Question

An astronaut is working on a satellite 200 miles above the ground. What is the measure of BD⌢, the portion of Earth that the astronaut can see? Round your answer to the nearest tenth. (Earth's radius is approximately 4000 miles.)

Answer 1

420 miles.

Explanation:

You would have to be infinitely far away from a sphere in order to see exactly 50% of its surface all at the same moment. Using simple geometry, you can prove that an observer that is a distance d away from the surface of a sphere with radius R can only see a percent area A of the sphere's surface as given by the equation:

A = 50%/(1+R/d)

Where A is the area seen,

R is the earth's radius 4000 miles

And D is the distance above the earth 200 miles

50% = 0.5 in fraction

Substituting values we have

A = 0.5(1 + 4000/200)

A = 0.5(1 + 20) = 0.5 x 21

A = 10.5%

10.5% of 4000 miles = 420 miles.