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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. 13.2 – The Falling Moon.

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13 1 the falling apple
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


13 2 the falling moon
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


Variation of falling acceleration
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)


13 3 the falling earth
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


13 4 newton s law of universal gravitation
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


Measuring g
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


Measuring g cont
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


13 5 gravity distance the inverse square law
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)



13 6 gravitational field
13.6 – Gravitational Field distance, as 1/r

  • 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


13 7 gravitational field inside a planet
13.7 – Gravitational Field Inside a Planet distance, as 1/r

  • Gravitational acceleration decreases as you move towards center

  • Because of mass above as well as below

  • Gravity in center = zero


13 8 weight weightlessness
13.8 – Weight & Weightlessness distance, as 1/r

  • 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 9 ocean tides
13.9 – Ocean Tides distance, as 1/r

  • 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



Other types of tides
Other Types of Tides than moon

  • 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


13 10 black holes
13.10 – Black Holes than moon

  • 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


Gravitational field near black holes
Gravitational Field Near Black Holes than moon

  • 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


13 11 universal gravitation
13.11 – Universal Gravitation than moon

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


Project orion
Project Orion than moon

  • http://www.youtube.com/watch?v=E3Lxx2VAYi8

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


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