1. Chapter 8 – Universal Gravitation
8.1 Motion in the Heavens and on Earth
8.2 Using the Law of Universal Gravitation

2. 8.1 Motion in the Heavens and on Earth
Observed Motion
Building upon what we observe
Tycho Brahe ( )
Johannes Kepler ( )
Laws of Planetary Motion
1. Planets travel in elliptical orbits
2. Equal areas in equal time
3. Ratio of period and distance
Kepler's Laws
Kepler Animation

3. 8.1 Motion in the Heavens and on Earth (cont.)
Universal Gravitation
Newton never questioned gravity…only how it worked and how far it extended into the universe!
Gravitational force: the attractive force that exists between all objects.

4. 8.1 Motion in the Heavens and on Earth (cont.)
Universal Gravitation (cont.)
The Law of Universal Gravitation:

5. 8.1 Motion in the Heavens and on Earth (cont.)
Universal Gravitation (cont.)
What does this imply?
Leads to: calculating planetary and satellite motion
Earths weight

6. Chapter 8 Assignment AC+P 1 pp. 194-195 # 17,18,20,25,27
# 32,33,34,36,37,38,48

7. 8.2 Using the Law of Universal Gravitation
Motion of Planets and Satellites
Isaac Newton and the “cannonball projectile”:
What if you shot a cannonball off a cliff with a horizontal velocity – at what velocity would it have to be to never hit the earth?
The earth curves away from the ball:
If it traveled fast enough it would never hit the earth! It would be in orbit – a satellite!

8. 8.2 Using the Law of Universal Gravitation (cont.)
Motion of Planets and Satellites (cont.)
We can calculate what this uniform circular velocity from the equation:
Further, we can rearrange Newton’s version of Kepler’s 3rd Law to calculate the period of the satellite in orbit:

9. 8.2 Using the Law of Universal Gravitation (cont.)
Weight and Weightlessness
Is there any place where gravity (and weight) would be zero?
Then what is “weightlessness” or “zero gravity”?

10. 8.2 Using the Law of Universal Gravitation (cont.)
Gravitational Fields, Mass, and Theories of Gravity
The concept of gravity is changing today – and there are competing models of gravity by scientists around the world.
Newton vs. Einstein vs. Hawking vs. Greene
Where does gravity come from?
What influences gravity?
Relativity, black holes, time travel, etc…

11. Chapter 8 Assignments AC+P 1 pp. 194-195 AC+P 2 pp. 194-196
# 17,18,20,25,27
# 32,33,34,36,37,38,48
AC+P 2 pp
# 22, 23, 29
# 40, 46, 50, 53,55