Law of Universal Gravitation

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Fg
W
mg
g
ag
Do you know the difference??
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Newtons Law of Universal Gravitation
Every body in the universe attracts every other
body with a force that is directly proportional
to the product of the masses of the bodies and
inversely proportional to the square of the
distance between the bodies.
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Newtons Law of Universal Gravitation
When 2 masses are separated by a distance (r)
r
Fg
-Fg
m1
m2
The proportionality constant, G is called the
universal gravitational constant. Its value in
the SI system of units is,G 6.67 ?
10-11Nm2/kg2.
Cavendish link
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The Law of Universal gravitation states that
every object in the universe is attracted to
every other object in the Universe! Greater the
masses greater the force of attraction Greater
the distance smaller the force of attraction
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Effects on Mass
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The more mass an object has, the greater its
force of attraction. You are extremely
attractive.
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Effects of Distance
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Sample Problems
Find the gravitational attractive force between
two identical 50 g spheres with centers .8
meters apart?
G 6.67x10-11 N m2/kg2

• So you use the equation
• Fg GMm/r2
• Fg 6.67E-11.05.05/.82
• Fg 2.61E-13 N

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Weight and Gravitational Attraction.

• Find the weight of a 75 kg person on the planet
  earth.
• 2. Find the gravitational force of attraction
  between a 75 kg person and the Earth?
• mearth 5.98 x 1024 kg
• rearth 6.37 x 106 m

• W 75 X 9.8735 N

• Fg GMm/r2
• 6.67E-11(5.98E24 )(75) / (6.37E6)2
• Fg 737.46 N

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Acceleration Due to Gravity
Calculate g for planet Earth at sea level.
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Example 6
The mass of the Hubble Space Telescope is 11,600
kg. Determine the weight of the telescope (a)
when it was resting on the earth and (b) as it is
in its orbit 598 km above the earth's surface.
Mearth 5.98 x 1024 kg Rearth 6.37 x 106 m G
6.67 x 10-11 N m2/kg2
Answer 114, 027 N 95,295 N
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INNER SPACE

• Down in a cave below the surface of the earth
  there is
• More gravity than at the earths surface
• Less gravity than at the earths surface
• The same gravity as at the surface

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Newtons Law of Universal Gravitation

• Conceptual Questions
• 1. The moon and the Earth are attracted to each
  other by gravitational force. Does the more
  massive earth attract the moon with a greater
  force than the moon attracts Earth? Explain.
• 2. What happens to the gravitational force
  between two masses when the distance between the
  masses is doubled?
• 3. If the Earth were twice as massive but
  remained the same size, what would happen to the
  value of G? g?
• 4. Jupiter has about 300 times the mass of Earth
  and about 10 times earths radius. Estimate the
  size of g on the surface of Jupiter.

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Newton's Thought Experiment on Orbital Motion
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Cannonball

• A cannonball is fired horizontally from a tall
  mountain to the ground below. Because of
  gravity, it strikes the ground with increased
  speed. A second cannonball is fired fast enough
  to go into circular orbit but gravity does not
  increase its speed. Why

Refer to 19 23 in conceptual physics
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Speed of a Satellite
Mem
mv2
Fg G
_________
____
r²
r
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Speed of a Satellite
v
GMe
v
r
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v velocity (m/s)
G gravitational constant
Me mass of Earth (kg)
r distance to center of the Earth (m)
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Satellites

• What is the minimum velocity needed for a
  satellite to stay in orbit at 1500 km above the
  earths surface.
• Given
• Mearth 5.98 x 1024 kg
• Rearth 6.37 x 106 m

And the answer is. 7913.047866 m/s