chapter 13 - universal gravitation

```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
 If the moon did not accel,
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
 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
 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
 Discovered gravity acts
 A constant is needed, G
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
 Later (much after
Newton) found to be
exceedingly small
 G = 6.67 x 10-11
 Shows that gravity is
extremely weak
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.
 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
 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
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
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
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
 Anytime something falls (free
fall), it is “weightless”
 Jumping off a building
 Astronauts in shuttle falling
around the earth
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
 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
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
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
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
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
Project Orion
om/watch?v=E3Lxx2V
AYi8
om/watch?NR=1&v=V
1vKMTYa40A&feature
=endscreen
```
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