Satellite Motion And Angular Momentum

Concept:
Physics - Kepler's Third Law of Planetary Motion.
The square of the time period ( ) of a satellite is directly proportional to the cube of the radius ( ) of its orbit: .
Step 1: Establish the ratio from Kepler's Law.
$ R_1 = R, \quad T_1 = t R_2 = 3R, \quad T_2 = ? T_2 \sqrt{27}t$.

Step 1: Understanding the Concept:
A satellite orbiting at an altitude of approximately above the Earth's equator is known as a geostationary or synchronous satellite.
Step 2: Key Formula or Approach:
The height of a geostationary orbit is specifically calculated so that the satellite's orbital period matches the Earth's rotational period.

Step 3: Detailed Explanation:
The Earth rotates once on its axis every 24 hours.
For a satellite to appear stationary over a single point on Earth (geostationary), it must complete one revolution in exactly the same amount of time as Earth takes for one rotation.
The height of is the standard altitude for such geostationary satellites.
Therefore, its time period must be 24 hours.
Step 4: Final Answer:
The time period of the satellite is 24 hours.