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The next figure in the history of the Copernican revolution is Johannes Kepler.

Kepler was a brilliant mathematician,

perhaps the best of his time, well reputed around Europe.

He had a star-crossed life.

He was weak and covered with boils, sickly, bedridden often.

His mother was accused of being a witch and he used a lot of his resources

to get her off that and stop her from being executed, and even later in his life

when he begged Galileo for a telescope, Galileo wouldn't send him a telescope.

So he had some hard luck stories, but his best stroke of fortune was working with

Tycho Brahe and inheriting his wonderful set of observations of the planets and

their motions.

Working with this dataset,

he recognized that the orbits of the planets could not be circular.

They had to be ellipses with the sun at one focus.

And that was a profound innovation and discovery.

It also went against two millennia of thinking the circles and

spheres with the perfection figures of the universe.

And so naturally astronomical objects should follow them.

Reading Kepler's work,

it's possible to see the attraction of that Greek idea from Pythagoras.

And the resistance it caused in him to letting go of the idea of circular orbits,

but he did.

And in his writings, he eventually comes up with three laws that codify the laws of

planetary motion, and still are true today.

The first is that the orbits are elliptical, with the sun at one focus, and

nothing at the other.

Now these ellipses are subtle.

The Earth deviates from circular motion around the sun only by 4%, and

some of the other planets even less.

So these are quite subtle effects, and

the precision of Brahe's data was required to tease that out.

The second observation is law of equal areas, as it's called,

it has a mathematical form, which in its non-uniform motion around the sun.

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Kepler noticed that the planets so

far known in the solar system, perfectly adhere to the scaling in this law.

These three laws of planetary motion do not imply the nature of the gravity force.

That was left for Newton to understand.

But they provided convincing evidence that the Copernican model was the correct model

of planetary motion.

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Kepler's mathematical analysis of Tycho Brahe's data confirms to him that

the orbits of the planets are described very simply as elliptical, and

not circular with the sun at one focus.

And with the speed of motion that varies,

being faster when the planet is closer to the sun than when it is further away.

And also finding a straight mathematical relationship between the mean distance

from the sun and the period of the orbit.

These laws of planetary motion describe the planets known to Kepler and

also the planets found after he died.