Kepler laws

Description

The purpose of this project is to understand the Kepler laws of planetary motion, and how they derive from the laws of motion and the universal law of gravitation. One needs to understand these key points:

1. What are the laws of motion?

• What is the universal law of gravitation?
• What are the three Kepler laws, and how do they differ from previous heliocentric systems.
• First Kepler law as a consequence of laws of motion. Is possible to have circular orbits?
• Understand the Kepler problem (also known as two-body problem).

Finally one can take several directions to complete the project:

• Explore the limitation of this approach. Newton’s law of gravitation was superseded by Einstein’s general relativity, revealing that the Kepler laws are in fact slightly modified.
• If you like computers and programming, solving the two-body problem by a computer simulation is lot of fun!

The Wikipedia page on the Kepler laws is a great point to start. There are many elementary derivations of Kepler’s laws on the web, like this one, or information from NASA about the Kepler laws.