Full Earth
 Q: How many miles away from the Earth must one travel
before he/she could look back and see the entire
circumference of the Earth?
A: A long ways. If you want to see an entire Earth hemisphere--like a full Moon--then you must see along a line that just grazes
one side of the sphere and along another line that grazes the
opposite side to encompass the whole hemisphere.
Figure: [NASA/JPL] Image taken about 1.3 million miles from
the Earth
For a sphere, those two lines are parallel, which means they can
never meet at your eye and you can never see both edges of a sphere at the same time. The Earth
is almost a perfect sphere. So, neglecting distortion due to Earth's atmosphere, the strict answer
to your question is: you must be an infinite distance away.
"...at the height of the International Space Station (about 380 kilometers [240 miles]) you can see
about 5 % of a hemisphere," says Chris Peat of Heavens Above. "At the distance of the Moon
(about 400,000 kilometers [250,000 miles]) this has increased to 98 %."
So, practically speaking--fly to the Moon to see a 98 % full Earth.
Further Surfing:
Heavens Above, satellites and astronomy
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