### Size of the Moon and Observatory Diameter

February 23, 2009

Photographer: Chris Kotsiopoulos
Summary Author: Chris Kotsiopoulos

The size of the Moon is readily available in all astronomy books or just one click away when using the world-wide web. But what about the size of a distant object like a tree, a geological formation or a construction? Is there a practical way to calculate these sizes? Can we use the Moon as a measurement unit to accomplish this goal? The answers: Yes and yes! The trick is to take a picture of the Moon and another one of the object in question at the same focal length or to combine them in one shot. Then, measure the size of the object compared with the Moon's diameter in your photo. There are a number of ways to do this. I’ve used a desktop screen ruler. What you also need is the distance between the photographer and the object. Google Earth is a great tool for the job. Finally, a simple trigonometry formula does the rest. In the photo above, the diameter of the observatory dome is calculate below.

What we know:

1. The distance between the photographer and the dome is 1,440 meters.
2. The dome's angular size based on the photo measurements is approximately 0.644 degrees.
3. Moon's angular size on November 12. 2008: 0.55 degrees
4. The tangent of 1 degree is 0.017455
The tangent of 0.6448275862 degrees = 0.017455 * 0.6448275862 = 0.0112554655

Now we can calculate the dome's diameter:

Dome angular size = Dome actual size / photographer to dome distance -->
0.0112554655 = Dome actual size / 1440 -->
Dome actual size = 1440 * 0.0112554655 = 16.2

Thus, the dome's diameter is approximately 16.2 meters (or almost 53').