Question

A space camera circles the Earth at a height of h miles above the surface. Suppose that d distance, IN MILES, on the surface of the Earth can be seen from the camera.

(a) Find an equation that relates d and h.

(b) If d is to be 3500 miles, how high must the camera orbit above Earth?

(c) If the camera orbits at a height of 400 miles, what distance d on the surface can be seen?

Answer 1

surely you could have looked up the radius of the earth for us, which is needed to do the question.

Answer 2

A space camera circles the Earth at a height of h miles above the surface. Suppose that d distance, IN MILES, on the surface of the Earth can be seen from the camera.
(a) Find an equation that relates d and h.
(b) If d is to be 3500 miles, how high must the camera orbit above Earth?
(c) If the camera orbits at a height of 400 miles, what distance d on the surface can be seen?

Draw a circle with center O. Locate a point C outside the circle.
Draw lines from point C to the tangency points on both sides of the circle.
The arc length between these two tangency points is the distance "d" visible to the camera.
With the earth's radius of 3963 miles. the central angle between the two tangency points is defined by µ = (2)arccos(3963/h + 3963))º.
Therefore, the visible distance "d" = Rµ, where µ is in radians.

This should enable you to find the other two answers you seek.

Answer 3

Here is the raidus of Earth as given in the book:

3960 miles.

Answer 4

Here is the raidus of Earth as given in the book:

3960 miles.