Newton

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Newtons Laws
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Achieving Scientific Literacy(Arons Article)

• Two types of knowledge
• Declarative (Learned Facts, book knowledge)
• Operative (actually knowing how to solve
  problems)
• Trouble with GenEd courses
• Too much in too little time
• Getting a feeling for the subject doesnt work
• Need to understand the underpinnings first (area,
  volume, scaling, energy, atoms,)

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How far away is the Moon?

• The Greeks used a special configuration of Earth,
  Moon and Sun (link) in a lunar eclipse
• Can measure EF in units of Moons diameter, then
  use geometry and same angular size of Earth and
  Moon to determine Earth-Moon distance
• See here
• for method

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Earths Shadow on the Moon (UT)
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Earths Shadow on the Moon (NASA)
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Geometrical Argument

• Triangles AFE and EDC are congruent
• We know ratio FE/ED f
• Therefore AEf EC, and AC (1f)EC
• AC108 REarth
• EC distance
• to Moon

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That means we can size it up!

• We can then take distance (384,000 km) and
  angular size (1/2 degree) to get the Moons size
• D 0.5/3602p384,000km 3,350 km

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How far away is the Sun?

• This is much harder to measure!
• The Greeks came up with a lower limit, showing
  that the Sun is much further away than the Moon
• Consequence it is much bigger than the Moon
• We know from eclipses if the Sun is X times
  bigger, it must be X times farther away

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Simple, ingenious idea hard measurement

•  

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Timeline
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Isaac Newton The Theorist

• Key question
• Why are things happening?
• Invented calculus and physics while on vacation
  from college
• His three Laws of Motion, together with the Law
  of Universal Gravitation, explain all of Keplers
  Laws (and more!)

Isaac Newton (16421727)
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Isaac Newton (16421727)

• Major Works
• Principia (1687)
• Full title Philosophiae naturalis principia
  mathematica
• Opticks sic!(1704)
• Later in life he was Master of the Mint, dabbled
  in alchemy, and spent a great deal of effort
  trying to make his enemies miserable

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Newtons first Law

• In the absence of a net external force, a body
  either is at rest or moves with constant
  velocity.
• Contrary to Aristotle, motion at constant
  velocity (may be zero) is thus the natural state
  of objects, not being at rest. Change of velocity
  needs to be explained why a body is moving
  steadily does not.

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Mass Weight

• Mass is the property of an object
• Weight is a force, e.g. the force an object of
  certain mass may exert on a scale

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Newtons second Law

• The net external force on a body is equal to the
  mass of that body times its acceleration
  F  ma.
• Or the mass of that body times its acceleration
  is equal to the net force exerted on it
• ma F
• Or aF/m
• Or mF/a

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Newtons 3rd law

• For every action, there is an equal and opposite
  reaction
• Does not sound like much, but thats where all
  forces come from!

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Newtons Laws of Motion (Axioms)

1. Every body continues in a state of rest or in a
   state of uniform motion in a straight line unless
   it is compelled to change that state by forces
   acting on it (law of inertia)
2. The change of motion is proportional to the
   motive force impressed (i.e. if the mass is
   constant, F ma)
3. For every action, there is an equal and opposite
   reaction (Thats where forces come from!)

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Newtons Laws
Always the same constant pull

• a) No force particle at rest
• b) Force particle starts moving
• c) Two forces particle changes movement
• Gravity pulls baseball back to earth
• by continuously changing its velocity
• (and thereby its position)
• 
  ?

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Law of Universal Gravitation

• Force G Mearth Mman / R2

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Orbital Motion
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Cannon Thought Experiment

• http//www.phys.virginia.edu/classes/109N/more_stu
  ff/Applets/newt/newtmtn.html

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From Newton to Einstein

• If we use Newton II and the law of universal
  gravity, we can calculate how a celestial object
  moves, i.e. figure out its acceleration, which
  leads to its velocity, which leads to its
  position as a function of time
• ma F GMm/r2
• so its acceleration a GM/r2 is independent of
  its mass!
• This prompted Einstein to formulate his
  gravitational theory as pure geometry.

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Applications

• From the distance r between two bodies and the
  gravitational acceleration a of one of the
  bodies, we can compute the mass M of the other
• F ma G Mm/r2 (m cancels out)
• From the weight of objects (i.e., the force of
  gravity) near the surface of the Earth, and known
  radius of Earth RE 6.4?103 km, we find ME
  6?1024 kg
• Your weight on another planet is F m ? GM/r2
• E.g., on the Moon your weight would be 1/6 of
  what it is on Earth

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Applications (contd)

• The mass of the Sun can be deduced from the
  orbital velocity of the planets MS
  rOrbitvOrbit2/G 2?1030 kg
• actually, Sun and planets orbit their common
  center of mass
• Orbital mechanics. A body in an elliptical orbit
  cannot escape the mass it's orbiting unless
  something increases its velocity to a certain
  value called the escape velocity
• Escape velocity from Earth's surface is about
  25,000 mph (7 mi/sec)