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Question

What is the minimum altitude from the equator needed to view the Earth as a whole?
Asked by: Illang Kumaran

Answer

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:

  1. It does not really matter whether you go up from the equator or any other place.
  2. You can never see "all" of the earth -- one face will always be hidden -- the most you can see is half of the surface.
  3. 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



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