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# Basic Principles and Laws of Planetary Motion

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Source:
Author: Jerry Silver

### The Idea

In this project, you build a simple model of a planet going around the sun. This model exhibits many of the physical properties found throughout the solar system. You can discover for yourself the basic principles of planetary motion as did Copernicus and Kepler, except you won't have to spend years squinting through a telescope on cold winter nights in the middle of the night to do this. This model also provides an intuitive way to visualize Einstein's theory that gravity is the result of a mass curving space.

### What You Need

• bucket or other circular frame
• sheet of Latex, large enough to cover the opening of the bucket
• mass (roughly 50 g)—a 1-inch diameter spherical steel ball would be ideal because it can position itself in the center of the sheet
• marbles, small steel balls

### Method

1. Stretch the Latex on the bucket. Remove the wrinkles.
2. Roll the marble across the sheet and observe the path it takes.
3. Now, place the mass in the center of the sheet. This should cause the sheet to become noticeably distorted. If this is not the case, it may be necessary to increase the mass, but avoid tearing the sheet. The central mass should maintain a fixed position, which can be facilitated, if necessary, by a little tape.
4. Roll a marble in a circular path around the central mass.
5. Observe the motion of the marble. See Figure 14-1.
6. Observe what happens if the marble is rolled faster or slower in a given path. What happens if the marble is closer or farther from the central mass?

### Expected Results

The key observation is that the path followed by the marble is an ellipse. The path may appear circular, but elliptical paths are certainly possible. This is comparable to one of Kepler's observations concerning planetary motion.

Kepler also observed that the closer a planet gets to the sun, the faster it goes. The marbles in this experiment exhibit the same property.

If the marble is given a velocity that is too high, it will not follow the type of elliptical orbit followed by the planets around the sun but, rather, the open hyperbolic orbit followed by meteors.

### Why It Works

Kepler's law can be derived by equating the centripetal force that keeps a planet in orbit to the gravitational attraction between the planet and the sun. The depression created by the central mass exerts a force on the circulating marble that varies with position. Although this force does not exactly decrease with the inverse square of the distance, as does the gravitational attraction between a planet and the sun, it does provide a good approximation.

### Other Things to Try

This experiment also provides an analogy for understanding an aspect of Einstein's theory of general relativity. The idea is that what we call gravity is really a distortion in space caused by the presence of a mass. The distortion of the sheet can be thought to represent the distortion in space, which guides the path of a planet going around the sun. As far-fetched as this may seem at first, light from stars emerging from behind the sun has been observed by astronomers to follow a bent path caused by the sun's mass, confirming Einstein's prediction.

### The Point

Objects in motion around a central mass follow an elliptical path. The closer they get to the central mass, the faster they go.

Gravitational attraction can be thought of as a distortion of space caused by the presence of the mass.