Circumference of the Earth

1
Circumference of the Earth

• What is the distance around the earth?
• What is the distance from New York to Los
  Angeles?
• What is the distance from Memphis to St. Louis?
• (Whenever we talk about distances, well try to
  relate those distances to others that we already
  know.)

2
Circumference of the Earth

• It is about 280 miles, or a bit over 400
  kilometers, from Memphis to St. Louis.
• It is about 3,000 miles from New York to Los
  Angeles, or about 10 times the Memphis to St.
  Louis distance.
• It is about 25,000 miles around the Earth, or
  about 8 times the New York to Los Angeles
  distance, and a little less than 100 times the
  Memphis to St. Louis distance.

3
Shape of the Earth

• The earth appears to be a sphere (since even on
  the earths surface we see the superstructure
  and/or sails of a ship before we see its hull).
  But is it a perfect sphere?

A true-color NASA satellite mosaic of Earth.
4
Shape of the Earth

• Of course it is not perfect since we have
  mountains and valleys. But how much difference
  does this make? How high are the highest
  mountains compared to the radius of the earth?

5
Shape of the Earth

• The radius of the earth (25,000 miles in
  circumference) is about 4,000 miles. The highest
  mountain is about 5 miles high. The deepest
  ocean trench is about 10 miles deep. This is not
  much compared to 4,000 miles to the center of the
  earth.
• Except for the mountains and valleys, is the
  shape of the earth a perfect sphere? And if so,
  why does it have the spherical shape?

6
Shape of the Earth

• It turns out that the earth is only approximately
  a sphere, with the distance around the equator a
  little bit longer (about 70 miles longer) than
  the distance around the poles.
• But why the essentially spherical shape, and why
  the slight difference?

7
Shape of the Earth

• The basic shape is a sphere because this is the
  shape that puts all of the mass as close as
  possible - a result of gravity.
• The slight bulging at the equator can be
  interpreted as a result of the spinning of the
  earth!

8
Mass of the Earth

• How much mass does the earth have, and how do we
  know that?
• What is the difference between mass and weight?
• How much mass or weight do the largest ships
  have?
• How much mass or weight do trucks carry?

9
Mass and Weight

• Our weight on earth depends on the gravitational
  attraction of the earth for our mass. The more
  mass we have, the more weight we have. One
  kilogram of mass has a weight on the earth of 2.2
  lbs.
• In outer space, far away from the earth, any
  object will have essentially zero weight, but it
  will still have its mass. We can tell how much
  mass it has by how much force it takes to change
  its motion.

10
Masses of large objects

• The weight of a large truck can reach several
  tens of tons (a short ton is 2000 lb, a metric
  ton has a mass of 1000 kg which is about 2200 lb
  or 10 larger than a short or British ton).
• The weight of an aircraft carrier can reach about
  100,000 tons.
• Therefore the mass of the earth must be much
  larger than 100,000,000 kg 1 x 108 kg which is
  the mass of 100,000 metric tons.

11
Mass of the Earth?

• How do we determine the mass of the Earth? We
  cant put the earth on a scale and determine its
  weight!

12
Mass of the Earth

• Since gravity depends on the masses of both
  objects, we can look at how strongly the earth
  attracts the moon. It is the earths
  gravitational attraction that keeps the moon
  going around the earth, rather than the moon
  going straight off into space.
• By looking at how fast the moon orbits the earth
  at its distance from the earth, we can get the
  mass of the Earth 6 x 1024 kg, equivalent to 6
  trillion trillion tons.

13
Generalizing

• We can determine the mass of any object in space
  by looking at how fast and how far away something
  is that goes around that object. We can
  determine the mass of the earth by watching the
  Moon go around the earth. We can determine the
  mass of Jupiter by watching how its moons go
  around it. We can determine the mass of the sun
  by watching the earth go around the sun.

14
Generalizing (cont.)

• We cant, however, determine the mass of the Moon
  by watching it go around the earth. We can only
  determine the mass of the earth that way. To
  determine the mass of the Moon, we would have to
  have something orbit the Moon.

15
Size, mass and density

• By knowing both the size and mass, we can
  calculate the average density of the earth. This
  gives a clue about what could make up the inside
  of the earth. (We conclude that the core must be
  mostly iron and nickel.)
• Also we know that the earths interior is very
  hot - due to the presence of volcanoes. What
  could cause this heat?

