Geoscience Reference
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involves using a GPS receiver to measure the distance between two lines of
latitude, determining the distance between the two, and calculating the cir-
cumference of the Earth from those two readings. Thanks to the accuracy of
GPS technology, you do not have to walk nearly as far as Eratosthenes' sur-
veyors did—only a few hundred meters, at most. After determining the polar
circumference, you can calculate the equatorial circumference, and then the
mass and volume of the Earth. From your stroll with an ordinary GPS receiver
and your calculations, your circumference estimate should be within 1% of the
accepted value of the circumference of the Earth, providing a perfect example
of the power of combining geography and mathematics.
2.3 Practice: Measuring the circumference of the Earth using GPS
With a GPS receiver, you and a group of colleagues can incorporate some of
Eratosthenes' methods to accurately measure the circumference of the Earth
to within 1% of the accepted value. This activity involves going into the field,
to a broad open area, to calculate the circumference in a variety of different
ways. Emulate Eratosthenes' methods in the field using modern technology,
specifically GPS. By so doing, you are integrating geography, mathematics,
Earth science, and physics to solve an applied problem.
We will calculate and consider both the polar and equatorial circumferences
of the Earth as well as the Earth's mass and volume. At the end of the field
work, evaluate how close your measurements are to the accepted values of the
Earth's circumference, mass, and volume!
2.3.1 Measuring the Earth's polar circumference using Table 2.1
1. Participants should organize into teams of two.
2. In each team, you will mark waypoints using the UTM (Universal
Transverse Mercator) coordinate system, where the units are in
meters. The numbers for UTM represent eastings (relative to the
Central Meridian in the UTM zone), and northings (relative to the
Equator). Important: Set each unit to the datum WGS 84 so that all
participants are working with the same datum (model of the Earth's
shape). To obtain decimal degree values (latitude-longitude coordi-
nates) for each point, you can set the units to decimal degrees (DD)
once you are back in the laboratory and access the waypoint infor-
mation page for that waypoint to obtain the coordinates in decimal
degrees. Alternatively, you could simply change the GPS units in the
field and gather the waypoints in decimal degrees. Or, you could
organize in teams of two with two GPS's, one set to latitude-longitude
decimal degrees, and the other in UTM eastings and northings.
3. Locate a safe place away from buildings, cliffs, trees, power lines, and
other obstacles such that you will be able to walk in a north/south
direction for at least 200 meters—the longer the better. You can use
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