Earth Satellites

Earth Satellites

An object that moves around a planet in a closed orbit is called a satellite. The Moon is Earth's natural satellite. But humans have also placed many artificial satellites in orbit around Earth — these are used for communication, weather monitoring, navigation, and scientific research.

The motion of an Earth satellite is governed entirely by the gravitational force of Earth. For a satellite of mass $m$ moving in a circular orbit of radius $r$ (measured from Earth's centre), the gravitational force provides the necessary centripetal acceleration.

Orbital Velocity

For a circular orbit, the gravitational force equals the centripetal force:

Here $M_E$ is Earth's mass, $G$ is the universal gravitational constant, and $v$ is the orbital speed. Cancelling $m$ and one factor of $r$ gives:

This is the orbital velocity — the speed a satellite must have to stay in a circular orbit of radius $r$. Notice that $v_o$ depends only on $r$, not on the satellite's mass. A satellite in a higher orbit (larger $r$) moves slower than one in a lower orbit.

Time Period of a Satellite

The time period $T$ is the time taken to complete one full revolution. For a circular orbit of circumference $2\pi r$: …