The angular velocity of a geostationary satellite is equal to the rotational speed of the Earth. A geostationary satellite is positioned in such a way that it orbits the Earth at the same rate as the Earth rotates, allowing it to appear stationary from the ground.
The Earth completes one full rotation on its axis in approximately 24 hours, which corresponds to 86400 seconds. Therefore, the angular velocity of a geostationary satellite is given by:
Angular Velocity = (2 * π) / Time Period
where π is the mathematical constant pi (approximately 3.14159) and the Time Period is 86400 seconds.
Substituting these values into the equation, we have:
Angular Velocity = (2 * 3.14159) / 86400 ≈ 0.0000727 radians per second
So, the angular velocity of a geostationary satellite is approximately 0.0000727 radians per second.