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 Summer 1997

  Michael Fowler

 1. Eratosthenes also figured out correctly the angle of tilt of the earth's axis. He found it to be 23.5° to the "vertical" where "vertical" is defined by taking the earth's orbit around the sun to lie in a "horizontal" plane.

What observations did he need to make to find that angle? Explain how it might be done.

2. Eratosthenes was also the first to draw a map using lines of latitude and longitude.

 Explain what those terms mean.

 What observation, using a protractor to measure an angle, could you do to measure your latitude?

 Why are lines of latitude often called "parallels", and why not use the term for lines of longitude as well?

Unlike latitude, longitude is relative, in that we can assign longitude zero to some place and start from there. The standard convention is that Greenwich, near London, has zero longitude.  

How can you determine your longitude relative to Greenwich? Or, how can you find the longitude difference between, say, Norfolk and Charlottesville? How was it done in Jefferson's time?

3. Many small models and textbook diagrams give a misleading impression of the solar system because the distances are drawn too small, compared with the sizes of the sun, earth, moon, etc. For example, looking at these models it's hard to believe the moon doesn't get eclipsed every month.

 Suppose we take our 12 inch globe and three inch moon, and place them the correct distance apart in the room to correspond to the earth-moon distance. Find the distance, and place them appropriately.

 Comment now on where the earth's full shadow (umbra) is on this scale.

Actually, the moon's orbit around the earth is not in the plane of the orbit around the sun, but is tilted at 5° to it. Can you explain why this means there won't be a lunar eclipse every month?

How large and how far away would a correctly scaled model sun be from our 12 inch earth and three inch moon?

Like the first quiz, this was really a set of problems designed to initiate discussion. The teachers worked in groups of four to a table, each table having a 12" globe and a 3" styrofoam moon, and there was a central bright light at globe level for the sun. The problems were to be attacked by working with these objects.