Measuring The Earth

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Measuring The Earth
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A. Earth Dimensions
How can the Earths shape be determined?
Who do you think was the first person to
determine the Earths?
Aristotle (4th century BC) showed that the Earth
is spherical.
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Using method developed by Eratosthenes
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• Eratosthenes

• was a librarian in the famous library of
  Alexandria

• was a Greek mathematician, geographer and
  astronomer.

• Lived approximately 2 x 103 years ago in Egypt

• Used geometry to calculate the circumference of
  Earth

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Eratosthenes discovered in his reading that there
was a yearly festival in the town of Syene
(modern Aswan) on June 20. On that date, and
only on that date, it was possible to look down
into a well and see the sun!
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Assumptions Eratosthenes made
1. All rays of the sun approach Earth in a
parallel manner
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• The Sun is very far away, compared to the size
  of the Earth
• this implies that a ray of sunlight striking
  Alexandria and a ray of sunlight striking Syene
  are essentially parallel.

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What do they mean by concentration?

• Hint Look at the surface area.

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Which area is receiving a stronger Sun ray?
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Is there any thing special about June 20?
Summer Solstice

• At the solstices the sun's apparent position on
  the celestial sphere reaches its greatest
  distance above or below the celestial equator,
  about 23 1/2 of arc.
• At the time of summer solstice, about June 22,
  the sun is directly overhead at noon at the
  Tropic of Cancer.

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VS. Winter Solstice
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Analemma
path that the sun makes in the sky is called the
analemma.
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Assumptions Eratosthenes made (cont.)
2. Earth is a perfect sphere

• The Earth is spherical - this had been known
  since Aristotle had figured it out a century and
  a half earlier.

Where are these two cities any way?
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Assumptions Eratosthenes made (cont.)
Alexandria is due north of Syene - this isn't
exactly true, but it only introduces a minor
error into the result.
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Distance from Alexandria to Syene 5000 stades.
1 stadion148.5 m
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Geometry that Eratosthenes used

• Alternate interior angles made by parallel lines
  of the Suns rays are equal

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Using his observations and assumptions,
Eratosthenes was able to make the diagram below
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• A ray of sunlight strikes Syene perpendicular to
  the ground. A parallel ray of sunlight strikes
  Alexandria at an angle of 7.2 degrees from the
  perpendicular.

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What are these parts of this formula?
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C the circumference of the circle
S the surface distance between cities
a the angle (shadow or from Earths center)
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S (surface distance between cities) 5000 stades
a the angle (shadow or from Earths center) 7.2
degrees
Now place the information in the Formula
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1800000os
7.2o
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C

250000s
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How do we determine the size of the Earth with
Modern Methods

• Ships appearing to sink as they go over the
  horizon.

The Earth's shadow on the moon during an eclipse
is always curved. This could only be possible if
the Earth was a sphere.

• Different time zones.

• Different angles to Polaris as you travel
• N. or S.

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How do we determine the size of the Earth with
Modern Methods (cont.)

• Photos from space- the best proof.

This brings us to Roundness of the Earth
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• Perfect Sphere equals a roundness ratio of ONE!

Average Diameter of Earth (Polar Diameter
Equatorial Diameter)/2
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Earth Diameter Circumference
Polar 12,714 km 40,008km
Equatorial 12,757 km 40,076 km
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Oblate Spheroid

• It is a sphere with a slight flattening at the
  polar regions and a slight bulging at the
  equatorial region.

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You can also indirectly measure the oblateness of
the earth with gravity measurements.
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• Altitude The latitude of the celestial body,
  measuring from the horizon up to the zenith of an
  observer (90 degrees).
• The angle is measured with a sextant or other
  navigational instruments.

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Sextant a navigation instrument that is used to
establish position by measuring the height of
stars from the horizon.
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• For any point between the Equator and the North
  Pole, latitude is obtained simply by measuring
  the altitude of Polaris

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The altitude of Polaris equals your latitude
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Earth

• The Earth is nearly a perfect sphere

• Very slightly flattened at the poles

• Very slightly bulging at the Equator

Called an Oblate Spheroid
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Model
Models are representations of something real
Examples

• A globe is a representation of Earth

• The Cylindrical Projection

• The Conical Projection

• Azimuthal Projection

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Equator

• Located at zero degrees latitude (North or
  South,) is 24,901.55 miles long and divides the
  Planet Earth into the Northern and Southern
  Hemispheres.

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• The planet's four hemispheres are shown on the
  map, and each is shaded a dark gray. The Equator,
  that imaginary horizontal line at 0º degrees
  latitude at the center of the earth, divides the
  earth into the Northern and Southern Hemispheres.
  
• The vertical imaginary line called the Prime
  Meridian, at 0º degrees longitude, and its twin
  line of longitude, opposite the Prime Meridian at
  180º longitude, divides the earth into the
  Eastern and Western Hemispheres.

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Prime Meridian

• Located at zero degrees longitude (East or
  West), it divides the Planet Earth into the
  Eastern and Western Hemispheres, and is the line
  from which all other lines of longitude are
  measured.

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Three of the most significant imaginary lines
running across the surface of the earth are

• Equator

2. Tropic of Cancer
3. Tropic of Capricorn
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The Cylindrical Projection
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Mercator Projection
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Regular cylindrical projections

• Lines of latitude and longitude are parallel
  intersecting at 90 degrees.

• Meridians are equidistant.

• Forms a rectangular map.

• Scale along the equator or standard parallels is
  true.

• Can have the properties of equidistance,
  conformality or equal area.

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• Has correct shapes of continents, but their
  areas are distorted.

• Lines of longitude are projected onto the map
  parallel to each other.

• As stated earlier, only latitude lines are
  parallel. Longitude lines meet at the poles.

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• When longitude lines are projected as parallel,
  area near the poles are exaggerated.

• Example
• Look at Greenland and South America

• Hint Size of landforms

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Mercator Projection
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• Invented in 1569 by Gerardus Mercator (Flanders)
  graphically.

• Standard for maritime mapping in the 17th and
  18th centuries.

• Used for mapping the world/oceans/equatorial
  regions in 19th century.

• Used for mapping the world/U.S. Coastal and
  Geodetic Survey/other planets in 20th century.

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Robinson Projection
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Robinson Projection

• was developed by Arthur H. Robinson in 1963.

• Has accurate continent shapes and shows accurate
  land area.

• Lines of latitude remain parallel, Lines of
  longitude are curved as they would be on a globe.

• Results in less distortion near the poles.

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Conical Projection

• a map projection of the globe onto a cone with
  its point over one of the earth's poles

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• meridians are straight equidistant lines,
  converging at a point which may or not be a pole.

• angular distance between meridians is always
  reduced by a fixed factor, the cone constant

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• Examples

• Road Map
• Weather Map

• Used to produce maps of small area.

• are made by projecting points and lines from a
  globe onto a cone.

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Gnomonic map projection

• displays all great circles as straight lines.

Also known as Azimuthal Map Projections
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Topographic Map