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Calculating the Circumference of Earth using Google Earth

VIEWS: 10 PAGES: 3

									       Calculating the
      Circumference of
         Earth using
       “Google Earth”

Written June 2008 by Park Hook, Paul Wilson and Alan Roy, as part of the BITL IV grant funded by the
Montana Office of the Commissioner of Higher Education.

Subject: Mathematics
Topics: Geometry and Measurement
Grade: 8
Time Needed: 45-60 minutes

Abstract:
   Students apply proportions to data gathered with “Google Earth” to calculate equatorial and polar
   circumference of the Earth.

Concepts:
   Proportions, Circumference, and Properties of Circles

Objectives:
   Students will demonstrate their abilities to apply proportions and properties of circles to calculate the
   circumference of the Earth.

Knowledge and Skills:
   Students must have knowledge of the properties of a circle including the number of degrees in a circle.
   Students must be able to set up and solve proportions.
   Students must use “Google Earth” to:
     1) Create location indicators (“places”)
     2) Measure distances between two places
     3) Use longitude and latitude grid
   Google Earth Tutorials: http://earth.google.com/userguide/v4/tutorials/index.html

Materials:
  Computers running “Google Earth” for each student or small group of students.
  Alternatively have students take turns running and following along on one classroom projected computer
  screen.
Procedure:
   Prior to using the computers:
    Students estimate the circumference of the Earth
    Problem solve to reinforce using proportion to find
       circumference. (See diagram to right.)
   At computers (students alone, in small groups or following along on
   a class projected computer screen):
    Demonstrate how to use Google Earth – ruler, points, grid,
       reading longitude and latitude.
    Equatorial Circumference – Students:
       1) Choose and mark two points on the equator using Google
           Earth
       2) Measure the distance using the ruler function on Google
           Earth
       3) Compute the longitudinal difference between the two points, in degrees, rounding to the nearest
           degree
       4) Use the data in proportion to calculate the equatorial circumference of the Earth.
    Polar Circumference – Students:
       1) Choose and mark two points on one line of longitude using Google Earth
       2) Measure the distance between the two points using the ruler function on Google Earth
       3) Compute the latitudinal difference between the two points, in degrees, rounding to the nearest degree
       4) Use the data in proportion to calculate the polar circumference of the Earth.

Analysis
   Have students compare results, noticing differences between groups, and between equatorial and polar
      circumference. Why would there be differences? (Measurement errors with Google Earth ruler,
      measuring over land verses water, distance between places selected, the fact that the world is not a
      perfect sphere.)
   Have students search the internet to find published scientific measures of the Earth’s circumference, or
      make published measurements available to the students at this time.
   Compare the results found in class to published numbers.
   Discuss the differences in terms of percent error.

                         MeasuredValue  AcceptedValue
       PercentError                                       100
                                  AcceptedValue

      Discuss what an acceptable percent error might be in this situation.

Extensions:
   1. Estimate the distance to the center and opposite side of the earth. Use the circumference calculations to
      calculate these dimensions.
   2. Estimate, then use the circumference calculations to calculate, the rate of travel (miles / day) necessary
      to navigate the circumference of the Earth in 80 days.
   3. Assuming that there is a way to navigate the circumference of the globe in an automobile, how many
      days of continuous driving would it take, at a rate of 60 mph, to circumnavigate the circumference of
      Earth?

Links:
    Google Earth: http://earth.google.com
    Google Earth Tutorials: http://earth.google.com/userguide/v4/tutorials/index.html
                                    Teacher’s Notes
Estimations:
   Estimations prior to using Google Earth are an important motivational and mathematical component to this
   lesson.

Earth’s Dimensions:
   Equatorial circumference: about 24,901 miles
   Polar circumference: about 24,860 miles

Answers to Extensions:
   1) Earth’s Diameter at the equator = 7,926 miles: Radius = ½ Diameter
   2) Rate of travel needed to navigate the globe in 80 days = 311 miles/day
   3) Number of days required to travel around the world at 60 mph = 16 2/3 days.

Example Problem:
This is a Polar Circumference example
showing two points on one line of longitude,
50° West, between latitudes 12° North and
38° North.

“Google Earth” ruler tool gives the distance
between the two places as 1767.95 miles.
Using this data results in the following
proportion:

Circumference / 1767.95 = 360° / 26°

Solution:
Polar Circumference = 24,479.30 mi.


Diagrams showing how degrees of longitude and latitude are numbered.




                                          http://www.lakelandsd.com/tutorial/lesson1.htm
                                          l

								
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