A crucial discovery: The fundamental physical laws that apply on Earth and can be tested in terrestrial laboratories also apply to astronomical objects. Physics can teach us about astronomy, and astronomy can teach us about physics.
100 = 1
101 = 10
102 = 10x10 = 100
103 = 10x10x10 = 1000
106 = 103x103 = 1 million
109 = 103x106 = 1 billion
10-1 = 1/10 = 0.1
10-2 = 1/102 = 0.01
10-3 = 1/103 = 0.001
etc.
In a full circle, there are 360 degrees or 2\pi radians.
1 radian = 57.3 degrees (360/2\pi = 57.3)
1 degree ~ fingertip at arm's length
10 degree ~ fist at arm's length
Astronomers often give angles in arc-minutes or arc-seconds.
Related to a degree as minutes and seconds are to an hour.
1 arc-minute = 1/60 degree
1 arc-second = 1/60 arc-minute
1 degree = 60 arc-min = 3600 arc-sec
Angular size of Sun and full Moon = 0.5 degree
Smallest angle resolvable with naked eye = 1 arc-min
Typical angle resolvable with telescope = 1 arc-sec.
The angle \theta at the apex of a triangle with two long sides of length d and one short side of length a is
\theta = a/d radians = 57.3 x (a/d) degrees.
If we know angle and distance, can solve for size:
a = d x (\theta / 57.3 degrees).
Example: The Sun is 1.5 x 108 km from Earth, and its angular size is 0.5 degrees. What is the Sun's physical diameter?
a = 1.5 x 108 km x (0.5 deg / 57.3 deg) = 1.4 x 106 km.