Enter the Physicists

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Enter the Physicists

• Reading Ch 3-3..3-5

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Galileo The Physicist
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Falling Objects
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Describing Motion

• Speed distance over time (miles per hour)
• Speed is a scalar, i.e. just a number (60 mph)
• Velocity speed AND direction
• Drive at 60 mph due East
• Velocity is a vector (magnitude and direction)
• Acceleration change in velocity over time
• Speed can increase or decrease
• Acceleration is also a vector

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Galileos Results

• A falling object feels a constant acceleration of
  gravity he called g (direction down)
• No matter what the composition or shape of the
  object, it fell with the same acceleration g
• For Earth g 9.8 m/s2

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How Galileo really did it
a g sin(q)
Needed to slow down acceleration
Best Timer Sand Clock
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Apollo 15 Galileo Demo

• http//www.youtube.com/watch?v4mTsrRZEMwANR1

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If there was no air
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Weight and Mass

• The mass of object, m, is determined by the
  number of molecules of what type make it up. So
  the mass of a book is constant no matter where it
  is in the SS
• Scientific units of mass are kilograms (kg)
• The weight, W, of an object is its mass times
  the acceleration of gravity
• W mg
• In scientific units weights are measure in
  Newtons (N). In common units weights are measured
  in pounds (lb)

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On the Moon or Elsewhere

• BUT, g will change from planet to planet and moon
  to moon. For example, on our moon g? (1/6) g?
• So the weight of an object will change as go to
  different bodies in the SS.

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Sir Issac NewtonThe Genius
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Newtons Leap of Intuition

• The same natural laws that work on the Earth,
  also work throughout the universe.
• By now, has been proved a countless number of
  times

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Describing Motion

• Speed distance over time (miles per hour)
• Speed is a scalar, i.e. just a number (60 mph)
• Velocity speed AND direction
• Drive at 60 mph due East
• Velocity is a vector (magnitude and direction)
• Acceleration change in velocity over time
• Speed can increase or decrease
• Speed can remain the same but direction change
• Acceleration is also a vector

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Centripetal Acceleration
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First Law of Motion

• Every body will stay in a state of rest or
  uniform motion in a straight line unless that
  state is changed by forces impressed upon it.
• Often called the Law of Inertia
• Property of matter that it resists having its
  state of motion changed.

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Second Law of Motion

• The size of an acceleration is directly
  proportional to the force applied, and inversely
  proportional to the mass of the body.
• The resulting acceleration is in the same
  direction as the applied force.

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The Second Law of Motion

• Expressed Mathematically
• a F / m
• Acceleration is proportional to force, and
  inversely proportional to mass.
• F m a
• Force is mass times acceleration.

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Force, Mass, Acceleration

• Second law has two parts
• 1) Quantifies "force" in terms of its effects on
  a massive body.
• Forces produce accelerations.
• The more mass a body has, the less it can be
  accelerated by a given force.
• 2) Forces and accelerations have directions
• Acceleration is in the same direction as the
  applied force.

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Newtons Third Law

• For every action there is a reaction
• If one object exerts a force on another object,
  it feels an equal and opposite force on itself
• Forces always come in pairs

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RocketPropulsion

• Spacecraft Dawn Ion Engine
• An electrical Force pushes Xenon ions out of the
  spacecraft
• Therefore, spacecraft feels an equal force from
  the ions. Dawn is constantly being accelerated

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Isaac Newton
Edmund Halley
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Gravitational Force

• The Force of Gravity between any two objects
  depends only upon
• The masses of the two objects
• More massive objects exert a stronger force.
• The distance between them
• The force gets stronger as they move closer.
• The force gets weaker as they move apart.
• It is an attractive force pulls to objects
  toward each other

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Newtons Gravitational Force Law

• F Force of Gravity
• M1 Mass of the first object
• M2 Mass of the second object
• d Distance between their centers
• G Gravitational Force Constant
• Example of an inverse square law.

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What if the distance changes?
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What if the masses change?
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Gravity extending to the Orb of the Moon
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Predictive Power of Gravity

• Halleys Comet
• Using Newtonian Gravity, Edmond Halley found that
  the orbit of the Great Comet of 1682 was similar
  to comets seen in 1607 and 1537.
• Predicted it would return in 1758.
• Seen again Christmas night 1758.
• Dramatically confirmed Newtons Laws of Motion
  and Gravitation.

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Universal Gravitation

• The Law of Gravity is truly Universal
• Governs the fall of apples on the Earth
• Governs the fall of the Moon around the Earth
• Governs the fall of the Earth/Moon system around
  the Sun
• Governs the fall of the Sun around the center of
  the Milky Way Galaxy.
• Governs the fall of the Milky Way and Andromeda
  Galaxies in their mutual orbit...

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Orbital Mechanics
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Newtons Generalization

• Newton showed that Keplers Laws can be derived
  from first principles
• Three Laws of Motion
• Law of Universal Gravitation
• Newton generalized the laws to apply to any two
  bodies moving under the influence of their mutual
  gravitation.
• Moon orbiting the Earth
• Two stars orbiting each other
• And beyond...

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First Law of Orbital Motion

• The shape of a gravitational orbit is a conic
  section
• Conic Sections
• Curves found by cutting a cone with a plane.
• Circles, Ellipses, Parabolas, and Hyperbolas

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Conic Sections
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Keplers First Law Expanded
v
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Closed and Open Orbits

• Closed (bound) Orbits
• Ellipses
• Circles special case of an ellipse with zero
  eccentricity
• Orbits are bound and objects orbit perpetually.
• Open (unbound) Orbits
• Hyperbolas
• Parabolas special case of a hyperbola
• Orbits are unbound and objects escape.

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Getting into orbit

• Shoot cannonball with high enough speed it will
  constantly be falling around the curvature of
  the Earth
• Experience Weightlessness
• Low-earth orbit, high-earth orbits
• Telescopes in Space
• Geosynchronous orbits

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Getting out of orbit
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Escape Velocity

• Escape Velocity is the minimum velocity needed to
  enter an unbound orbit
• Unbound Parabola Hyperbola
• NEVER escape gravity
• For Earth 25,000 mph
• If below Escape Velocity, will enter closed or
  bounded orbit Ellipse Circle

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Escape Velocity

• More massive a planet or moon higher the escape
  velocity
• Smaller a planet or moon higher the escape
  velocity

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Mars Sojourner
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Perfect Interplanetary Trajectory