1. 13.1 – The Falling Apple
Newton realized all accelerations are caused by net forces
The apple accel to earth in the same way the moon accel to earth
The apple experiences linear accel
The moon rotational
Both are caused by the same net force – earth’s gravity

2. 13.2 – The Falling Moon
If the moon did not accel, it would follow a straight line – and leave orbit
It acts like a projectile with such a high velocity the earth curves before the moon can hit the surface
Thus, the moon “falls” around the earth

3. Variation of Falling Acceleration
Acceleration reduces as distances increase
Objects fall 4.9 m in 1 second at the surface, but only 1.4 mm for the moon
Newton used geometry to show gravity lessens by a square of the distance (center to center)

4. 13.3 – The Falling Earth
The earth orbits the sun in a circular path like the moon does
It does this because of gravitation, like the moon
Therefore, the earth “falls around” the sun
If we could stop these objects, they would accel toward one another

5. 13.4 – Newton’s Law of Universal Gravitation
Discovered gravity acts on all objects with mass
Deduced the attractive force is proportional to the masses & inversely proport to distance (from center to center) squared
F α m1 m2 / r2
A constant is needed, G
Later (much after Newton) found to be exceedingly small
G = 6.67 x 10-11
Shows that gravity is extremely weak

6. Measuring G
150 years later (1798), Henry Cavendish measured the first true value
Often referred to as “weighing the earth”
Once “G” is determined, the masses of all celestial objects can be determined

7. Measuring G – Cont. Von Jolly developed a simpler method
Of the 4 fundamental forces, gravity is weakest
Aside from gravity, almost all other “real” forces are due to electromagnetism – another fundamental force

8. 13.5 – Gravity & Distance: The Inverse Square Law
Much like spraying butter on toast, gravity is diluted as a square of the distance
2 times as far = 2 squared the force (4x)
3 times distance = 3 squared the force (9x)

9. Gravitational strength drops off rapidly as you increase distance, as 1/r2, but never gets to zero

10. 13.6 – Gravitational Field
Something created by mass that cause other masses to experience a force
The closer to the surface the stronger the field, and the more force on other masses
The arrows point in direction of force

11. 13.7 – Gravitational Field Inside a Planet
Gravitational acceleration decreases as you move towards center
Because of mass above as well as below
Gravity in center = zero

12. 13.8 – Weight & Weightlessness
Net forces cause accelerations, and present themselves as changes in “weight”
This is the “pushing back” of some surface (normal force)
No “pushing back”, we experience weightlessness

13. Anytime something falls (free fall), it is “weightless”
Jumping off a building
Astronauts in shuttle falling around the earth

14. 13.9 – Ocean Tides
Caused by differences in gravitational pull of moon on opposite sides of the earth
Water closest to moon is pulled closer (high tide)
On opposite side, earth is pulled and deformed away from water – also high tide
Water perpendicular is lower than normal – low tide

15. The sun also causes tides, the overall force is much greater than moon
But, the difference between sides is much smaller
Sun, Earth & Moon line up – Spring Tide – extremes in tides
Sun, Earth & Moon perpendicular – Neap tide – leveling of tides

16. Other Types of Tides
Part of earth’s interior is molten, causing “Earth tides”
The atmosphere is a fluid (it flows) creating “atmospheric tides”
Small bodies of water do not experience tides because the difference from one side to another is too small
Tilt of earth also effects tides

17. 13.10 – Black Holes
Stars are in state of equilibrium – gravity trying to make it smaller & fusion trying to make it bigger
At the end of star’s lives, they swell into red giants
Once out of fuel, it collapses to a black dwarf
More massive stars, the collapse never stops and forms black holes

18. Gravitational Field Near Black Holes
The black hole has the same mass as the star creating it, therefore the same gravity
Mass is so concentrated, the space surrounding it is distorted and warped
We “see” them because of their effect on objects around them

19. 13.11 – Universal Gravitation
Perturbations in Solar System
All planets tug on all others
This causes deviations in orbits – perturbations
Distant planets were discovered using this technique
The Expanding Universe
Universe began with Big Bang (Theory)
All matter spewing outward
Gravity should slow it down, but there appears to be acceleration
Due to dark matter/dark energy

20. Project Orion http://www.youtube.com/watch?v=E3Lxx2VAYi8