Transcript Newton`s Law of Universal Gravitation

Moon
Apple
The Law of Universal Gravitation
Isaac Newton’s Big Idea
Earth
Newton’s Big Idea
• The centripetal force that holds the moon
in orbit is the same force that pulls an
apple toward the ground
• Orbiting objects are in free-fall!
– They never hit the ground because they are
moving sideways fast enough
– Recall that an object in free-fall experiences
only one force: gravity
Gravitational Force
• Gravitational force is the mutual force of
attraction between objects with mass
– Gravity acts between any two objects with
mass
– The closer the objects, the greater the force
– Gravity holds the Moon in orbit around Earth
– Gravity holds the planets in orbit around the
Sun
– The gravity we feel on Earth comes from the
enourmous size of the Earth’s mass
Gravitational Force (cont.)
• Newton’s Law of Universal Gravitation:
m1m2
Fg = G
r2
where
Fg is the gravitational force
m1 is the mass of object 1
m2 is the mass of object 2
r is the dist. between the objects
G is the constant of universal
gravitation (= 6.673  10-11 N·m2/kg2)
Details of NLUG
•
Gravitational force:
1. Is attractive
2. Points toward the center of the other object
3. Comes in force-pairs that are equal in
magnitude, opposite in direction
4. Distance, r, is center-to-center
Moon
Fg
Earth
Fg
r
Example
• What is the force of the Earth on the Moon?
Fg = Gm1m2/r2 =
(6.673  10-11 Nm2/kg2 )(5.97  1024 kg)(7.35  1022 kg)
(3.84  108 m)2
= 1.99  1020 N
• What is the force of the Moon on the Earth?
Gravity on Earth
• Let’s apply NLUG to objects near the
surface of Earth
– We already know that Fg = mg where m is the
mass of an object at the Earth’s surface
– Let M = mass of Earth, R = radius of Earth
– Objects on Earth are approx. a distance R
from the center
m
R
Earth
mass = M
Gravity on Earth (cont.)
– Combine Fg = mg with NLUG:
mg = Fg = GmM/R2
– We get the formula for the acceleration due to
gravity, “little g”, in terms of G, M, and R
g = GM/R2
• This formula can be generalized for any
planet P
gP = GMP/RP2
Examples
• On Earth we have
g = (6.673  10-11 Nm2/kg2 )(5.97  1024 kg)
(6.38  106 m)2
= 9.79 m/s2
• On Mars we have
g = (6.673  10-11 Nm2/kg2 )(6.42  1023 kg)
(3.40  106 m)2
= 3.71 m/s2
What was Newton’s Big Idea?
1. The force that holds the moon in
orbit is a different kind of force
than the force that makes an
apple fall.
2. Both the Moon and a falling apple
are in free-fall in the Earth’s
gravitational field.
3. What goes up, must come down.
4. Gravity doesn’t affect the Moon; it
only affects falling objects like
apples.
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The Moon doesn’t crash into the
Earth because the Moon
1. does not experience the pull
of gravity.
2. moves in a perfectly circular
orbit.
3. is moving sideways fast
enough to stay in orbit.
4. experiences other forces
from the sun and planets.
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The Earth and Moon put gravitational
forces on each other. What can we say
about the size of those forces?
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Force on Earth < Force on Moon
Force on Earth > Force on Moon
Force on Earth = Force on Moon
It varies: sometimes the force on
the Moon is bigger than the force
on the Earth, or vice versa
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The direction of the gravitation force
between two objects is such that
1. the two objects attract each other 100%
exactly along the line connecting
their centers.
2. the two objects repel each other.
3. the two objects sometimes attract
each other and sometimes repel
each other.
4. the two objects attract each other
but at an angle of up to 90.
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What is the role of distance on
gravity?
1. The closer two objects are, the
smaller the force of gravity.
2. The closer two objects are, the
greater the force of gravity.
3. Gravity doesn’t change with
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distance.
4. The force of gravity decreases
as objects get closer together.
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