1. Announcements Homework 4 due Monday Happy equinox (tomorrow)!

2. Universal Gravitation 22 September 2006

3. Why does the apple fall? Gravity: A force exerted on the apple, by the earth (How is this possible? No idea.)

4. Gravity acts continuously!

5. Do apples fall faster than pumpkins? The same force would accelerate an apple much faster than a pumpkin. Gravity must compensate by pulling harder on the pumpkin.

6. Experimental Proof

7. Why doesn’t the moon fall? It does! But it’s also moving sideways.

8. Apples vs. Moons A dropped apple falls 5 meters in the first second. The moon “falls” 0.0014 each second. 5 / 0.0014 = 3600 = (60) 2 But the moon is 60 times farther from earth’s center than the apple, so earth’s gravity weakens in proportion to the square of the distance from earth’s center.

9. Newton’s Law of Gravity Force of Gravity = (constant) x So at double the distance, the force is 4x weaker; at triple the distance, the force is 9x weaker; at 10x the distance, the force is 100x weaker; and at 60x the distance, the force is 3600x weaker. (Mass 1) x (Mass 2) (Distance) 2

10. Kepler’s first law

11. Rules, Phenomena

12. Propositions

13. The Newtonian Universe Planets and moons are just chunks of ordinary nonluminous matter, like the earth. Planets and moons just drift through empty space, held in their orbits by gravity. The particular sizes and shapes of the orbits are artifacts of the past. Our sun is the source of all light in the solar system. The stars are probably other suns, scattered through space, dimmed by their enormous distances from us. The universe has no obvious center. Nature is governed by universal, mathematical laws.

14. Orbit Illustration