13.1 – the falling apple newton realized all accelerations are caused by net forces the apple...
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13.1 – The Falling AppleNewton realized all
accelerations are caused by net forces
The apple accel to earth in the same way the moon accel to earthThe apple experiences
linear accelThe moon rotationalBoth are caused by the
same net force – earth’s gravity
13.2 – The Falling MoonIf 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 AccelerationAcceleration reduces as
distances increaseObjects 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 EarthThe 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 GravitationDiscovered 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 G150 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.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 LawMuch like spraying butter on toast, gravity is
diluted as a square of the distance2 times as far = 2 squared the force (4x)3 times distance = 3 squared the force (9x)
13.6 – Gravitational FieldSomething created by mass that cause other
masses to experience a forceThe closer to the surface the stronger the field,
and the more force on other massesThe arrows point in direction of force
13.7 – Gravitational Field Inside a PlanetGravitational acceleration decreases as you
move towards centerBecause of mass above as well as belowGravity in center = zero
13.8 – Weight & WeightlessnessNet 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 buildingAstronauts in shuttle
falling around the earth
13.9 – Ocean TidesCaused by differences in gravitational pull of
moon on opposite sides of the earthWater closest to moon is pulled closer (high
tide)On opposite side, earth is pulled and
deformed away from water – also high tideWater 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 smallerSun, Earth & Moon line up – Spring Tide –
extremes in tidesSun, Earth & Moon perpendicular – Neap tide –
leveling of tides
Other Types of TidesPart 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 HolesStars 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 HolesThe black hole has the same mass as the star
creating it, therefore the same gravityMass is so concentrated, the space surrounding
it is distorted and warpedWe “see” them because of their effect on
objects around them
13.11 – Universal GravitationPerturbations in Solar
SystemAll planets tug on all
othersThis 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 Orionhttp://www.youtub
e.com/watch?v=E3Lxx2VAYi8
http://www.youtube.com/watch?NR=1&v=V1vKMTYa40A&feature=endscreen