16
Hot interior of the Earth

• If the earth has a molten interior due to heat,
  this leads to the plate tectonics theory plates
  float on this molten interior. Volcanoes and
  earthquakes happen at the edges of the plates.
• But what is the source of this heat?

17
Source of interior heat

• If the earth formed out of a dust cloud by
  gravitational attraction of the parts of the
  cloud for each other, then the formation would
  generate a lot of heat. The earth may be cooling
  down from that formation.
• Also we observe that there are radioactive decays
  happening, and they also generate heat.

18
Working backwards Age of the Earth

• If some atoms are radioactively decaying, then we
  can work backwards to try and determine when this
  began.
• We notice that only the very long lived
  radioactive elements are still found, except for
  a few that we see continually being made (like
  Carbon-14 and Radon-222). The next slide
  contains a list of what we still see around.

19
Half Life

• Before we look at numbers, we need to talk about
  how atoms decay in radioactive decay. We have
  found that an individual radioactive atom has a
  certain probability of decaying in a given time
  interval. An analogy is that of a die - it has a
  certain probability of turning up 3 in a roll.
  If we roll the die, it may come up 3 on the first
  roll, or it may take quite a few rolls before it
  turns up 3.

20
Half Life

• A useful measure of this probability of decay is
  the half life. It is the time (on average)
  that half of the atoms will have decayed.
• If we wait another half life, then half of the
  remaining atoms will have decayed, and so on.
• If we start with 100 atoms, then after one half
  life, we would have approximately 50 atoms left.
  After another half life, we would have about 25
  left. After another half life, we would have
  about 12 or so left.

21
Radioactive Elements

• Uranium-238 half life of 4.5 billion years
• Uranium-235 half life of 0.7 billion years (but
  only 0.7 of Uranium is U-235)
• Thorium-232 half life of 14 billion years
• Potassium-40 half life of 1.3 billion years
• (but only 1 out of 5000 Potassium atoms are
  K-40)
• Neptunium-237 has a half life of 2.2 million
  years but is not found in nature.
• Plutonium-244 has a half life of 76 million years
  but is not found in nature.

22
Age of the Earth

• By looking at the radioactive elements, we come
  up with an age for the earth of about 4.5 billion
  years.
• This age appears consistent with other methods of
  aging the earth such as rock weathering and
  sedimentation rates.

23
Surface of the Earth

• The varied surface of the earth can be explained
  by the amount of gravity, plate tectonics
  (earthquakes and volcanoes), and by weathering
  (the effects of wind and water).
• There are very few signs of craters due to
  collisions with asteroids, but that may be due to
  the effects of plate tectonics and weathering
  that tend to erase the visible scars.

24
Earths atmosphere

• The earth obviously has an atmosphere. At the
  surface, this atmosphere is composed mostly of
  diatomic Nitrogen (79) and diatomic Oxygen
  (20), with a little bit of Argon (0.9) and
  Carbon Dioxide (0.03) and other stuff. Water
  vapor is not included since it varies widely
  (Memphis versus Phoenix, jungle versus deserts).

25
Atmospheric Pressure

• Due to the earths gravity, this atmosphere is
  held to the earth. Due to the atmosphere above
  the surface, the weight of this atmosphere
  provides an atmospheric pressure of 1 atmosphere
  14.7 lb/in2 at the earths surface.
• To account for this pressure, the atmosphere, if
  it were uniform, would have to be about 10
  kilometers (6 miles) high. But the atmosphere is
  not uniform - it decreases in density with height.

26
Atmosphere

• In fact, most of the atmosphere and all of the
  weather is concentrated in a thin layer about 8
  miles thick. The rest gradually thins out as you
  get further from the earth.
• This layer of atmosphere is extremely thin when
  compared to the 4,000 mile radius of the earth.

27
Atmospheric Effects

• There are three main effects the atmosphere has
  on our ability to see through it
• 1. It absorbs some of the light that goes
  through it.
• 2. It reflects some of the light (from outer
  space back out, and from the earth back towards
  the earth).
• 3. It bends some of the light (going from vacuum
  to air - just like going from air to water).

