Newton’s Law of Gravity

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Newtons Law of Gravity
I wonderwhats forlunch?
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Where did it come from?

• Newton was watching the full moon one day,
  wondering why inertia didnt cause the moon to
  fly off into space.
• He realized that some force must be holding the
  moon near to the earth.

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Where did it come from?

• When an apple fell near Newton, he realized that
  the force pulling the apple down towards the
  earth was the same force holding the moon in its
  orbit.

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Newton realized 3 things

• There was a force of attraction between the earth
  the moon, and the force was somehow related to
  the earths mass.

Hey, baby,Im attractedto you!
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Newton realized 3 things

• From his 3rd law of motion, Newton knew that if
  the earth was pulling on the moon, the moon was
  also pulling on the earth equally hard.
• Therefore, the force of gravity also depended on
  the mass of the object orbiting the earth (the
  moon.)

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Newton realized 3 things

• Just like a magnetic force, as the distance
  between the two masses increased, the force of
  gravity would grow weaker, not slowly evenly,
  but very quickly. Think about how magnets
  attract each other.

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The Inverse Square Law

• As the distance between the 2 objects increases,
  the force of gravity decreases with the square of
  the distance.
• F is proportional to 1/d2, not just 1/d.

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Inverse Square Law
F 1

• If you double the distance between 2 objects, the
  force of gravity between them shrinks to ¼.

F ¼
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Inverse Square Law

• If you triple the distance between 2 objects, the
  force of gravity between them shrinks to (1/3)2
  or 1/9th .
• It works the opposite way when 2 objects move
  closer together

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Inverse Square Law

• If the distance between the earth the moon
  somehow were decreased to ½ what it is now, the
  force of gravity between the earth the moon
  would increase to 4 times stronger than it is
  right now.

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Lets put it all together

• F is the force of gravity.
• F G x Massearth x Massmoon (distance between
  them)2
• The G in the formula is just a factor that
  makes all the units work out correctly.

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Law of Gravity Equation

• The equation can be applied to any 2 objects in
  space.
• F G x Mass1 x Mass2 (distance)2
• G is a constant (a scaling factor) equal to 6.67
  x 10-11 Nm2/kg2

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Consequences for Astronomy

• This means that every object in the universe,
  every planet, star, even hydrogen atom, attracts
  every other object in the universe.
• When the 2 objects are very far apart, the
  attractive force is very small, but its still
  present.

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I can still feelyou, even wayover there!
Gravity never sleeps!
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Consequences for Astronomy

• The gravity law explains why planets orbit stars
• why stars orbit the center of the galaxy
• why all the galaxies in the universe should be
  attracted to one another.

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Some examples

• The acceleration due to gravity is 9.8 m/s2 at
  the earths surface.
• If you climbed to the top of the highest
  mountain, you would be a little further from the
  earths center. An object dropped here would
  weigh a little less and drop slightly slower than
  it would at the earths surface.

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What would happen if?

• If the earth suddenly shrank to ½ its current
  sizethe acceleration due to gravity would be 4
  times what it is now.
• You would feel 4 times heavier.

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I simply MUSTlose someweight!
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What would happen if?

• If you visited a planet that was the same size as
  the earth, but had twice the massyoud feel
  twice as heavy, and youd accelerate twice as
  fast in a fall.

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What would happen if?

• If you visited Mars, where the gravity is less
  than it is on earthyoud be able to lift 2.5
  times what you can lift on earthyoud be able to
  throw a baseball 2.5 times farther.

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What would happen if?

• if you were in a spaceship orbiting a star, and
  the star suddenly shrank to become a black hole
  only 1/1000th of its former size?
• Would you be instantly sucked in?

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What would happen if?

• Neither your mass, nor the mass of the star has
  changed.
• Your distance from the center of mass of the star
  hasnt changed.
• The force of gravity between you and the new
  black hole would be exactly the same as it was
  before the star became a black hole. You would
  NOT be sucked in.

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But, I thought

• But dont black holes have enormous gravity?
• Yes, they doat their surfaces!
• If you were standing on the surface of the star
  when it shrank and became a black hole, you would
  be instantly crushed by the increase of gravity.

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Im confused

• Look at the law of gravity.F G x Mass1 x
  Mass2 (distance)2
• The only thing that changes between when the star
  is large and when it shrinks to become a black
  hole is the distance between you (at its surface)
  and the center of the stars mass.

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UhOKmaybe

• In the equation, the distance factor between you
  and the black holes center, d, gets very small,
  making the force of gravity very large.

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Lets add just a little more

• Newton realized that his new law of gravity could
  be combined with Keplers 3rd law the one that
  relates the size of an objects orbit to its
  orbital period.
• (period)2 (orbit radius)3 or
• p2 a3

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The combined equation looks like

• p2 4 ?2 a3 . G (Mass1
  Mass2)
• It may look complicated, but its soooo useful.

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What can this equation do?

• There are 4 terms in the equation that are
  unknowns. These are p, a, Mass1 and Mass2.
• If you are able to measure any 3 of the terms,
  you can calculate the 4th term.

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What can this equation do?

• The equation can be used to
• calculate the mass of the sun
• calculate the mass of any planet that has a moon
• look for planets orbiting other stars
• discover new planets!

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What can this equation do?

• This equation was used by a British astronomer,
  John Couch Adams, and a French astronomer, Urbain
  Leverrier, to predict the position of the planet
  Neptune in 1845a whole year before it was ever
  observed with a telescope!

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Wow! They found a planet?

• The 2 astronomers noticed that the planet Uranus
  would sometimes speed up, then slow down in its
  orbit. They believed that this change in speed
  was due to the gravitational tug of another, more
  distant planet. The other planet was Neptune.

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Lets use the equation!!

• The equation has been used to calculate the mass
  of the sun, starting with the orbit of the earth.
• We know that the earth takes 365.24 days to make
  1 orbit. Converting this to seconds equals
  31,600,000 seconds.

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Keep going

• We also know that the earth orbits the sun at a
  distance of 1 A.U. or 150,000,000 kilometers
• Convert this distance to meters, equals
  150,000,000,000 meters.
• Now, lets re-arrange the equation.

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A re-arrangement

• p2 4 ?2 a3 . G (Masssun
  Massearth)becomes (Masssun Massearth) 4
  ?2 a3 G p2

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Keep going

• Now, if you realize that the mass of the earth is
  tiny, compared to the enormous mass of the sun,
  you can just ignore Mearth in the calculation,
  without being very far off in your answer.

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So the equation becomes

• it becomes
• Masssun 4 ?2 a3 G p2

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If youve been paying attention

• If youve been paying attention, and writing
  everything down to this point, you now have
  enough information to solve Newtons equation for
  the mass of the sun.
• Go ahead, give it a try. Its question 17 on
  your homework!

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Thanks for watching

• now its homework time!