My law office recently moved to a new building in downtown St. Louis, Missouri. We’re now on the 17th floor, and we have unobstructed views in many directions. That led to conversations about how far we could actually see. That led to the purchase of a good set of binoculars (we bought a pair of Nikon 7223 16 x 50 mm binoculars at Amazon for about $100).  We also invested in a tripod for the binoculars (another $24). This equipment has led to some rather surprising discoveries.

For instance, we can clearly see the McKinley Bridge, which is almost three miles away.   Aiming upwards, we can clearly see the Chain of Rocks Bridge, which is almost ten miles away.  We can clearly see the Mississippi water flowing under both of these bridges.

Looking even further in the distance, we can see several manmade structures in Alton, Illinois.   That is 35 miles away by car, at least 25 miles away by air.  Alton is also on the Mississippi River.  We can’t see the river itself in Alton; the structures we can see are on elevated land past the river on the Illinois side.  These sites are all to the north–we have yet to explore the other vistas.

I didn’t know that you could see so far with a good set of binoculars.  Rumor has it that one can even see the moon, which is a quarter million miles away.   More seriously, and much more impressive, I’m waiting for a clear night to train the binoculars onto Jupiter; it is apparently easy to see the four largest moons of Jupiter from Earth using only binoculars.

Back down to earth the question arises:  how far can one see, before the Earth’s curvature drops the scene too far down?   There are formulas to calculate this distance. Assuming the land is relatively flat, the answer depends on how high one’s eye are above the ground.  Up on the 17th floor, we can supposedly see more than 16 miles over flat ground.   Assuming most of that view is not blocked by other buildings, this gives us the ability to “see” (based upon the formula A= pi times r(squared).   With a radius of 16, we can see an area of more than 800 square miles, an impressive area of land (I designated a reference-area based upon an 18 mile radius on the attached map).

I’ll end this post here.  I’m now a king ruling over a large kingdom, and my subjects need me to keep a careful lookout.