1. Gravity

2. Classical Mechanics Physics Thermodynamics Electromagnetism Modern
1600 to
1900
Classical
Physics
Mechanics
Thermodynamics
Electromagnetism
1940
Modern
Relativity
Large speeds (108 m/s).
Quantum Mechanics
Very small scales (10-10 m).
present
Current
Particle Physics
Cosmology

3. From the marriage of Particle Physics and Cosmology in the early 1970s a picture of the universe began to emerge. WMAP has contributed some of the most accurate data to date.

4. Carina Nebula in our Galaxy

5. Andromeda Galaxy – a “close neighbor”

6. Spitzer shows Andromeda much larger than previously thought
Spitzer shows Andromeda much larger than previously thought. Eventually our galaxy will collide with Andromeda in about 5 – 10 billion years.

8. Hole in Universe billions of light years. August 24, 2007
Hole in Universe billions of light years. August 24, WMAP shows a cold spot and their radio wave data show the hole is nearly devoid of matter.

11. 13.1 Newton’s Universal Law of Gravity

12. Do 13-6

14. Caveats to Universal Law
Does 1/r2 hold to very small scales (~1 mm)?
Is G(t)?
3 Body Problem
General Relativity

15. Concept Question 13.1 A. B. C. D. E.

16. 13.2 Measuring the Gravitational Constant
G = 6.67 x Nm2/kg2

17. 13.3 Freefall Acceleration and the Gravitational Force
Problem
Using Newton’s framework (Newton’s Laws) and the Universal Law of Gravity, find an expression for g (acceleration of gravity) at the surface of the Earth given ME, RE, and G.

18. 13.4 Kepler’s Laws and the Motion of Planets
K1: Planet orbits about Sun are ellipses.

20. K2: Planets sweep out equal areas in equal times as the orbit the Sun.
K3: The square of the planet’s period is proportional to the cube of the planet’s semimajor axis (a). The semimajor axis is roughly the average distance of the planet from the Sun.
Squeak Demo

21. Show how to obtain the Universal Law from Kepler’s Third Law.
T2 = KSa3
Do P (p. 413)

22. Concept Question 13.2 A. B. C. D. E.

23. This question is asking about the dependence of the force of Earth’s gravity on mass. The force of the Earth on a mass m is directly proportional to m. F = mg = ma so a = g a constant Common misconception - The student indicates that the gravitational force is the same magnitude for all objects near the earth. Correct answer

24. Common misconceptions - Objects in water have a smaller gravitational force by Earth because the water pushes up (e.g., the scale reading underwater is interpreted as a measure of the gravitational force) or Earth's pull on an object is a magnetic force or Earth's gravitational force of an object is proportional to the water pressure acting down on it. Correct answer

25. Common misconceptions - The student thinks the distance between objects does not affect the size of the gravitational force or the student does not understand the factors that affect the strength of the gravitational force. Correct answer

26. 13.5 The Gravitational Field^ r mT M ^ k
“Point” Mass
Uniform Field near Earth’s Surface
Gravity Fields – Two Cases

27. 13.6 Gravitational Potential Energy

29. 13.7 Energy Considerations in Planetary and Satellite Motion
E = K + U is conserved because gravity is a conservative force (work is independent of the path).
For a circular orbit:
K = GMm/2r U = -GMm/r E = -GMm/2r
Note: K  0 K = |E| K = |U|/2

30. 13.7 Energy Considerations in Planetary and Satellite Motion
Do 13.32, and 13.51

31. Concept Question 13.3
total energy A. B. C. D. E.

32. Force Law(s): Universal Law of Gravity
Thinking Map
Reflect: How can this be used? Is it reasonable?
Simplifications: Earth uniform and perfect sphere, neglect air resistance
Input Parameters: G, ME, RE
Newton’s Laws: Calculate the acceleration of gravity at the Earth’s surface
What do I need to know?
Output: g
Generalizations: What is g(r)? Other planets?
Mathematics: algebra
Force Law(s): Universal Law of Gravity