Appendix VI The Horizon
AVI.1
Schematic of the approach used to analyze the distance, A, to the horizon. R is the radius or the earth and h is the height of the observer. Applying Pythagorean’s theorem with an approximately 2-m tall observer results in a distance to the horizon of only 3 miles!
The Horizon
What, exactly, is the horizon and how far away is it? The answer is actually easier to determine than you might think, and the results may startle you. If we examine the schematic in Figure A.VI.1, we see that the distance to the horizon perceived by an observer of height h is the length of the tangent line, A, that connects the eyes of the observer to the closest tangent point on the earth’s surface. The radius of the earth is represented by the symbol R, and is 6.37 × 106 m. The familiar Pythagorean theorem gives us the simple relationship:
| (Eq. App. 3) |
Rearranging this relationship, inserting the values for the radius of the earth and the height of a typical observer, say 2 m and solving for the quantity, A, gives the result that a typical horizon is approximately 5,047 meters, or about 3 miles away.