Understanding Orbits

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Understanding Orbits
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Understanding Orbits

• Orbital Motion
• Baseballs in Orbit
• Analyzing Motion
• Newtons Laws
• Laws of Motion
• Weight, Mass and Inertia
• Momentum
• Changing Momentum
• Action and Reaction
• Gravity

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Orbital MotionBaseballs in Orbit

• If a baseball player throws a baseball
  horizontally from a mountain top
• Gravity pulls the ball toward the ground.
• The faster a ball is thrown horizontally, the
  farther it will go before gravity pulls it to the
  ground.
• When an object moves fast enough, it will go far
  enough as it falls to miss the Earth and stay
  in orbit.

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Orbital MotionBaseballs in Orbit (contd)

• The Earths curvature causes a 5 meter decrease
  in altitude for every 8 kilometers across the
  ground.
• If the ball is moving fast enough across the
  ground so it falls 5 meters or less every 8
  kilometers, it will never hit the ground (as long
  as theres no air resistance).

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Orbital MotionBaseballs in Orbit (contd)

• A ball thrown fast enough to cover exactly 8
  kilometers in the time it takes the ball to fall
  5 meters will be in a circular orbit.
• Increasing velocity (adding more energy) will
  make it an elliptical orbit.

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Orbital MotionAnalyzing Motion

• To analyze objects in motion, follow a Motion
  Analysis Process (MAP) Checklist
• Define a coordinate system.
• Develop an equation of motion.
• Apply simplifying assumptions.
• Assign initial conditions.
• Perform error analysis.
• Test the model.

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Newtons LawsLaws of Motion

• Newtons Laws of Motion are unbreakable.
• Newtons Laws of Motion can explain
• The motion of the heavens
• The paths of the stars
• The future position of Earth

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Newtons LawsWeight, Mass, and Inertia

• A scale measures how much Earths gravity is
  pulling an object's mass.
• Mass tells us
• How much matter an object has.
• How much the object resists motion (inertia).
• How much gravitational attraction it has to other
  masses (gravity).

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Newtons LawsMomentum and Inertia

• Newtons First Law of Motion
• A body continues its state of rest or of uniform
  motion in a straight line unless compelled to
  change that state by forces impressed on it.
• Objects at rest stay at rest.
• Objects in motion continue in straight-line
  motion.
• UNLESS acted upon by an outside force, like
  gravity.

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Newtons LawsMomentum and Inertia (contd)

• For an object at rest, resistance to movement is
  its inertia, which is determined by how much mass
  it has.
• For an object moving, its resistance to change in
  that movement (speed or direction) is its
  momentum.

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Newtons LawsLinear Momentum

• An objects linear momentum is its resistance to
  changes in its straight-line motion.
• Depends on both its mass and its velocity.
• The direction of the objects linear momentum is
  the same as the objects velocity (speed).

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Newtons LawsLinear Momentum (contd)

• A spacecraft in orbit is in motion.
• Motion is not in a line.
• Because motion isnt in a straight line,
  something must be acting on itgravity.

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Newtons LawsAF Linear Momentum Example

• Which scenario would require a pilot to
  anticipate speed changes more during aerial
  refueling?
• A jumbo C-5 transport
• An F-15 fighter aircraft
• A fully loaded C-5 has about 20 times the mass of
  an F-15more momentum.

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Newtons LawsAngular Motion

• Objects at rest resist spinning .
• The resistance to start spinning for an object is
  its moment of inertia.
• An objects angular momentum is its resistance to
  changes in direction or speed of its spinning
  motion.
• Depends on how spread out mass is from the
  center of spinning (mass moment of inertia).
• Depends on how fast the spin is (angular
  velocity).

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Newtons LawsAngular Momentum

• Angular momentum keeps the spin direction (as
  determined by the right-hand rule) pointed in the
  same direction.
• If you curl the fingers of your right hand in the
  spin direction, your thumb will point in the
  direction of the angular momentum.
• Quarterbacks put a spiral on a football to give
  it angular momentum and keep it from tumbling.
• Barrels of rifles and handguns have rifling to
  spin a bullet and keep it from tumbling.

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The Right-Hand Rule

• Use the right-hand rule to find the direction of
  the angular velocity and the angular momentum.
• Curl the fingers of your right hand in the
  direction of spin and the thumb points in the
  direction of the angular velocity and angular
  momentum.

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Newtons LawsChanging Momentum

• Newtons Second Law of Motion The time rate of
  change of an objects momentum equals the applied
  force.
• Changing an objects momentum requires a force.
• How quickly the momentum is changed determines
  the size of the force.
• Newtons Second Law when mass is constant Force
  equals mass times acceleration.

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Newtons Laws Changing Momentum (Example)

• Bulldozer and baby carriage are traveling at the
  SAME SPEED.
• Momentum is mass times velocity.
• A bulldozer has much higher momentum because it
  has more mass traveling at the same velocity.
• To stop both objects in the same amount of time,
  we must apply a much higher force to the
  bulldozer (higher rate of momentum change).

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Newtons Laws Action and Reaction

• Newtons Third Law of Motion When body A exerts
  a force on body B, body B will exert an equal,
  but opposite, force on body A.

A
B
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Newtons Laws Gravity

• Newtons Law of Universal Gravitation The force
  of gravity between two bodies is directly
  proportional to the product of their two masses
  and inversely proportional to the square of the
  distance between them.
• If we double the distance between the two masses
  (R) in the upper part of the figure to (2R) in
  the lower figure, the gravity force (Fg) is
  decreased by four (Fg/4).

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Newtons Laws Gravity (contd)

• Acceleration due to gravity on an object near
  Earth depends on
• Earths mass times the universal gravitational
  constant.
• Square of the distance between the object and the
  Earth.
• The farther you are from Earths center, the less
  the acceleration due to gravity.

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Newtons Laws Gravity (contd)

• Acceleration of gravity has nothing to do with
  the falling objects mass.
• Galileo was correct objects of different masses
  will fall at the same rate.

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Summary

• Orbital Motion
• Baseballs in Orbit
• Analyzing Motion
• Newtons Laws
• Laws of Motion
• Weight, Mass, and Inertia
• Momentum
• Changing Momentum
• Action and Reaction
• Gravity

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Next

• Based on tools developed in this lesson well
  describe the path that spacecraft make as they
  fly over the Earth.
• Well also figure out how spacecraft change from
  one orbit to another.