4th August 2011 - 3 The Horizon

Assuming the Earth is a sphere leads to simple calculation, based on Pythagoras' Theorem, of the distance to the horizon given the height, h,  of the viewer's eye. The details are nicely explained by Phil Plait in his blog Bad Astronomy.

The distance, d (in km),  to the horizon is

d = square root of  h(h+2R)

where h is the height of the eye (in km) and R = 6365 km, an approximation of the radius of the Earth.

For instance, if you eye is at ground level, the horizon is 0 metres away, but if your eye is at 1.65 m (about 5'5"),  then the horizon is at 4.6 km (2.9 miles). At the top of Mount Everest, which is 8,848 m high, it would be 335.75 km (208 miles).