Thursday, January 15, 2009

How far away is the horizon?

I have heard the answer many times but, before Phil Plait asked and then answered his own question, I also had totally forgotten. The answer is found with some simple math which Phil lays out nicely. I'll leave the details to the reader but will grab just a few of his results.

Height (meters) Distance (km) Height(feet) Distance (miles)
0 0.0 0.0 0.0
1 3.6 3.3 2.1
2 5.1 6.6 3.0
12,000 391.0 39,360.0 234.6
100,000 1,132.7 328,000.0 679.6
500,000 2,572.0 1,640,000.0 1543.2
1,000,000,000 1,006,344.9 3,280,000,000.0 603,806.9

The first three items might be useful in limiting a search if you see your rocket come down. Of course these results assume a smooth Earth, i.e. no hills, valleys, or obstructions. The fourth altitude is around where jet airliners cruise. The sixth is around the highest Shuttle orbit. The last item is a limiting case showing that as you get very far away you apporach seeing half of the planet. The mean radius of the earth is around 6,365 km or 3,955 miles. At a height of one million kilometers, the distance to the horizon is approximately that height plus the Earth's radius.