Models of the Earth

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• Models of the Earth

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Models in Science

• Making models of things in Science can be thought
  of as the "Art" of constructing models which
  approximate the Real World. Model makers in
  Science do not unearth some Absolute Truth about
  Nature, but rather build mathematical structures
  which reflects a close example of Nature. This
  example is like a geological map of some
  territory. A map has a lot of useful information
  about the territory, but the map is not the
  territory.

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Models in Science

• Models in Science are not equal to, identical
  with, or a one-to-one match with the aspects of
  Nature they describe.
• There is always some limited range over which a
  Model is a useful predictor of Nature.
• The rules for the acceptance or rejection of a
  Model is determined by how close the Model
  predicts the outcome of measurements and
  observations.
• Models of Science are not unique. There may be
  two or more Models which describe the same
  observations equally well.  
•  Preference between competing Models is judged
  bya. Size of the error. The smaller the size of
  the error between actual measurements and
  predictions, the more accurate the Model. A good
  Model will be able to predict the uncertainty
  within its predictions
• b. Range of Application. The larger the range
  over which a Model faithfully reflects Nature,
  the more universal the Model.
• c. Simplicity. How simple the model is to use
  and understand determines how it will be used.

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Flat Earth - Round Earth

• A carpenter building a house uses the model that
  the Earth is flat expect for local
  irregularities, which are usually flattened out
  before building. A carpenter makes no practical
  errors in the accuracy of his measurements in
  assuming that the Earth is flat. For an airline
  pilot, the model that the Earth is perfectly
  spherical, like a ball, is useful for navigating
  over long distances. The path that uses the least
  fuel, the shortest path, is the arc of a great
  circle on a sphere, and not a straight line on a
  map.
• A more complicated model of the shape of the
  Earth's surface is that of a triaxial ellipsoid
  of rotation, since the Earth is slightly flatter
  (about 17 km) at the poles. At one time
  astronomers did use this model in order to
  compare measurements of celestial objects made at
  different observatories scattered across the
  Earth's surface.
• To within the limit of accuracy of a carpenter's
  tape measure, the Flat Earth Model gives as good
  predictions as that of the spherical trigonometry
  of a Round Ball Model or the Triaxial Ellipsoid
  trigonometry. The Triaxial Ellipsoid Model is
  more accurate that the Spherical Ball Model which
  is more accurate than the Flat Earth Model. None
  of these models, constructed by scientists,
  represent the "TRUE" shape of the Earth. Which
  Model you use depends upon the amount of accuracy
  needed in your measurement.

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Globe Models of Earth

• Raised relief globe

• Flat surface globe

How is the raised relief globe a more accurate
model than the flat surface globe?
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Raised Relief Globe

• Look close-up photograph of the raised relief
  globe below.

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Raised Relief Globe Problems

• Possible model problems When you look closely at
  the raised relief globe, you see an attempt to
  demonstrate differences in elevation. Mountains
  are shown as being raised well above the Earth's
  surface. While it is true that mountains are
  higher than the average surface of the Earth, the
  scale does not match the globe. At the scale of a
  globe, the entire surface would appear flat. At
  this scale, when compared with the enormous size
  of the entire earth, even Mt. Everest would
  appear flat!

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Maps as models

• Anything wrong with map models?

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Map Problems

• The main problem with maps is that they distort
  things.
• Remember, the Earth is really round. When you
  flatten the Earth out on a map it distorts things
  making them distorted (especially at the poles).

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True Shape of Earth

• Oblate Spheroid