2.1 Latitude and Longitude
1. To get started, use the globe to find approximate map coordinates for the following major cities around the Earth:
a) Chicago, Illinois b) Honolulu, Hawaii c) Tokyo, Japan d) Sydney, Australia e) Kinshasa, Zaire f) Sao Paulo, Brazil g) London, England h) Cairo, Egypt i) Moscow, Russia2. One natural question about map coordinates is whether you can tell the distance between two points from the difference of their coordinates. Collect some data from your globe to explore this question:
1. What big ideas about the size and shape of our Earth seem prerequisites for defining longitude and latitude, and in what order do you think those ideas were discovered?
2. The system of latitude and longitude coordinates is only one of many locator systems used in a whole variety of tasks. Think about and describe several other coordinate locator systems that you are familiar with. Then compare them with the basic features of Earth longitude and latitude coordinates.
3. What is it about 90o, 180o , and 360o that makes them common in angle measurement?
4. The Equator is the line (circle) of latitude with measure 0; the prime meridian is the line (circle) of longitude with measure 0. Which of these two great circles pretty much has to have a coordinate of 0o and which has that coordinate pretty much by historical accident?
5. How do you think satellite dishes for television are "tuned in"?
6. The U. S. Defense Department now has a global positioning system that uses orbiting satellites and a portable piece of apparatus on the ground that can be carried by an individual soldier. It will tell the soldier his or her location on the Earth to within 1 meter of his true location! How do you suppose it does that?
1. To get a rough idea of the kind of scale model that would be needed to do accurate Earth-Sun simulations, consider these data:
1. What geometric shapes and measurements play key roles in a solar system model and in explaining days and nights and years and seasons?
2. Because the Sun is so much larger than the Earth and so far away from the Earth, it is hard to make true scale model drawings of the relationship between them. However, the following drawing (inaccurate as it is in some respects) can be used to describe some important aspects of the relationship. Imagine that you are looking at a side view of the Sun and Earth with your eye directed along the orbital plane.
1. Imagine that the year is 240 B. C. and you live in Alexandria. You accept the general idea that the Earth is round, so you can imagine it marked up with lines of latitude and longitude, but you don't know its size. First bright idea: If you knew the connection between change in latitude and distance on the earth's surface, you could estimate the circumference of the earth.
If a one-degree change in latitude corresponds to a known distance d, how would you calculate the circumference of the Earth?
2. Imagine next that someone phones you from a place due south of your home and says "Whew, is it hot! I just went outside and the Sun is directly overhead." You hang up and go outside to find that the Sun is not directly overhead where you live.
3. One observation that might help your reasoning is the fact that, because the Sun is so large and so far from Earth, its light comes in a beam that can be thought of as parallel light rays.
How, if at all, does this assumption change your thinking about using Sun rays to measure change in latitude between two spots on the Earth?
4. The following sketch shows a side view of the Earth with Sun rays falling at two places, one directly north of the other. The Sun is directly overhead at point A, but not directly overhead at point B. Suppose that it is you standing outside in the Sun at point B and your friend at point A.
He found the angle to be about 7f(1,5) o . What does that tell you about the latitude of Alexandria, in relation to Syene?
1. The latitude and longitude of Washington, DC are about 39o N and 77o W; the location of Nassau in the Bahamas is about 25o N and 77o W. How far apart (in miles) are the two cities?
2. Chicago, Illinois is located at about 42o N and 87o W while Managua, Nicaragua is at about 12s (o) N and 87o W. How far apart (in miles) are those two cities?
3. The city of Madison, Wisconsin is located at about 89o west longitude and New Orleans, Louisiana at about 90o west longitude. How could you get friends in those two cities to collaborate with you to make the measurements needed in Eratosthenes method of estimating the circumference of the Earth, using the fact that it is about 1000 miles on land from Madison to New Orleans?
4. Without access to a modern clock or telephones to communicate, how could observers at Syene and Alexandria know that their Sun shadow observations were occurring at the same time on the same day?
5. Without knowledge of the magnetic compass, how could people have known about directions of North, South, East, and West?
6. On the following sketch of parallel lines cut by a transversal, what pairs of angles are congruent and how do those facts play a critical role in Eratosthenes' method for estimating the circumference of the earth?
1. How could you reproduce the experiment of Eratosthenes without leaving Spain?
Use whatever current globe or atlas information you need and write up a careful explanation of your method and conclusions.
2. Use your result from (1) and further reasoning to figure the distance around the Earth at a latitude of 30o. The following sketch might be a helpful guide in calculating the circumference of that circle of latitude.