Orbiting Satellites

As a satellite such as the Moon orbits the Earth, it is pulled toward the Earth with a gravitational force that is acting as a centripetal force. As described in chapter 8, the inertia of the satellite would cause it to tend to follow a straight-line path, but the centripetal gravitational force pulls it toward the center of the orbit. Although we often approximate the orbits of satellites around the Earth (or Sun, in the case of the orbits of the planets) as circular, they are actually elliptical, with the Earth (or Sun) located at one focus of the ellipse.

Comets follow highly elliptical orbits around the Sun. Halley’s comet takes only a few months to get around the Sun on its closest approach, but it takes more than seven decades to reach its farthest point from the Sun and then return.

This means that there are times when the satellite is closer to the Earth than other times. If the satellite is at point A in the figure above, the gravitational force acting on the satellite is greater than at point B, and the speed at A is greater than at B. This is consistent with the law of conservation of angular momentum discussed in chapter 8:

This equation shows that the closer the satellite gets to the planet (smaller r), the faster it goes (larger v). As the satellite orbits, potential energy and kinetic energy each change, but total energy (potential plus kinetic) remains constant.

Both the total energy and angular momentum of a satellite remain constant.

Example: A satellite orbiting the Earth moves from point A to point B in an elliptical orbit as shown below.

Fill in the table below with increases, decreases, or constant to describe the quantities related to the orbit as the satellite moves from point A to point B.

Quantity	Increases, Decreases, Constant
Speed
Angular momentum
Kinetic energy
Total energy
Gravitational force

Solution:

Quantity	Increases, Decreases, Constant	Explanation
Speed	Decreases	The satellite is moving farther away from the planet and slowing down.
Angular momentum	Constant	Conservation of angular momentum
Kinetic energy	Decreases	Since the speed is decreasing, the kinetic energy must also be decreasing.
Total energy	Constant	Conservation of total energy
Gravitational force	Decreases	The satellite is getting farther away, thus the force is getting weaker due to the inverse square law.

Things to Remember

• Newton’s law of universal gravitation
  • Gravitational force
  • Gravitational acceleration
• Orbiting satellites