2. Goals
Explain how accurate observations led to Heliocentric model
Review contributions of Galileo and Kepler
Explain Kepler’s Laws
Explain Newton’s laws of motion and gravity

3. Our life has always depended on the stars
Our life has always depended on the stars. Seafarers needed to navigate and farmers needed to know when to plant.
Our modern calendar was based on the changing heavens.
We have seven days of the week because there were seven movable objects in the heavens.
We have 12 months in a year because there are about 12 lunar cycles in a year.
We have 360 degrees in a circle because it takes about 360 days for the Sun to return to the same spot among the stars.

4. Planetary Motion
Early astronomers were abscessed with perfection and thought the motions of the heavenly bodies should be circles.
They also thought the Earth was stationary because they could not fell the Earth move beneath them.
This led to the Earth centered or Geocentric model of which Ptolemy was the main supporter.
While observations were crude the model seemed to work, but as observation improved it became clear that something was wrong.

5. In order to modify his theory, Ptolemy had to add circles to circles (deferent and Epicycle) to explain retrograde motion.

6. Retrograde motion is defined as the brief westward motion that a planet appears to take when a slower outer planet is passed by a faster inner planet.
While the geocentric model required a complicated set of circles on circles to explain retrograde motion, the Sun centered (Heliocentric) model easily explained the observations. Copernicus was the main supporter for the Heliocentric model.

7. While the Copernican theory did explain the observations better with a simpler model, civilization at the time resisted the model partly because the church of the time had declared the geocentric model as correct with out regard for scientific observations.
What finally convinced everyone was the observations of Galileo Galilei.

8. Using his telescope, Galileo discovered:
the Moon had creators and mountains like the Earth and was not perfect.
the Sun was imperfect (sunspots) and rotated on its own axis.
Jupiter had four moons in orbit around it which showed things could orbit other things besides the Earth.
Venus showed complete set of phases only explainable if it was in orbit around the Sun not the Earth.
Because of his insistence of the Heliocentric model based on his observations, Galileo was excommunicated from the church and was not forgiven until 1992.

10. Kepler
Now that we have the correct heliocentric model we need to explain why it is the way it is.
What causes the planets to orbit the Sun ?
Why do the different planets have different speeds?
How can we predict their positions in the future?

11. Kepler’s Laws of Motion
First Law: The orbits of the planets are in the shape of an
ellipse with the sun at one focus.

12. Second Law: a vector from the sun to the planet sweeps out equal areas in equal times (conservation of angular momentum).

13. Third Law: the period of a planet and its semimajor axis are related by.
P2 = a3

14. Newton’s Laws
While Kepler discovered certain relationships and facts concerning how the planets moved about the Sun he could not explain why.
First Law: objects remain in motion or at rest unless acted upon by a force.
Second Law: F = Ma: where F = force, M= mass, a = acceleration
Third Law: Fg = GMm/d2 Where Fg is the force due to gravity, G is a constant, and M and m are the mass of the two objects, and d is the distance of their separation.

15. Thus gravity provides the force which causes objects to orbit other objects. Newton invented calculus to help him solve his problems

16. Newton’s third law allows us to detect planets around other stars and determine their mass.