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G r a v i t y Chapter 9 Isaac Newton (1642 - 1727) m M d Newton’s Universal Gravitation Two masses separated by a distance Newton’s Universal Gravitation Newton’s Universal Gravitation Inverse Square Law Separation Force

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g r a v i t y
G r a v i t y

Chapter 9

newton s universal gravitation




Newton’s Universal Gravitation

Two masses separated by a distance

newton s universal gravitation5
Newton’s Universal Gravitation
  • Inverse Square Law

Separation Force


2R ¼F

3R 1/9F

½R 4F

¼R 16F

newton s universal gravitation6
Newton’s Universal Gravitation

The force of gravity cannot be made zero.

  • Mass causes gravity
    • Only one kind of mass
    • Contrast with the electric force
  • G is small
    • 6.67 X 10-11 N m2/kg2
apparent weightlessness
Apparent Weightlessness
  • All objects fall at the same rate in a gravitational field.
    • Apparent weightlessness
    • Lack supporting force
  • Examples:
    • Space Shuttle
    • Elevator
    • Amusement Park Rides
ocean tides
Ocean Tides
  • Gravity decreases with distance



ocean tides10
Ocean Tides
  • Differences in gravity on different parts of the Earth produce tidal bulges

Low Tide

High Tide

High Tide

Low Tide

ocean tides11
Ocean Tides
  • Should expect two high tides, two low tides per day
    • Moon moves in its orbit so that it returns to the same place in your sky every 24h 50 m
  • Sun has one-half the influence of the moon
    • The gravitational force is greater but tides depend on the gravitation difference on opposite sides of the Earth
ocean tides12



Full Moon

New Moon

Ocean Tides
  • Spring Tide
    • Full or New Moon
ocean tides13
Ocean Tides
  • Neap Tide
    • First or Last Quarter Moon

First Quarter



Last Quarter

ocean tides14
Ocean Tides
  • Complications
    • Friction with ocean bottom
    • Irregular shape of continents
  • Bay of Fundy (Video)
    • Tides can come in very fast and exceed 15 m
crustal atmospheric tides
Crustal & Atmospheric Tides
  • Tides in ionosphere produce electric currents and alter the magnetic field
    • Affects penetration of cosmic rays
    • Can have effects on living things
  • Tides in the crust mean that volcanoes and earthquakes are more common at new or full moon
    • Measured for the moon
gravitational field


Gravitational Field
  • Alternate view of gravitational influence
    • Properties of space surrounding object are changed so that another mass entering the region experiences a force.
gravitational field17
Gravitational Field
  • Objects accelerate in the direction of the arrows
  • Field is stronger where field lines are closer together
gravitational field18

a = g

a = ½g

a = ½g

a = 0

a = g

Gravitational Field
  • Inside the Planet
gravitational field19





Gravitational Field
  • Uniform Sphere
    • Linear inside
    • like Earth outside
  • Hollow Sphere
    • Zero inside
    • like Earth outside





No mass

Distortion caused by mass

general relativity
General Relativity
  • Mass distorts space-time
  • Objects move in the straightest path they can in the distortions caused by mass

Apparent position of the star


Light from star bent by the gravity of the Sun

Bending of Starlight

low gravity
Low Gravity

Very small amount of bending

stronger gravity
Stronger Gravity

Light at an angle is bent noticeably

schwarzschild black hole

Event Horizon




Schwarzschild Black Hole

Rs = 3(Mass)

Mass Rs

3 M 9 km

5 15

10 30

what can we know
What Can We Know?
  • Mass
    • gravity
  • Charge
    • Electric Fields
  • Rotation Rate
    • Co-rotation
red shift and distance
Red Shift and Distance

24 Mpc

1200 km/s

300 Mpc

15,000 km/s

780 Mpc

39,000 km/s

1220 Mpc

61,000 km/s

raisin cake model36



Raisin Cake Model


1 cm/hr

2 cm/hr

3 cm/hr

Distance Distance

from Home from Home

(before baking) (afterbaking)

1 1 cm 2 cm

2 2 cm 4 cm

3 3 cm 6 cm

universal expansion
Universal Expansion
  • Space-Time itself is expanding
    • Carries galaxies along with it
  • Conflicting cosmologies
    • Big Bang
      • Draw the expansion back in time until space-time occupies a point (12 - 15 billion years ago)
    • Steady State
      • Requires continual creation of matter