Gravity and Its Interactions

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Gravity and Its Interactions
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Falling Apples and the Falling Moon

• Newtons inspiration triggered by
• the idea that gravity caused both
• motions
• Apple falls toward earths center
• 4.9 m in 1 sec
• Moon falls toward earths center
• a smaller amount

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Falling Apples and the Falling Moon

• Newton stated the moon would fall beneath its
  straight line path of tangential velocity and it
  would only be affected by distance from earth
• Moon 60 times further than apple
• Should fall or 1.4 mm in one
  second
• This was verified by Edmund Halley

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Falling Earth and Other Planets

• Just as moon falls around earth, the earth falls
  around the sun in a circular path
• Other planets likewise fall around the sun
• Kepler discovered the relation between distance
  and time T2 is constant R2

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Gravitation Law

• Newtons calculations led to a mathematical law
  where G is a constant,
  m1 and m2 the masses ,
  and d the distance between
  centers
• The value of G was determined by Henry
• Cavendish and verified by
• Philipp von Jolly to be
• 6.67 x 10-11 Nm2/kg2
• Weakest of fundamental forces,
• only sensible when masses are large

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Inverse Square Laws

• Gravity is reduced by the square of the distance
• Effect is spread over larger and larger area, but
  at less intensity

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Inverse Square Laws

• The strength of gravity becomes less as distance
  increases 2d gt 1/4 F 5d gt 1/25
  F 3d gt 1/9 F Note 1d is at earths
  surface

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Universal Gravitation

• Effective throughout the universe
• Seen in effect one planet has on another
• Neptune and Pluto were discovered due to their
  effects on Uranuss orbit
• Such an effect is called perturbation

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Homework 12

• RQ 3, 4, 5, 12, 14
• TE 1, 4, 7, 10, 11

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Gravity Fields

• The gravity force is non-contact, acting through
  space
• This force shows itself in a field-effect,
  causing attraction to masses nearby
• All objects have a gravity field, small objects
  field is very weak, large objects much stronger

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Gravity Fields Within

• The gravity field inside a planet is theoretical
  due to the impossibility of drilling a hole
  through a planet
• The field strength weakens upon entering into
  such a hole, getting to 0 at the center
• Due to pull from opposite sides of earth
• Pulls oppose one another by distance to object in
  hole

1/2g
0g
1/2g
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Weight and Weightlessness

• Your weight depends on the force your support can
  provide
• Elevator accelerating upward more force so more
  weight
• Elevator accelerating downward less support so
  less weight
• Elevator in free fall no support so no weight
• Only accelerating elevator counts, not constant
  speed

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Weight Weightlessness (cont)

• Free fall makes no support and
• a weightless condition
• Space shuttle as high flying
• parabolic aircraft
• Outer space also - no support,
• thus no weight

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Gravity and the Tides

• Moon pulls on earth - we see the effect in tides
  of ocean water (and of big lakes)
• Caused by different pulls on opposite sides of
  earth
• Earth water bulges both toward and away from moon

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Gravity and the Tides

• Sun has greater gravity force than moon, but less
  difference in its pull on opposite sides
• Biggest effect is when sun and moon pull
  together these are spring tides (not seasonal,
  but springy)
• Air and land tides also happen
• Least effect when sun/moon pull at right angle
• Called neap tides

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Sun Moon Earth Alignment

• Eclipses happen when moon/earth/sun align
• Lunar if earth between Solar is moon between
• Alignment is not always exact due to tilt of
  moons orbit (about 5 )

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Black Holes

• Conjecture due to observations from space
• Theory is a supergiant star collapses in on
  itself creating super strong gravity at at small
  point

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Black Holes

• Gravity is great due to small distance with huge
  mass
• Gravity only great near the object, at distance
  gravity is no different

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Homework 13

• RQ 1, 4, 5, 10, 13, 14, 16, 20
• TE 1, 4, 7, 10
• good luck!

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Satellites and Gravity

• Controlling factor in fall of an object is
  gravity
• Faster an object is projected, less likely it
  will fall enough to contact surface again
• Orbit velocity of earth is 8000 m/s, when it
  could fall 4.9 m and remain above surface

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Circular Orbits

• Gravity does not affect the tangential velocity,
  since it pulls at right angles to that velocity
• Orbital velocity of 8000 m/s carries a period of
  90 minutes close to earth
• Farther from earth longer period (Kepler)
• At about 6.5 earth radii, period becomes 24
  hours, and satellite appears to be stationary in
  earths sky
• This is very useful for communications satellites

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Elliptical Orbits

• At over 8000 m/s, the orbit will become
  elongated, or elliptical
• Ellipse - closed curve with all points
  equidistant from sum of distances to foci

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Conservation of Orbital Energy

• In circular orbit, PE KE is constant - no
  variation

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Conservation of Orbital Energy

• In elliptical orbit, PE is greatest at apogee
  (furthest point from earth) and least at perigee
  (closest point to earth). At these two points,
  KE is opposite to PE, but sum of KE PE is still
  constant

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Velocity Changes in Orbit

• Only in elliptical orbits can velocity change
• A component of gravity force occurs along the
  path, causing acceleration
• Only in an elliptical orbit can work (F d) be
  done

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Escape Velocity

• Orbital velocity of 8000 m/s only causes orbit if
  launched horizontally
• Vertical launch requires 11,200 m/s in order to
  fight gravity and escape earth
• Escape velocity depends on gravity of the planet
  or celestial object
• Suns escape velocity is 620,000 m/s
• Moons is 2400 m/s

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Homework 14

• RQ 1, 4, 7, 8, 11
• TE 1, 4, 6, 12