At night sky, we can see a lot of object of our universe. The one most important for observation is our Moon. Well, if we discover nice surface of Moon, craters and dark places called "black seas", after some time, we are boring. We need to check some information on internet, e.g. names of craters, size of Moon etc. Well, astronomers sometimes use "angle" system sometime, where distance of objects are not important. What is important, is relative size measure in degrees. We call it angular distance. It is angle between two lines goes from our eye to measured distance on object.
Step 1: What You See in Binoculars?
Binoculars have in objective 2 scale. One which is curved - not important for our observations and second one, which we interest, in shape of cross, bigger one. There are several long commas and several shorter and has center where is small cross. From this small cross to first small comma are 5 parts, from small cross to first longer comma are 10 parts. For most european binoculars is 1 degree of angular distance equal 16,7 parts :
1 ° = 16,7 parts
Step 2: How Many Parts Has Moon and How Many Degrees It Is?
So, when I take a photo of Moon, I just measure with ruler, that 10 parts equal 20 cm on screen of my monitor, then Moon has 17 cm. So to calculate diameter of Moon (that's is what want know) we get:
10 parts........... 20 cm
x parts .............17 cm
x: 10 = 17 : 20
x = (17 : 20) * 10 = 8,5 parts = 0,5 °
So, Moon has diameter around 0,5 ° of angular distance.
Step 3: Extras: Calculate Distance Moon - Earth
If we know how many parts has Moon (or any object), we can calculate how far is Moon (or any object) from us. We need to know his diameter or height in normal SI units (like miles, kilometers or any...., depend on units of diameter,height). The basic equation is like this:
L = (1000 * B ) / parts ,
where L is distance from us (unit of L depend on unit of B) , B is height, diameter or just size of object we must know, parts is how many parts in objective has object.
So, Moon has:
B = 3474 km L = (1000 * B ) / parts
parts = 8,5 L = (1000 * 3474 ) / 8,5
L = ? km L = 408 706 km that's is around 408 000 km.
When I take photo of Moon, from my lattitude and longtitude, at certain time, I check distance of Stellarium, which was around 401 000 km. So it is not exactly accurate, but with that binoculars, it is good result.