Universal Gravitation

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Universal Gravitation
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Universal Gravitation

• Gravity
• Makes things such as leaves and rain fall
• It made the Earth round
• Builds up the pressures that kindle every star to
  shine
• But What is Gravity?

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Universal Gravitation

• GRAVITY
• Albert Einstein
• Discovered that gravity arises from the
  warping of space and time
• The way in which masses communicate with each
  other
• Every mass in the universe reaches out to attract
  every other one, and every mass feels an
  attraction from every other one

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Universal Gravitation

• The Falling Apple
• Issac Newton
• Credited for the idea that gravity extends
  throughout the universe
• According to the popular legend
• Idea of gravity occurred to Newton while he was
  sitting underneath an apple tree on his mothers
  farm

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The Falling Apple

• Newton
• Understood the concept of inertia developed
  earlier by Galileo
• Without an outside force, moving objects continue
  to move at constant speed in a straight line
• Force is necessary for an object to undergo a
  change in speed or direction

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The Falling Apple

• The Falling Apple, Newton observed, triggered
  what was to become one of the most far-reaching
  generalizations of the human mind
• Newton saw the apple fall or perhaps felt it hit
  his head (Story unclear)
• Perhaps he looked up through the apple tree
  branches and noticed the moon
• Newton was probably puzzled by the fact that the
  moon does not follow a straight-line path, but
  instead circles the Earth
• He knew circular motion is accelerated motion,
  which requires a force
• But what was this force?

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The Falling Apple

• Newton had the insight to see that the moon is
  falling toward the earth, just as the apple is
• He reasoned that the moon is falling for the same
  reason the apple is
• They are both pulled by Earths GRAVITY

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The Falling Moon

• Newton compared the falling apple with the
  falling moon
• He realized if the moon did not fall, it would
  move off in a straight line and leave its orbit
• The moon must be falling around the earth
• He hypothesized that the moon was simply a
  projectile circling the earth under the
  attraction of gravity ? falling toward the earth
  but with a great enough tangential velocity to
  avoid hitting the earth

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Gravitational Force

• Earth and many of the other planets in our solar
  system travel in nearly circular paths around the
  sun
• A centripetal force is keeping them in orbit
• This centripetal force that holds the planets in
  orbit is the same force that pulls an apple
  towards the ground ? GRAVITATIONAL FORCE
• One of Newtons greatest discoveries

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Orbiting Objects are in Free Fall

• Newton developed a Thought Experiment
• Consider a cannon sitting on a high mountaintop
• The path of each cannonball is a parabola
• The horizontal distance that each cannonball
  covers increases as the cannonballs initial
  speed increases
• Newton realized ? if the initial speed of the
  cannonball was great enough, the curvature of
  Earth will cause the cannonball to continue
  falling without ever landing
• In other words, it would orbit Earth

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Orbiting Objects are in Free Fall

• The gravitational force between the cannonball
  and Earth Centripetal force that keeps the
  cannonball in orbit
• Satellites stay in orbit for the same reason
• Similarly, a gravitational attraction between
  Earth and our sun keeps Earth in its orbit around
  the sun

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Newtons Law of Gravitation

• The attractive force of gravity between 2
  particles is proportional to the product of their
  masses and inversely proportional to the square
  of the distance between them
• Gravitational Force
• Fg G (m1m2 / r2)
• Fg Gravitational Force (Newtons)
• G Constant of universal gravitation
• (G 6.67 x 10-11 N x m2/ kg2)
• m1 Mass of object 1 (kg)
• m2 mass of object 2 (kg)
• r2 (Distance between the centers of the
  spherical masses (m)2

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Gravitational Force

• Gravitational Force
• Exists between any two masses, regardless of size
• Always attracts objects to one another
• The force that the moon exerts on Earth is equal
  and opposite to the force that Earth exerts on
  the moon ? Newtons Third Law of Motion

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Gravitational Force

• If gravitational force acts between all masses,
  why doesnt Earth accelerate up toward a falling
  apple?
• In fact, it does!
• But, Earths acceleration is so tiny ? you cannot
  detect it
• Because Earths mass is so large and acceleration
  is inversely proportional to mass, the Earths
  acceleration is negligible
• The apple has a much smaller mass and thus a much
  greater acceleration