,
and each arcminute can be divided into sixty arcseconds.
Now, when you see the Moon setting, you can tell someone how far above the horizon it is.
I've heard people try to measure such things in inches. If you hold a ruler up and look at the
sky, an inch will cover more sky if you have short arms, and less sky if you have long arms!
This doesn't work. A good estimate is that your hand spread wide at arm's length is about
twenty-five degrees from thumb-tip to pinky-finger-tip. If you have short arms you probably
also have smaller hands, so this works better than a ruler.

Your pinky finger held up at arm's length is about one degree wide. If you know that a galaxy
is a certain number of arcminutes across, you can decide whether you want to use high or
low magnification to look at it.
Next month we'll cover some more advanced applications of this geometry, like latitude,
longitude, and celestial coordinates.
A whole circle has 360 degrees; a degree contains 60 arcminutes; an arcminute contains 60
arcseconds. You can only see half the dome of sky at any one time, so if you go all the way
across the sky from horizon to zenith (directly overhead) to the opposite horizon, you've
measured 180 degrees. From the horizon to the zenith is 90 degrees.
The standard notation uses the symbol ° for degrees, ' for arcminutes, and " for arcseconds.
You can measure the
angular size
of an object on the sky by measuring the angle between
one side of it and the other. Here are some examples of the angular sizes of things in the
sky:
The Milky Way
almost 150° from the centre in Sagittarius to the edge in Perseus
The Big Dipper
about 25° from handle-end to bowl rim
Binocular field of view
7° 30', or 7.5°, for a 7x50 pair
Andromeda Galaxy, M31
over 3° across, although the outer parts are very faint
Telescope field of view
between 1° and 2° for a backyard scope and typical eyepiece
The Sun or the full Moon
about 32' in diameter, or just over 0.5°
Hercules Cluster
M13 about 20' in diameter
Ring Nebula, M57
1' 20" in diameter, or 1.33'

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A very thin crescent Moon
if it's thinner than 1' you probably can't see it naked-eye

- Fall '19