Geometry of the Sphere - Spatial Mathematics: Theory and Practice through Mapping - page 19

across large regions. We will return to the topic of datums when we address
elevation data in a later chapter.
In the following section, you will have the opportunity to put the concepts
of absolute location, latitude and longitude, precision, accuracy, and GPS into
practice. In the first activity, you will use an online mapping service to deter-
mine the positions on the opposite side of the Earth, the antipodal points. You
will also use a latitude-longitude finder to determine the position opposite
from your current location, and you will examine land areas on the opposite
side of the Earth using two antipodal maps.
1.6 Practice using selected concepts from this chapter
In this section, you will have the opportunity to practice with routes, coor-
dinates, and precision and accuracy to enhance your understanding of the
concepts presented in this chapter.
1.6.1 Antipodal points
Start a web browser and access Google Maps ( http://maps.google.com ). Access
the “Earth” view to start Google Earth with its 3-D capabilities in your browser.
If you do not see the “Earth” choice, install the Google Earth plug in from www.
google.com . In the search box, enter the latitude and longitude of London as
follows: 51.5, 0. Antipodal points are a pair of diametrically opposed points on a
great circle; they are 180 degrees apart. The antipodal component to latitude is
the negative of that latitude. The antipodal component to a western hemisphere
longitude is that longitude plus 180. The antipodal value to an eastern hemi-
sphere longitude is that longitude minus 180. Thus, the antipodal component
to 51.5 degrees (north) latitude would be - 51.5 degrees (south). The antipodal
component to zero degrees longitude is 0 + 180, or 180 degrees longitude. The
antipodal component to 40 degrees north latitude and 105 degrees west lon-
gitude is 40 degrees south latitude and - 105 + 180 = 75 degrees east longitude.
Enter the latitude, longitude value of 45, - 90 into the search box in Google
maps. In what region of the world are you located? You should be in Wisconsin
in the United States. Next, enter - 45, - 72. You should be in the country of Chile.
Calculate the antipodal point. Enter the coordinates of the antipodal point. You
should be in Mongolia. Find the latitude and longitude of your own community.
One tool that enables you to do this task is the Esri EdCommunity latitude-longitude
finder. After you calculate it, enter that latitude and longitude coordinate pair into
Google maps. Then, calculate the antipodal point, and enter those coordinates. What
location is directly opposite your community on the globe? http://edcommunity.esri.
com/maps/geocoder/AGS_EdComm_Geocoder.html . Answers will vary; for example,
the antipodal point to New Orleans at 30 North 90 West is 30 South 90 East, which is
west-northwest of Perth, Australia, in the Indian Ocean.