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# Kepler and his Three Laws

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Queen's University

Physics, Engineering Physics and Astronomy

ASTR 101

Prof.

Fall

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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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