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13.1 – The Falling Apple

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- 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

- 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

- 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)

- 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

- 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

- 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

- 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

- 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)

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

- 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

- Gravitational acceleration decreases as you move towards center
- Because of mass above as well as below
- Gravity in center = zero

- 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

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

- 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

- 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

- 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

- 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

- 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

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

- http://www.youtube.com/watch?v=E3Lxx2VAYi8
- http://www.youtube.com/watch?NR=1&v=V1vKMTYa40A&feature=endscreen