Gravitational Fields

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Gravitational Fields Tides
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Gravitational Fields

• The force field that surrounds massive objects
• Gravitational fields cause objects to accelerate
  in the direction of the massive object that
  creates the field.
• On Earth, the gravitational field strength is
  9.8N/kg.
• That is, every 1 kg of mass is pulled to the
  Earth with a force of 9.8N.
• This should look familiar when a 1 kg object is
  pulled to Earth with a force of 9.8 N, then its
  acceleration (by Newtons 2nd Law) is 9.8 m/s2.
• GRAVITATION FIELD STRENGTH IS EQUAL TO FREE FALL
  ACCELERATION

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Calculating the STRENGTH

• What is Newtons Law of Universal Gravitation?
• What is Newtons Second Law?
• Use this to calculate the gravitational field
  strength on the surface of the Earth.
• Remember mass 6 x 1024 kg and radius 6.4 x
  106 m
• You can use this formula and appropriate
  constants to find the gravitational field on any
  planet, moon, etc.

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Journey to the Center of the Earth

• I. Suppose Felix Fizix (m60kg) was standing on
  the surface of the earth as shown in the diagram.
• 1. If Felix dropped a coin, which way would it
  fall and with how much acceleration? Explain.
• 2. If Felix stepped on a bathroom scale, what
  would the reading on the scale (Felixs weight)
  be? Explain.

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Journey to the Center of the Earth

• II. Suppose Felix Fizix was standing in a chamber
  at the center of the earth as shown in the
  diagram.
• 1. If Felix dropped a coin, which way would it
  fall and with how much acceleration? Explain.
• 2. If Felix stepped on a bathroom scale, what
  would the reading on the scale (Felixs weight)
  be? Explain.

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Journey to the Center of the Earth

• III. Suppose Felix Fizix was standing in a
  chamber halfway between the center and the
  surface of the earth as shown in the diagram.
• 1. If Felix dropped a coin, which way would it
  fall and with how much acceleration? Explain.
• 2. If Felix stepped on a bathroom scale, what
  would the reading on the scale (Felixs weight)
  be? Explain.

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So how does that work???

• Newton determined that the force acting on Felix
  in situation III would be the same as if he were
  standing on a planet consisting only of the mass
  beneath him as shown on the diagram.
• The whole earth has a mass corresponding to its
  full radius R, when Felix is at a distance r from
  the center of the earth, his weight is as if he
  were on a planet with the same density as the
  earth, but with a radius r instead of R.
• So how much does an object weigh when it is
  somewhere between the center of the earth and the
  surface of the earth?
• 1. What is the relation between mass, density,
  and volume?
• 2. What is the volume V of a sphere of radius r?
• 3. What is the mass M of that sphere if its
  density is D?
• 4. What is the equation for the law of universal
  gravitation?
• 5. Substituting the expression for M in Q3 into
  the equation in Q4 gives

In terms of mass If you are half-way to the
center of the Earth ¾ of the mass is below you,
while ¼ is above you. Mass is pulling on you
both ways. ¼ of the mass pulling up will cancel
out ¼ of the mass pulling down. With some (a
little more simple) math, ¾ pulling down ¼
pulling up ½. Half of your weight!
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Tides

• What are tides?
• How many tides occur each day?
• What do you think gravity has to do with tides?
• The tides at a given place in the Earth's oceans
  occur about an hour later each day.
• Since the Moon passes overhead about an hour
  later each day, it was long suspected that the
  Moon was associated with tides.

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(Over simplified)ExplanationDifference is

• Every object on the Earth is gravitationally
  attracted to the moon.
• Water is less rigid than the rest of the Earth
  therefore, the tides you observe are in the
  ocean.
• The water at point A is attracted more to the
  moon than the center of the Earth at point B and
  the water at point C. This produces the high
  tide on the right side.
• The high tide at point C can be explained by the
  fact that the Earth at point B is being pulled
  away from the water at point C creating another
  high tide.
• Since the Earth rotates around on its axis once a
  day, there are 4 tides in a day (2 low and 2
  high)

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Why not the sun?

• The sun has some effect on tides especially
  when tides are very strong or weak.
• But the key for tides is DIFFERENCE.
• Because the moon is closer to the Earth the
  difference in the pull of the moon on the
  opposite sides of the Earth is greater than that
  of the sun.
• Are you sure??? See for yourself.
• Find the difference in the gravitational force on
  each side of Earth by the moon and by the sun.
• Important numbers mass of Earth 6x1024kg,
  radius of Earth 6.4x106m mass of sun
  2x1030kg, sun-Earth distance 1.5x1011m mass of
  moon 7.4x1022kg, moon-Earth distance
  3.8x108m.

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Black Hole

• A black hole is a region of space in which the
  gravitational field is so powerful that nothing,
  not even visible light, can escape its pull.
• In stars there are two ongoing processes.
  Gravitation and thermonuclear fusion.
• These two processes balance each other.
  Gravitation holds it together, fusion makes it
  expand.
• Eventually if the star runs out of hydrogen (i.e.
  fusion fuel), gravitation takes over and the star
  collapses until there are no more empty spaces
  within the star.
• Gravitation near the shrunken configuration
  becomes so enormous that nothing can escape it.
• What would happen to Earth if our sun became a
  black hole?

Simulated view of a black hole in front of the
Milky Way. The hole has 10 solar masses and is
viewed from a distance of 600 km.