Question 478787
Hi Yash Shah:

A diagram of the situation would be most helpful in solving this problem:

Draw a circle representing the earth's equator.

Draw a point somewhere outside of the circle to represent the orbiting satellite.

Draw a line connecting the satellite and the centre of the circle.

Draw a line from the satellite to the circumference of the circle so that the line is tangent to the circle.

Draw a line from the centre of the circle to the point of tangency (this is the radius of the circle).

Now you have a picture of a right triangle whose base is the radius of the circle and whose hypotenuse is the line from the centre of the circle to the satellite.

The length of the radius is 4000 miles while the length of the hypotenuse is radius (4000) plus the altitude of the orbiting satellite (22,300) for a total of 26300 miles.

The goal is to find the angle (angle A) between the triangle's base and hypotenuse.

Use the inverse cosine function:

{{{A = Cos^(-1)(4000/26300)}}}
{{{A = 81.25}}}degrees.
But, as you will see from the diagram, this view from the satellite would encompass only half of the visble equator, so double this angle to 162.5 degrees.
Now you need to find out how much of the circle's circumference is subtended by a central angle of 162.5 degrees.
Use the ratio of:
{{{162.5/360 = 0.451399}}} Now multiply by 100 to get the percentage.
{{{(0.451399)(100) = 45.1399}}} or 45.14%