Next: Kepler's Third Law
This is an extremely useful formula which is never directly stated in the text.
Basically this formula relates the angular size of an object 
\
(how big the object appears to an observer),
the actual physical size d of the object
, and
the distance D from the observer to the object.
There are three variables in the equation: 
, d, and D. In
each problem involving Equation 
, you will be given two of the
three and be asked to solve for the other.
The number 
means 206,265 seconds of arc (or
arc seconds).
Some examples. A 1000 m high mountain is 50 km away. How big does the
mountain appear? Here we have d = 1000 m (physical size), D =
50,000 m (distance) and 
is the unknown. Solving for 
\
gives:
Another example. If the human eye can just make out an object 
in angular size, how high would a 20 cm diameter balloon have to float
before it becomes effectively invisible?
Here we have 
(it is a
good idea to always convert angles to arc seconds before beginning) and
d = 20 cm. The unknown is thus D.
After rearranging the small-angle
formula, we have:
Two notes. 1) When plugging into the formula, your value for 
\
should always be converted to arc seconds. 2) It doesn't matter what units
you use for d and D as long as they are the same.
Next: Kepler's Third Law