Question

The farthest distance a satellite signal can directly reach is the length of the segment tangent to the curve of Earth’s surface. If a satellite signal could reach an unlimited distance, could half of the Earth’s surface be reached by the signal at one time? Explain.

Answer 1

No.  cos a=r/(r+h), where r is the radius of the earth, h is the distance from the surface of the earth and a is the half angle of the earth subtended.  While a would approach 90 as h approached infinity it could never actually get to 90 degrees.  It is like an asymptote, close but no cigar :)