Another interesting question with an interesting answer. First, let us assume that the earth is a perfect sphere. That's not a bad assumption, since the earth is about as much a sphere as a basketball is (Mt. Everest is about the size of the dimples on a basketball). We will also ignore the slight deformation of the earth (it's a bit like a pancake in reality, but not by much).
So we can make the following points:
- It does not really matter whether you go up from the equator or any other place.
- You can never see "all" of the earth -- one face will always be hidden -- the most you can see is half of the surface.
- You can never see that half fully either, but you can get pretty close.
The rest of it is some geometry, and knowledge about solid angles (or surface of a sphere), which is not really interesting and hard to demonstrate without boring figures. But, overall, the formula comes out to be extremely simple. The fraction of (one-half of) the surface of earth one can see at an altitude h is simply given by:
F = h / (h + R)
where R is the radius of the earth. So, if you go about one earth radius high (which is about 6370 kilometers or 3960 miles) you can see 1/2 of the most you can see. Once you go as far as the moon (roughly 400 000 kilometers away) you can see about 98.4% of one face.
Once again, the answer really depends on the exact definition of the question. If 90% is good enough for you, you only need to go 57000 kilometers (35600 miles) high from the surface of the earth. If you want 100%, that you just are not going to get at any finite distance.
Answered by:
Yasar Safkan, Ph.D., Instructor, Yeditepe University, Istanbul, Turkey
