Measurement started with counting segments of the human body
(forearm, hand, finger, foot). So, if you find yourself without a ruler,
make sure you know how to count it old-school.
It’s good to know things like the width of the open and closed spans
of your hand, the length of a finger and its joints, the actual length
of your foot. Memorize them. Write them on your body for a day to
remember them.
Measuring The Sky
Many new stargazers have trouble understanding our reference to
“degrees”, “arc minutes”, and “arc seconds” when talking about the
separation of celestial objects. So here’s a primer on measuring angular
distances.
Astronomers measure angular separation of objects in degrees. There
are 360 degrees in a circle. And the angular separation of any point on
the horizon and the point directly overhead (the zenith) is 90 degrees.
Halfway from the zenith to the horizon is 45 degrees.
Smaller angles are a little trickier. But your hands and fingers are a
remarkably accurate (and convenient) measuring tool. When you hold your
hand at arm’s length, you can estimate angles like this:
- Stretch your thumb and little finger as far from each other as you can. The span from tip to tip is about 25 degrees
- Do the same with your index finger and little finger. The span is 15 degrees
- Clench your fist at arms length, and hold it with the back of your hand facing you. The width is 10 degrees
- Hold your three middle fingers together; they span about 5 degrees
- The width of your little finger at arm’s length is 1 degree.
Now let’s go smaller. When you look through a telescope, you see a field of view of 1 degree or less… a very small slice of sky.
Astronomers measure angles smaller than 1 degree in arc-minutes, or
“minutes of arc”. There are 60 arc-minutes in one degree, so 1 arc-minute
is 1/60 degree. The symbol for arc-minutes is ‘. So the full Moon, for
example, is about 30′ (thirty arc-minutes) across. Coincidentally, so is
the Sun.
Each arc-minute is divided into 60 arc-seconds, or
“seconds of arc”. So
1 arc-second is 1/60 arc-minute and 1/3600 degree. The symbol for
arc-seconds is “. The face of Jupiter, which you can see this summer, is
about 50″ across. A good optical telescope in steady skies can resolve
down to about 1″ (one arc-second)
Measuring Angle and Distance with your Thumb
I hold out my arm, look at my thumb, and see a distant car half as
high. Cars are about 5 feet (1.5 meters) high. So my thumb appears
10 feet (3 meters) wide. And since I know (see below) my thumb is x30
times as far as it seems tall... I know the car is something like 300
feet (90 meters) away!
Hold your arm straight out in front of you. Make a fist. Point it at
a window. The window will appear a couple of fists high. The further
away the window, the fewer the fists. Windows in nearby buildings
won't even be a fist tall, they will perhaps be a couple of
thumb-widths high. Or less. Stick your thumb out sideways. Point
your arm at a nearby building. Count how many thumbs high its windows
are.
Ok, but how do you tell how far away it is?
You need to know two things:
very roughly how big windows are (I don't know, say something like 5 feet),
and that your thumb covers things 30 times bigger.
So, a 5 foot window, which seems 2 thumbs high, makes your thumb look
3 feet wide
(5 feet / 2 thumbs), and thus something
like 90 feet
(3 x 30) away.
Source
http://www.vendian.org
http://makezine.com
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