Question

Given that the Moon orbits Earth every 27.3 days and that it is an

average distance of 3.84 x 10° m from the center of Earth, calculate
the period of an artificial satellite Given that the Moon orbits Earth every 27.3 days and that it is an
average distance of 3.84 x 10° m from the center of Earth, calculate
the period of an artificial satellite orbiting at an average altitude of
1,500 km above Earths surface. (Radius of Earth is 6380 km.) at an average altitude of
1,500 km above Earths surface. (Radius of Earth is 6380 km.)

Answer 1

To calculate the period of an artificial satellite orbiting at an average altitude of 1,500 km above Earth's surface, we can use Kepler's third law. By adding the height above Earth's surface to the radius of Earth, we can find the orbital radius of the satellite. Using Kepler's third law, we can then calculate the period of the satellite.

The period, or time for one orbit, is related to the radius of the orbit by Kepler's third law. We can use this law to calculate the period of an artificial satellite orbiting at an average altitude of 1,500 km above Earth's surface.

Let's use the subscript 1 for the Moon and the subscript 2 for the satellite. The given information tells us that the orbital radius of the Moon is r₁ = 3.84 × 10⁸ m, and the period of the Moon is T₁ = 27.3 days.

To calculate the period of the satellite, we need to find the orbital radius of the satellite by adding the height above Earth's surface (1,500 km) to the radius of Earth (6,380 km).

Now that we have all the quantities, we can use Kepler's third law to calculate the period (T₂) of the satellite.