Chapter 13
Universal Gravitation
Observations:
http://www.youtube.com/watch?v=_-gdzOxe7aE
an apple always falls to the ground.
Newton reasoned:
if the tree was twice as tall, would the apple still fall?
If the tree was taller still , would the apple still fall?
What if the tree as as tall as the Moon….
http://www.youtube.com/watch?v=D5BQkdyAw8A
thought experiment
http://www.youtube.com/watch?v=MpiknSRTmT4
horizontal projectile: if the speed is high enough, the cannonball
will fall and never reach the ground.
Science in a minute: universal gravitation law
http://www.youtube.com/watch?v=Jk5E-CrE1zg
Newton did not discover gravity.
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Newton discovered gravity is universal.
The Moon is a projectile that falls around the Earth
The tangential speed of the moon is so high that it falls parallel
to the surface of the Earth.
Similarly, the Earth falls around the Sun
Newton’s law of gravitation:
Fgrav = G M1 M2
R2
G = universal gravitational constant
G = 6.67X10-11 N • m2
kg2
G was measured by Cavendish
https://www.youtube.com/watch?v=rpH5I9fN1sI
Gravitational force is an inverse-square law
Gravity weakens by 1/distance2
if two objects are moved 2X further apart, the Fgrav is reduced
to ¼ of original amount
if objects moved 3X further apart, Fgrav reduced to 1/9 of
original amount.
2
A gravitational field surround the Earth. Any object near the
Earth experiences the Earth’s pull.
Field lines close to Earth’s surface
Field lines in near Earth:
Notice:
The direction of the field lines is towards the Earth = attraction
Field lines are perpendicular to the Earth’s surface
Field lines never cross.
The gravitational force on Earth’s surface is “constant”.
3
The gravitational field inside the Earth VARIES.
Nova:
http://www.youtube.com/watch?v=NOHBDiR5urE
gravitational force ½ distance to center of Earth = ½ gravity on
Earth’s surface.
gravity at center of Earth = 0. Why??
Weight = mg = mass X acceleration due to gravity
If you free fall, then you experience “weightlessness”
http://www.youtube.com/watch?v=ry8Eqx7VFSQ
http://www.youtube.com/watch?v=tAUXIEr-VzM
ocean tides: caused by difference in the gravitational pull of the
Moon [and Sun] on opposite sides of the Earth.
moon tides : neap and spring
4
http://www.youtube.com/watch?v=YHnNGAwcDls
http://www.youtube.com/watch?v=VJPPFs81JbY
http://www.youtube.com/watch?v=wpkBEiHtjsE
Black holes
Stars are formed by gravity.
5
Gravity ultimately crushes a star when the fuel runs out.
When extremely massive stars collapse, the density of the
shrunken star is so great that even light cannot escape from the
gravitational field.
http://www.youtube.com/watch?v=p_o4aY7xkXg
And if you travel too close to a black hole…
http://www.youtube.com/watch?v=AUSVtjjWu3g
http://www.youtube.com/watch?v=lcEHQzWhGsw
Effects of Universal Gravitation
Formation of the Solar System
Used to predict presence and location of Neptune
Acceleration and expansion of Universe: dark matter and dark
energy - only 4% of Universe is ordinary matter [atoms and
molecules]
Newton’s law of Universal Gravitation is his most important
achievement.
The planets, stars, galaxies can be described by simple
universal mathematical relationships.
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bang: http://www.youtube.com/watch?v=LdtnU69PsqM
http://www.youtube.com/watch?v=iQOHRKKNNLQ
http://www.youtube.com/watch?v=S3toymNZ0Po
http://www.youtube.com/watch?v=zdQ3DNo_sFc
http://www.youtube.com/watch?v=pI47HsCNhjM
http://www.youtube.com/watch?v=_q6CXni6yTE
http://www.youtube.com/watch?v=ByoV7iFNz7Y
http://www.youtube.com/watch?v=MpiknSRTmT4
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http://www.youtube.com/watch?v=Jk5E-CrE1zg
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