Kepler and his Three Laws

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Queen's University
Physics, Engineering Physics and Astronomy
ASTR 101

Kepler and his Three Laws • Kepler wanted to make sense of Brahe's data by making a radical assumption (against Brahe's last wish) that Copernicus's heliocentric model was a good basis to start with  Assumed the heliocentric model and that Earth's orbit around the sun was nearly circular  A very bold/dangerous assumption, however it is correct  If Earth's orbit was not near circular, there would be extremely variable climate that humans could not withstand  Assuming a circular orbit also allow Kepler to work out the clearly elliptical orbits of the other planets • To map the orbit of other planets, Kepler used Brahe's database of planetary data  Mars orbits the sun once every 687 days, or 1.88 years, meaning that once every 687 days Mars will have made a complete orbit, yet appears in a different location than observed 687 days ago  This occurs because Earth too is moving, and by knowing how long our orbit takes and determining the position of Mars before and after one complete orbit, Kepler mapped out its entire orbit as a series of points  Brahe's data provided MANY observations about Mars's position, allowing Kepler to determine its ecliptic orbit  Kepler and his model were not to scale as he did not know Earth's distance from the sun, thus could only determine Mars's orbit relative to the Earth Kepler's Three Questions • What are the shapes of the orbits? • Do particular planets travel around the sun at constant speeds? What determines a planet's speed at a given moment? • Do particular planets travel at the same speed relative to other planets? How do their orbital periods compare? Kepler's Three Laws • Kepler used Brahe's data to determine the shapes of the planetary orbits  Used the geocentric epicycle and different model to predict where Mars would be at a particular time, however Brahe's data was not in agreement with the prediction  Although the inconsistency was only by 1/8th of a degree, Kepler had so much faith in Brahe he rejected the entire geocentric theory rather than assuming his data was off • Law 1: The orbits of the planets are an ellipse with the sun at one of the fo
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