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Kepler believed the Copernican model and sought to prove that it was correct using Brahe’s data for the positions of the planets.

He found that

Planets orbit in elliptical paths (not circles!) with the Sun at one focus of the ellipse.

A line from the Sun to a planet will sweep out the same area in a certain time interval, regardless of where the planet is in its path.

The ratio of the (period)2 to (semi-major axis)3 was the same for every planet.

He described the planets’ orbits, but could they be explained? Kepler answered “What?” but didn’t know “Why?”

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Isaac Newton formulated three laws of motion and a law of gravitation.

This model for understanding motion (how motion is related to forces) and gravitation explained Kepler’s three laws.

When “Why?” matches “What?” (theory matches observation), we must reexamine our dearly held beliefs.

This happened again in 1911 with Einstein’s publication of the General Theory of Relativity

an entirely different explanation of gravity

explained phenemena that Newton’s law of gravitation could not explain.

has been verified by experiment to this day

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details

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Kepler’s first law

planet’s orbit the Sun in ellipses, with the Sun at one focus.

the eccentricity of the ellipse, e, tells you how elongated it is.

e=0 is a circle, e<1 for all ellipses

e=0.02 e=0.4 e=0.7

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Experiment and theory

Slide 13

eccentricity of the planets

Slide 14

Kepler’s second law

The line joining the Sun and a planet sweeps out equal areas in equal time intervals.

As a result, planets move fastest when they are near the Sun (perihelion) and slowest when they are far from the Sun (aphelion).

simulation 1

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If it sweeps out equal areas in equal times, does it travel faster or slower when it is far from the Sun?

- Topics
- A little drama
- Aristotle’s shoes
- Then came Ptolemy
- Finding a needle in a haystack
- Standing on the shoulders of giants
- Kepler’s laws of planetary motion
- Practice
- Newton’s laws of motion
- Newton’s law of gravitation
- Gravitational force and distance
- Deriving Kepler’s laws

- Solar Energy
- Upcoming Classes
- Newton’s Laws of Motion
- Ch 9 Nuclear Radiation
- Geophysical Concepts, Applications and Limitations
- Mechanics Lecture
- Buoyancy

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