Universal Gravitation

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Universal Gravitation
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Key Ideas

• By the end of this unit you should know and
  understand
• Keplers 3 Laws of planetary motion
• Newtonian Gravitation
• Gravitational Force
• Free Fall
• Gravitational Field Intensity
• Geosynchronous Orbits
• Newtonian Gravity as evidence of Dark Matter

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Isaac Newton (1642-1727)
The ultimate nerd Able to explain Keplers
laws The Three Laws of Motion
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Newton Science in Reverse

• Newton used his ideas on motion (Three Laws)
  along with the data that was already available
  from Brahe and Kepler to come up with

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Universal Gravitation

• Every particle in the Universe attracts every
  other particle with a force that is directly
  proportional to the product of the masses and
  inversely proportional to the square of the
  distance
• between them.

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Relating it to Newtons Laws of Motion

• The force that mass 1 exerts on mass 2 is equal
  and opposite to the force mass 2 exerts on mass 1
• The forces form a Newtons third law
  action-reaction example
• Gravitational forces are exerted
• from an objects centre of mass (think back to
  torque and balance).

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Fg force of gravity (N) G universal
gravitational constant (Nm2/kg2) 6.67 x
10-11 m1, m2 masses (kg) r distance between
the centres of masses (m)
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• https//www.youtube.com/watch?vvD-wKcp9ABU
• Start at 330

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What about the equation for weight?

• How are these two things related???
• http//www.aplusphysics.com/courses/honors/videos/
  UniversalGrav/UniversalGrav.html

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How does this relate to Newtons Laws of Motion?

• 3rd Law Equal and opposite reaction forces.

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• Question - If an apple weighs 1N at distance 1d,
  as in the diagram at left, what will be its
  weight at a distance of 4d?
• Inverse square relationship
• Answer 1/d2 1/(4d)2 1/16 N
• 1/16 N

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Example 1

• A 65.0 kg astronaut is walking on the surface of
  the Moon, which has a mass of 7.35 x 1022 kg and
  a mean radius of
• 1.74 x 103 km. What is the weight of the
  astronaut?
• 105 N

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Some Hints

• The r value is sometimes given as d or distance
  of separation between two objects.
• If the altitude is given, you must add the
  altitude to the radius of the planet (etc) to get
  the actual orbital radius.

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Page 580

• Questions 1 to 8
• 7 and 8 are more challenging