1. Johannes Kepler December 27, 1571 – November 15, 1630
Kepler is most remembered for "cracking the code" that describes the orbits of the planets.

2. His works provided one of the foundations for Isaac Newton's theory of universal gravitation.
But prior to Newton……
Ptolemy (Greek) geocentric model of the universe
Copernicus -heliocentric, Earth revolved around the Sun
Tycho Brahe - detailed measurements of planets

3. The Law of Ellipses
-explains that planets are orbiting the sun in a path described as an ellipse (with the sun being located at one of the foci of that ellipse)
...Newton calculated that satellites (moon) are circular and comets are parabolas or hyperbolas

4. The Law of Equal Areas
-describes the speed at which any given planet will move while orbiting the sun.
The speed at which any planet moves through space is constantly changing.
A planet moves fastest when it is closest to the sun and slowest when it is furthest from the sun.

5. The Law of Equal Areas..relates speed/distance
As a planet moves in its orbit, it sweeps out equal amounts of areas in equal amounts of time

6. The gravitational slingshot effect
The gravitational slingshot is a way that scientists have truly harnessed the gravitational pull of a planet by using it to launch satellites and other useful projectiles towards their desired locations

7. Review
Earth’s orbit is slightly elliptical. In fact, Earth is closer to the Sun during winter. (in the northern Hemisphere) than it is during the summer.
Is the speed of Earth during the winter greater than, less than or the same during summer?

8. The Law of Harmonies
The period of a planet (the time for one revolution) depends on the mass of the planet it is orbiting (not the planet or moon itself)
Unlike Kepler's first and second laws that describe the motion characteristics of a single planet,the third law makes a comparison between the motion characteristics of different planets.

9. T²/R³ Planet Period Average Mercury 0.241 0.39 0.98 Venus .615 0.72
(yr)
Average
Distance (au)
T²/R³
(yr2/au3)
Mercury
0.241
0.39
0.98
Venus
.615
0.72
1.01
Earth
1.00
Mars
1.88
1.52
Jupiter
11.8
5.20
0.99
Saturn
29.5
9.54
Uranus
84.0
19.18
Neptune
165
30.06
Pluto
248
39.44
Observe that the T2/R3 ratio is the same for Earth as it is for mars. In fact, if the same T2/R3 ratio is computed for the other planets, it can be found that this ratio is nearly the same value for all the planets (see table below). Amazingly, every planet has the same T2/R3 ratio.

10. Geosynchonous satellites...being on the same rotation as the Earth
Communications and weather satellites have a period of one day IF the radius is at the correct value
A lower satellite will orbit quickly
A higher satellite too slowly

11. Kepler’s legacy
The three laws of planetary motion are an intellectual high water mark.
The Sun was now firmly at the center of the Solar system.
For the first time, Kepler introduced celestial motion that was not circular. (The Greek idea that motion in the heavens must be circular had lasted over 2,000 years.)
Kepler was aware of the fact that his model was lacking in dynamics. He had discarded Ptolemy’s model, and with it his theory of motion, but there was now no theory to say what made the planets move in these ellipses.