Around The World

To model how satellites orbit Earth.

BACKGROUND:

The manner in which satellites orbit Earth is often explained as a balance that is achieved when the outward-pulling centrifugal force of a revolving object is equal to the inward pull of gravity. However, if we examine Isaac Newton's First Law of Motion, we can see why this explanation is incomplete. According to this law, objects in motion remain in motion in a straight line unless acted upon by an unbalanced force. Because Earth-orbiting objects follow elliptical paths around Earth and not a straight line, forces cannot, by definition, be balanced. Force is directional. It is a push or a pull in a particular direction. At any one moment, the force of gravity on a satellite is exerted in the direction of a line connecting the center of mass of Earth to the center of mass of the satellite. Because the satellite is not stationary, the direction of this line, and consequently the direction of the force, is constantly changing. This is the unbalanced force that curves the path of the satellite.

A second problem with the satellite orbit explanation is that centrifugal force is not an actual force but an effect. The difference is important. For example, if you are a passenger riding in a car that makes a sharp turn to the left, you feel yourself pushed against the right side door. This is interpreted as an outward directed force but is it really an outward directed force? What would happen to you if the door were to open suddenly? Rather than try to answer these questions in an automobile, a simple demonstration can be done. Attach a ball to a string and twirl the ball in a circle as you hold the other end of the string. The ball travels on a path similar to a satellite orbit. Feel the outward pulling force as you twirl the ball. Next, release the ball and observe where it goes. If that force you experienced were really outward, the ball would fly straight away from you. Instead, the ball travels on a tangent to the circle.

What is actually happening is that the ball is attempting to travel in a straight line due to its inertia. The string acts as an unbalanced force that changes the ball's path from a straight line to a circle. The outward pull you feel is really the ball's resistance to a change in direction. Through the string, you are forcing the ball from a straight path to a circle. In the case of the automobile example, if the door were to pop open during a turn, you would fall out of the car and continue moving in the same direction the car was moving at the moment the door opened. While you perceive your motion as outward, the automobile is actually turning away from you as you go in a straight line.

In this demonstration, a simple model of a satellite orbiting Earth is created from a large stationary ball and a smaller ball at the end of a string. The ball and string become a pendulum that tries to swing toward the middle of the globe. However, the ball travels in an orbit around the globe when it is given a horizontal velocity in the correct direction. Although the small ball attempts to fall to the center of the larger ball, its falling path becomes circular because of its horizontal velocity.