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Universal Gravitation

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Title: Universal Gravitation


1
Universal Gravitation
  • Chapter 8

2
Isaac Newton and Gravity
  • Newton realized an apple falls because of force
  • Moon follows circular path, force needed
  • Newton first to realize gravity causes both.
  • Moon is actually falling towards earth
  • Tangential velocity (sideways) keeps it going
    around earth instead of into it

3
Law of Universal Gravitation
  • Newton extended gravitation theory to all
    objects,
  • Realized gravitational attraction is property of
    all mass
  • Attractive force is directly proportional to
    product of two masses
  • Inversely proportional to square of distance
    between them

4
Law of Universal Gravitation
  • F m1 m2/d2
  • Proportionality constant G must be used to make
    quantities equal
  • F Gm1 m2/d2
  • G force between 2 1-kg masses, 1 m apart
  • Its value is G 6.67 x 10-11 Nm2/kg2
  • Henry Cavendish first to measure G

5
Law of Universal Gravitation
  • Gravity very weak force
  • Force of attraction with earth is weight
  • Weight depends on distance from center of earth
  • On top of high mountain, you weigh less
  • Using G and radius of earth we can calculate mass
    of earth 6 x 1024 kg

6
An Inverse-Square Law
  • Force of gravity varies inversely with square of
    distance between objects
  • For a spherical body, distance is measured from
    its center
  • If distance is doubled, force is one-fourth as
    much if tripled, force is one-ninth (1/3)2
  • If distance is halved, force is 4 times as much
    if distance is 1/3 as much, force is 9 times as
    great.

7
An Inverse-Square Law
  • Other inverse-square relationships light and
    sound intensity, magnetic and electric force.
  • Force of gravity weakens rapidly with distance
    due to spreading of force into surrounding space,
    but never really zero, even in deep space.

8
Gravitational Fields
  • Gravitational force acts over a distance without
    contact
  • Caused by interaction with gravitational field
  • Field can be thought of as lines of force
    radiating from objects
  • Strength of field is force per unit mass exerted
    on object g F/m

9
Gravitational Fields
  • Earths grav. field strength is actually
    acceleration due to gravity at any location
  • Combining g F/m and F G mM/R2, we find g
    GMe/ R2, where Me mass of the earth and R
    distance from center of earth.
  • g for any planet can be found using this formula.

10
Gravitation and the Universe
  • Planets, moons, stars are spherical due to
    gravity
  • All planets affect each other, can cause
    perturbations (wobbles) in orbits
  • Neptune and Pluto were discovered because of
    perturbations in Uranus orbit.
  • Perturbations of distant stars have led to
    discoveries of planets, double stars

11
Gravitation and the Universe
  • Big Bang theory says universe hurled outward
    from big explosion
  • Universe is expanding, only pull of gravitation
    can stop it.
  • Unknown whether enough matter exists to stop
    expansion and begin contraction leading to Big
    Crunch and another big bang-expansion-contraction
    cycle.

12
Gravitational Field Inside Earth
  • If hole were drilled through earth and you fell
    in, what would happen?
  • As you fall, mass below you pulls down, mass
    above you pulls up.
  • No force at center of earth, pull equal in all
    directions
  • You would accelerate with decreasing acceleration
    until you reached the center, then decelerate as
    you approach opposite surface.

13
Satellites--Circular Orbits
  • In circular orbit, gravity always pulls
    perpendicular to velocity
  • Speed doesnt change, only direction.
  • Time (period) for close orbit about 90 min.,
    greater for higher orbits
  • If period of revolution is 24 hours, satellite
    remains over same point on earth--communication
    satellites do this (geosynchronous orbit)

14
Satellites--Elliptical Orbits
  • If speed is faster than needed for circular
    orbit, elliptical orbit can result
  • Ellipse is oval with two focal points (foci)
  • Speed varies in elliptical orbit
  • Faster speed close to earth, slower when farther
    away
  • All planets follow elliptical orbits around sun

15
Tides
  • Change in sea level due to difference in
    gravitational pull between earth and moon on
    opposite sides of earth.
  • Causes elongation of earth and moon along line of
    force, bulging on near and far side.
  • Earth turns underneath high water levels causing
    2 high tides and two low tides per day.

16
Tides
  • Sun also creates tides but effect is less than
    moon because distance difference is not as large
    a part of total distance.
  • Extra large spring tides caused by sun-moon
    alignment on same side of earth
  • Smaller neap tides occur when sun and moon are on
    opposite sides of earth

17
Eclipses
  • When sun-moon-earth alignment is perfect,
    eclipses occur
  • When earth is between sun and moon, moon is in
    shadow and lunar eclipse occurs.
  • When moon is between sun and earth, parts of
    earth in moons shadow see solar eclipse.

18
Black Holes
  • In stars, expansion forces due to nuclear fusion
    are balanced by contraction force of gravity.
  • When solar fuel runs out, stars collapse
  • Small stars will become dense, cool, black dwarfs.

19
Black Holes
  • Large stars will continue collapse to enormous
    density with gravitational forces too strong for
    anything to escape
  • Even light, radio communications are
    trapped--nothing can escape black hole (except
    small amounts of radiation).
  • Edge of black hole is called event horizon

20
Black Holes
  • Fabric of space-time is warped by tremendous
    gravity inside black hole
  • Mass of black hole is same as star that created
    it so gravity outside black hole is same as if
    original star were still there.
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