# Python: Kepler's Laws

## Table of contents

## Activity 1

Kepler's three laws can be stated as:

- Planets move about the sun in elliptic orbits, with the sun at one focus.
- A radius vector connecting any planet to the sun will sweep out equal areas in equal times.
- The square of the period of a planet is proportional to the cube of its mean distance from the sun.

You have access to a simple Python code that integrates the motion of a planet around a fixed star using Newton's laws of motion and Newton's law of gravity. Modify the code as necessary to prove that Newton's laws reproduce Kepler's laws. You might need to brush up on your knowledge of geometry with respect to ellipses. Wikipedia might be helpful.

Your proofs should come in the form of pictures or graphs produced by Python. Print 1 picture per law, and write a little on the sheet if it needs some explaining.

last modified: April 18, 2023, 2:27 p.m.