chapter 13 - universal gravitation
Download
Report
Transcript 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,
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
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
http://www.youtube.c
om/watch?v=E3Lxx2V
AYi8
http://www.youtube.c
om/watch?NR=1&v=V
1vKMTYa40A&feature
=endscreen