1. Gravity and Motion

2. Kepler’s Theory of Planetary Motion
1. Paths are ellipses and sun at the focus
2. Planets move faster when closer
3. Relationship between distance and period of orbit

3. Isaac Newton ( )
Published Principia in 1687 that introduces mass, his laws of motion, and mathematical description of gravity
Key: Gravity provides a mechanism and explanation for Kepler’s Laws (explains why Kepler’s laws worked)

4. Newton’s Laws
1st Law: Object in motion…stays in motion (straight line, constant speed) if no net force acts on it.
Ex. Voyager satellite is still moving outside the solar system in a straight line

5. Newton’s Laws 2nd Law: F=ma
A total net force on an object causes an acceleration.
Ex. A 40 N force is applied to an 8 kg bowling ball. What is the acceleration?
F = ma
40 = (8)(a)
a= 5 m/s2 [divide on each side by 8]

6. The Balance of Forces

7. Newton’s 3rd Law of Action and Reaction--if A pulls on B, then B pulls on A
(the gravitational force between both galaxies is the same…but the smaller one will experience a greater acceleration because it has less mass)

8. Newton’s Law of Universal Gravitation
Plain english: mass attracts mass for no other reason than just that….but they need to be large masses.
Ex. Cloud of gas particles will collect together
Ex. Planets will pull on each other
Ex. The moon pulls on earth and vice versa
Ex. You are pulled down toward the earth

9. Collection of Gases--a stellar nursery…gas clouds pull together to form stars

10. Gravity
Depends on the two masses attracting each other…if both double, then the force between them will (2x2=4) quadruple.
Depends on the inverse square of the distance between them. If the distance between them doubles, then F  1/d2 
F  1/22  ¼ of the force
…if the distance triples, then
F  1/32 1/9 of the force

11. Centripetal Forces and Circular Motion--anything orbiting must have a force acting on it…in astronomy, that’s usually gravity.

12. Newton’s Thought Experiment on Orbital Motion -
the same gravity that causes things to fall down is what causes the moon to orbit earth
Gravity pulls satellites around the earth…

13. Why do astronauts in a space shuttle orbiting Earth experience weightlessness?
There is no gravity in space
They are too far away from Earth
The space shuttle does not allow them to feel gravity’s effects
They are free-falling around Earth

14. They are free-falling around Earth
Analogy: standing on a scale while in mid-air, falling

15. The Elliptical Orbit of a Planet

16. Kepler’s Third Law Explained by Newton
Balancing the force (called “centripetal force”) necessary to keep an object in circular motion with the gravitational force  expression equivalent to Kepler’s third law,
Py2 = aAU3

17. Also, revised understanding of gravity
Einstein and Relativity (p.100)
Einstein (1879 – 1955) noticed that Newton’s laws of motion are only correct in the limit of low velocities, much less than the speed of light.
 Theory of Special Relativity
Also, revised understanding of gravity
 Theory of General Relativity

18. Two Postulates Leading to Special Relativity (1)
Observers can never detect their uniform motion, except relative to other objects.
This is equivalent to:
The laws of physics are the same for all observers, no matter what their motion, as long as they are not accelerated.

19. Two Postulates Leading to Special Relativity (2)
The velocity of light, c, is constant and will be the same for all observers, independent of their motion relative to the light source.

20. General Relativity A new description of gravity Postulate:
Equivalence Principle:
“Observers can not distinguish locally between inertial forces due to acceleration and uniform gravitational forces due to the presence of massive bodies.”

21.  New description of gravity as curvature of space-time!
This bending of light by the gravitation of massive bodies has indeed been observed:
During total solar eclipses:
The positions of stars apparently close to the sun are shifted away from the position of the sun.
 New description of gravity as curvature of space-time!

22. Another manifestation of bending of light: Gravitational lenses
A massive galaxy cluster is bending and focusing the light from a background object.

23. Problem
Light has no mass, thus has no gravitational force. So, why does light bend toward objects?

24. Gravity according to general relativity
Mass curves space-time
In essence, light is traveling straight through curved space
You feel gravity because Earth’s mass causes a curvature of space-time. The mass of your body responds to that curvature by accelerating towards Earth’s center.
All masses cause curvature. The larger the mass, the more severe the curvature. That’s gravity.
Trampoline analogy

25. The Tides (see p. 98 in textbook)
Caused by the difference of the Moon’s gravitational attraction on the water on Earth
Forces are balanced at the center of the Earth
Excess gravity pulls water towards the moon on the near side
Excess centrifugal force pushes water away from the moon on the far side
 2 tidal maxima
 12-hour cycle

26. Differences in Gravitational Force
--why there are tides on earth

27. The Tidal Distortions of the Earth and Moon

28. Tidal Acceleration

29. Spring and Neap Tides