A satellite completes its full rotation around the Earth in a circular path every hours.
If the radius of the Earth is approximately km, and the distance between the satellite and the surface of the Earth is km, find the distance that the satellite covers in 2 hours approximating the result to the nearest kilometer.
The path of the satellite is a circle with a radius equal to the sum of the radius of the Earth and the distance between the surface of the Earth and the satellite.
Since the satellite completes one full rotation around the Earth every 6 hours, the arc it travels in during this time is subtended by a central angle measuring , which can be converted to . In 2 hours, the arc the satellite travels in is subtended by a central angle , or , as large, so the central angle measures
The radian measure of the central angle of a circle is equal to the ratio of the length of the arc the angle subtends to the radius of the circle. Thus, for an angle , an arc length , and a radius , it holds true that
Multiplying both sides of this equation by gives
Using the Symmetric Property gives
Substituting into for and km for gives
Simplifying gives km, so the satellite covers approximately km in 2 hours.