Given that the Moon orbits Earth each 27.3 d and that it is an average distance of 3.84 x 10⁸ m from the center of Earth, calculate the period of an artificial satellite orbiting at an average altitude of 1500 km above Earth's surface.

Strategy
The period, or time for one orbit, is related to the radius of the orbit by Kepler’s third law, given in mathematical form in Let us use the subscript 1 for the Moon and the subscript 2 for the satellite. We are asked to find T₂. The given information tells us that the orbital radius of the Moon is r₁ = 3.84 x 10⁸ m, and that the period of the Moon is T₁ = 27.3 d. The height of the artificial satellite above Earth's surface is given, and so we must add the radius of Earth (6380 km) to get r₂ =(1500+ 6380) km = 7880 km. Now all quantities are known, and so T₂ can be found.

Transcribed Image Text:

2 2 || 3 3