## Measuring Sky Angle

One of the most important early measures handed down to the Greeks
was the theory for measuring Sky Angles. We are familiar with
**linear distances**, but in the sky we must measure **angular
distances**. That is, relative distances on the sky (or the celestial
sphere) are measured based on angles. Angles where measured in
a sexagesimal (60-based) system, 60 seconds in a minute, 60 minutes
in a degree, 360 degrees make up a full circle. This same system of measure,
which originated thousands of years ago by the Babyonions (perhaps because they
used a 360 day year),
has not only survived until today, but is used
in modern time keeping.

You can use your hands and
fingers to measure angles in the sky. Your fingers are
about 1/2^{o} wide when you view it at
arm's length. Your fist is about 10^{o}
wide. Your hand with fingers spread wide, thumb-tip to
pinkie-tip **subtends** an angle of about 20^{o}.

The angular diameter of an object is related to its linear diameter
and distance. If the diameter
(D) of an object is small compared to its distance (d, typically the
case in astronomy!) from the observer O (this is the
`small angle approximation'), its angular
measurement (theta) is calculated as D/d in **Radians**, where 1 rad = 57.3^{o}.