## What to Remember from Lesson

There is much misunderstanding of the history of early cosmology up to just before Galileo (whom we'll revisit in the next lesson). Here are some takeaways that speak to some of the legends.

* There were Greeks who proposed models (we talked about one) in which the Sun was at the center of the solar system. These models were rejected for perfectly sane empirical reasons.
* The "crystaline spheres" model of Aristotle, and hence all of the West up to the Baroque period was not compatible with the epicyles model of Ptolemy. In fact almost nobody believed that there were real epicycles, rather that the Aristotelian picture was how things really were. But if you were a doctor and needed to predict the motions of the planets, Ptolemy's model gave you correct answers. It's really remarkably contradictory!
* The picture of the solar system that's taught to every child and credited to Copernicus of all of the planets moving in circles around the Sun is not what Copernicus' model actually said. It couldn't have been his model since we know that the orbits are elliptical, not circluar. So Copernicus would get the wrong answer. He knew that, so he built in his own system of epicycles – as many as Ptolemy – so that his model would predict planet positions correctly. It was no more accurate than Ptolemy's and so everyone pretty much kept using the Egyptian's model, not the Pole's. 
* Kepler is a true intellectual hero in the history of science. Not one person conceived of the orbits being other than circular. They look circular. Circles matched a preconception of the perfection of the heavens. But Kepler all alone proposed that this was wrong. 

Kepler's three laws are essential to an appreciation of a more modern view of planetary science.

1. His First law: the planets travel in elliptical orbits around the Sun, which is positioned at one of the foci of the ellipse. 
2. His Second law: The speeds of the planets in their orbits are not constant. They move faster near the Sun than away from the Sun. What is constant for their orbits is that in the same amount of time, a planet always "sweeps" out the same area between it's orbit and the Sun. 
3. His Third law: in words...The square of the period (the time to complete one orbit) of a planet is proportional to the cube of the mean distance of the planet from the Sun. This proportionality is written as an equation:

$$
\begin{align*}
T^2 &= k_S R^3 \\
k_S &= \frac{T^2}{R^3}
\end{align*}
$$

The constant of proportionality is explicitly written with the subscript "S" since it refers to orbits around the Sun. Anything– a planet, an asteroid, an artificial satellite – that's gravitationally bound (using a Lesson 9 phrase!) to the Sun obeys precisely this relationship with the same value for $k_S$ as the planets. 

Kepler went very close to imagining a force created by the Sun to cause this almost-circular motion to take place. He called what we refer to as a force, a "soul." He also assumed that there must be another forcee that points along the trajectory, which we know is not required or possible in circular or any non-straight motion. He anticipated Newton in many ways.