Transcript The Law of Universal Gravitation

The Law of
Universal
Gravitation
1
A little background…


Legend has it that Sir Isaac Newton was struck on
the head by a falling apple while napping under a
tree. This prompted Newton to imagine that all
bodies in the universe are attracted to each other
in the same way that the apple was attracted to the
Earth.
Newton analyzed astronomical data on the motion
of the Moon around the Earth and stated that the
law of force governing the motion of the planets
has the same mathematical form as the force law
that attracts the falling apple to the Earth.
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Newton’s Law of Universal Gravitation

every particle in the universe attracts every other
particle with a force
 The
force is directly proportional to the product of
their masses
 The force is inversely proportional to the square of the
distance between them.

So, if the particles have masses m1 and m2 and are
separated by a distance d, the magnitude of the
gravitational force is:
G  m1  m2
F
2
d
3
A closer look…

G is the universal gravitational constant, which
has been measured experimentally as
2
N

m
-11
6.67 x 10
.
2
kg

The distance, d, between m1 and m2 is
measured from the center of m1 to the center of
m2.
4
Remember Third Law?

By Newton’s third law,
the magnitude of the
force exerted by m1 on
m2 is equal to the force
exerted by m2 on m1,
but opposite in
direction. These
gravitational forces
form an actionreaction pair.
5
Properties of the Gravitational Force:


The gravitational force acts as a long range force,
which exists between two particles, regardless of
the medium that separates them.
The force varies as the inverse square of the
distance between the particles.
 This
means force decreases rapidly with increasing
distance between the particles.

The force is directly proportional to the mass of
each particle.
 This
means, a larger mass will yield a larger force
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Weight and Gravitational Force

Weight was previously defined as FW = m·g, where g is
the magnitude of the acceleration due to gravity. So,
m g 

GM p m
d
2
The object’s mass, m, cancels out, giving us (surface
gravity). Or, the gravitational acceleration experienced
when above the surface of earth:
G  Mp
g
2
d
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Formula Summary
G  m1  m2
F 
2
d
= 5.97 x 1024 kg
rE = 6.37 x 106 m
G = 6.67 x 10-11 Nm2/kg2
ME
g
GM p
d
2
5280 ft = 1 mile
 3.28 ft = 1 m

8
Try calculating these…
6.67
-11
10
x
x 2000 =
6.67 x 10-11 x 52 =
-11
24
6.67 x 10
x 5.98 x 10 =
9
Example 1) Two masses, 25000 kg and 80000
kg, are separated by 200 meters. What is the
force of attraction between them?
10
Example 2) What is the force of attraction
between a 2000 g mass and a 4000 g mass if
their centers are 15 cm apart?
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