1. Homework #1 is due tomorrow, Wednesday, September 15, 5:00 pm
Homework #2 will be posted shortly
A number of out-of-class activities will be posted to the class website later this week.

2. Kepler's Laws
1. The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus.
2. The Law of Areas: Planets move faster in their orbit the closer they are to the Sun.
3. The Law of Periods: Planets on larger orbits take longer to complete an orbit than planets smaller orbits.

3. Kepler’s Laws are extremely accurate in their predictions of planetary motions.
They are “empirical”, i.e., they are derived from experiment, experience, and observation rather than from theory or logic
Isaac Newton subsequently demonstrated that Kepler’s laws are the natural outcome of gravity.

4. Two models of the Universe
Geocentric
Heliocentric

5. Which model more accurately depicts nature?
Both make predictions for the apparent motions of the Sun, planets and stars.
The Heliocentric model, with modifications incorporating Kepler’s Laws, gives more accurate predictions
But, the Geocentric model might be made more accurate through appropriate modifications.
Need additional predictions that clearly differentiate between the two models. (need tests)

6. Contemporary with Kepler was the “founder of experimental science”
Galileo Galilei ( ),
the “founder of experimental science”
First person known to point a telescope at the sky
He wanted to connect the physics understood on earth with objects in the heaven
His work got him in trouble with the Church and led to his house arrest for many years.

7. (Some of) Galileo’s Observations
Galileo saw craters and shadows cast by the mountains on the Moon (Moon had a landscape; it was a “place”, not a perfect heavenly body)

8. (Some of) Galileo’s Observations
Galileo saw craters and shadows cast by the mountains on the Moon (Moon had a landscape; it was a “place”, not a perfect heavenly body)
Sunspots (sun not “perfect”)

9. (Some of) Galileo’s Observations
Galileo saw craters and shadows cast by the mountains on the Moon (Moon had a landscape; it was a “place”, not a perfect heavenly body)
Sunspots (sun not “perfect”)
Rotation of sun

10. (Some of) Galileo’s Observations
Galileo saw craters and shadows cast by the mountains on the Moon (Moon had a landscape; it was a “place”, not a perfect heavenly body)
Sunspots (sun not “perfect”)
Rotation of sun
Moons of Jupiter (Heavenly bodies existed which did not orbit the earth)

11. (Some of) Galileo’s Observations
Galileo saw craters and shadows cast by the mountains on the Moon (Moon had a landscape; it was a “place”, not a perfect heavenly body)
Sunspots (sun not “perfect”)
Rotation of sun
Moons of Jupiter (Heavenly bodies existed which did not orbit the earth)
Phases of Venus: the two models of the Universe made two very different predictions.

12. Phases of Venus

13. Galileo observed all phases!
Galileo’s observation of the phases of Venus was the final evidence that buried the geocentric model.
Geocentric
Heliocentric
No gibbous or full phases!
All phases are seen!
Galileo observed all phases!

14. A hallmark of science is that theories are testable

15. Now, a short film describing the scale of the universe and its contents
“Cosmic Voyage”

16. The structure of the universe had been totally changed.
With Galileo’s observations, the revolution begun by Copernicus was nearly complete…
The structure of the universe had been totally changed.
The motions of the planets were understood, at least from a geometrical perspective.
Earth was no longer a “special” place in the universe.
The crowning achievement was yet to come - discovering the laws of nature and that naturally led to the newly determined structure.

17. Sir Isaac Newton (1642-1727) Invented calculus
Invented the reflecting telescope
Connected gravity and planetary forces

18. Universal Law of Gravitation
Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects.

19. Orbital Paths from Law of Gravitation
Extending Kepler’s Law #1, Newton found that ellipses were not the only orbital paths.
All orbits are “conic sections”
ellipse (bound)
parabola (unbound)
hyperbola (unbound)
Orbital motion takes place around the center of mass

20. The Center of Mass
In Kepler's Laws, the Sun is fixed at a point in space (a focus of an ellipse) and the planet revolves around it. Why is the Sun privileged?
Kepler had mystical ideas about the Sun, endowing it with almost god-like qualities that justified its special place.
Newton demonstrated that the the Sun does not occupy a privileged postion and in the process he modified Kepler's 3rd Law.

21. The center of mass is familiar to anyone who has ever played on a see-saw. The fulcrum point at which the see-saw will exactly balance two people sitting on either end is the center of mass for the two persons.
m1d1 = m2d2

22. Recall Kepler’s 3rd law: P2 / a3 = constant
Newton realized that in the planet-Sun system the planet does not orbit around a stationary Sun (a planet exerts as much gravitational force on the Sun as the Sun does on a planet).
Instead, Newton proposed that both the planet and the Sun orbited around the common center of mass for the planet-Sun system.
This led Newton to modify Kepler's 3rd Law.
Fg = Gm1m2/d2
Recall Kepler’s 3rd law:
P2 / a3 = constant

23. Newton’s Version of Kepler’s Third Law
P2 = 42 a3 / G (m1 + m2)
G is known as the universal gravitational constant.
If you can measure the orbital period of two objects (P) and the distance between them (a), then you can calculate the sum of the masses of both objects (m1 + m2).