28
Absorption of Light

• The atmosphere absorbs almost all of the x-rays
  and gamma rays coming from space, as well as most
  of the ultraviolet light. It absorbs some of the
  infrared light as well - but this works both
  ways it absorbs some of the IR from space
  coming to the earth but it also absorbs some of
  the IR coming from the earth and decreases the
  earths ability to cool off. This last effect is
  called the greenhouse effect.

29
Reflection of Light

• The earths atmosphere causes about 25 of the
  light from the sun to be reflected from the
  earth. This causes the earth to be not quite as
  warm as it might otherwise be. This also
  somewhat limits the light we receive from stars.

30
Refraction of Light

• Due to the differences in density of the
  atmosphere, the light coming from vacuum is bent
  when it enters the atmosphere.
• This bending of light causes mirages and the
  wavering of light above hot objects. It also
  causes the stars to twinkle. It also causes the
  sun to appear to rise earlier and set later than
  it really does - because of the way the light is
  bent.

31
Earths magnetism Radiation Belts

• Due to the fact that the earth has a magnetic
  field associated with it (the reason compasses
  work), and due to the fact that some of the
  radiation from the sun is in the form of
  electrons and protons (rather than purely light),
  the earth has what are called radiation belts.
• The magnetism of the earth traps most of the
  electrons and protons that stream out from the
  sun that would otherwise hit the earth.

32
Northern Lights

• These radiation belts trap the protons and
  electrons well above most of the atmosphere.
  However, these belts allow the particles to
  escape near the poles. When these particles hit
  the atmosphere near the poles, they cause the air
  to glow - hence the Northern Lights (aurora
  borealis).

http//www.iww.is/art/shs/pages/thumbs.html
http//www.youtube.com/watch?vqIXs6Sh0DKs
33
Rotation of the Earth about its axis

• The sun-centered view requires the earth to
  rotate about its axis.
• Which way does the earth spin? As viewed from
  the North, does it spin clockwise or
  counterclockwise?
• Is there any evidence for this rotation?

34
Rotation about the axis

• Since New York sees the sun rise before Memphis,
  the earth must be rotating eastward and hence
  counterclockwise as viewed from above the North
  Pole.
• One result of this rotation is the existence of
  low pressure and high pressure centers and the
  winds that accompany them.
• In the northern hemisphere, the winds go
  counterclockwise around a low pressure center
  instead of going directly toward it. This can be
  explained as an effect of the rotation of the
  earth!

35
Winds around a low pressure area

• The opposite happens in the Southern Hemisphere
  the winds rotate clockwise around a low pressure
  system

Slower moving winds North miss the Low Pressure
and end up behind it and are now moving South
Low Pressure
Faster moving winds South miss the Low Pressure
and end up ahead of it and are now moving North
36
Rotation of the Earth

• Which way does the earth rotate about its axis
  and about the sun as viewed from the North
  Pole, does it rotate clockwise or
  counterclockwise - and how do we tell?

37
Rotation about the earths axis
Sizes are NOT drawn to scale!

• 1

View is looking down from above the North Looking
at the earth from the sun with North out of the
slide, which direction is East and which is West?
Sunset or sunrise
midnight
noon
Sunrise or sunset
38
Rotation about the earths axis
Sizes are NOT drawn to scale!

• 1

View is looking down from above the North.East
is on the right and West is on the left as you
face North (which is out of the screen).
Sunset
East
West
noon
midnight
West
East
Sunrise
Since the East sees the sunrise before the West
and East sees the sunset before the West, the
earth must rotate counterclockwise as viewed from
above the North pole.
39
Rotation about the earths axis
Sizes are NOT drawn to scale!

• 1

View is looking down from above the North.East
is on the right and West is on the left as you
face North (which is out of the screen).
London
West
East
Sunset
East
West
noon
Memphis
midnight
West
East
Sunrise
Since the East sees the sunrise before the West
and East sees the sunset before the West, the
earth must rotate counterclockwise as viewed from
above the North pole.
40
Rotation about the Sun

• Since the sun seems to move East with respect to
  the stars (the stars rise a little earlier each
  day), the since the sun seems to go around the
  earth 365 times a year but the stars seem to go
  around the earth 366 times a year, the earth must
  rotate counterclockwise around the sun as viewed
  above the North Pole. This is the same direction
  as its spins about its axis.

41
Rotation about the Sun

Earth rotates counterclockwise as viewed from
above North pole
Sunrise and star rise
to star
Star rise comes before sunrise