Lecture 5 Newton Tides

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Lecture 5 Newton -Tides

• ASTR 340
• Fall 2006
• Dennis Papadopoulos

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ACCELERATING MOTION
Motion at constant acceleration a in
meters/sec2 Start with zero velocity. Velocity
after time t is v(t)at. The average speed during
this time was vav(0at)/2at/2 The distance
traveled svavtat2/2 Suppose you accelerate from
0 to 50 m/sec in 10 secs The distance s will be
given by S(1/2)(5 m/sec2)102 250 m The general
formula if you start with initial velocity v(0)
is
sv(0)t(1/2)at2
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Conservation Principles

• N1 with v?0 comes directly from Aristotles
  concept (object at rest remains at rest) by
  applying Galilean Relativity change to frame
  with initial v0 F0 so object remains at rest
  change frames back and v initial v
• N3 is exactly whats needed to make sure that the
  total momentum is conserved.
• So Newtons laws are related to the symmetry of
  space and the way that different frames of
  reference relate to each other.

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ActionReaction
If friction and pull balance exactly cart moves
with constant velocity otherwise it slows down or
accelerates depending on what dominates
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Force and acceleration

• Forces between two bodies are equal in magnitude,
  but the observed reaction --the acceleration --
  depends on mass
• If a bowling ball and ping-pong ball are pushed
  apart by spring, the bowling ball will move very
  little, and the ping-pong ball will move a lot

• Forces in a collision are equal in magnitude, too

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Circular or Elliptical
Motion

• Velocity, as used in Newtons laws, includes both
  a speed and a direction. V and also F and a are
  vectors.
• Any change in direction, even if the speed is
  constant, requires a force
• In particular, motion at constant speed in a
  circle must involve a force at all times, since
  the direction is always changing

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What happens when there is no force
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NEWTONS LAW OF UNIVERSAL GRAVITATION

• Newtons law of Gravitation A particle with mass
  m1 will attract another particle with mass m2 and
  distance r with a force F given by
• Notes
• G is called the Gravitational constant
  (G6.67?10-11 N m2 kg-2)
• This is a universal attraction. Every particle in
  the universe attracts every other particle! Often
  dominates in astronomical settings.

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Gravitational Mass vs.
Weight

• Defines gravitational mass
• Using calculus, it can be shown that a spherical
  object with mass M (e.g. Sun, Earth) gravitates
  like a particle of mass M at the spheres center.

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Measuring G Gravitational forces
Same as if all the mass was at O
Total force zero
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First Unification in
Physics
1/3600 g
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First grand unification
Moon falls about 1.4 mm in one sec away from
straight line
Earth
REM/RE60
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Inverse square law
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Orbital and Escape Velocity
Vorb7.8 km/sec Vesc 11 km/sec
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Vesc(2GME/RE)1/2
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KEPLERS LAWS EXPLAINED

• Keplers laws of planetary motion
• Can be derived from Newtons laws
• Just need to assume that planets are attracted to
  the Sun by gravity (Newtons breakthrough).
• Full proof requires calculus (or very involved
  geometry)

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• Planets natural state is to move in a straight
  line at constant velocity
• But, gravitational attraction by Sun is always
  making it swerve off course
• Newtons law (1/r2) is exactly whats needed to
  make this path be a perfect ellipse hence
  Keplers 1st law.(use calculus)
• The fact that force is always directed towards
  Sun gives Keplers 2nd law (conservation of
  angular momentum)
• Newtons law gives formula for period of orbit

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TIDES
1/R2 law
Daily tide twice Why?
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TIDES
Twice monthly Spring Tides (unrelated to Spring)
and Twice monthly Neap Tides
Sun
moon
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TIDES
Sun moon at right angles
Twice monthly Neap Tides