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Global Exercises

Michael Fowler

Physics Department, UVa

1. Orient the globe towards the light corresponding to 1 p.m. EDT in Charlottesville (that's noon EST) on June 21. At that instant, where in the world would an exactly vertical stick cast no shadow? (It might have to be on the deck of a level ship).

2. Is there only one spot in the whole world where this is true? Explain your answer.

3. By turning the globe around slowly with the base not moving, come up with an estimate of the times of sunset and sunrise in Charlottesville on June 21. (Give your answers in EDT.)

4. Find how long the night of June 21 is in Edinburgh, Scotland; Barrow, Alaska, and Quito, Ecuador. (And what does that name "Ecuador" mean?)

5. Eratosthenes found that on June 21 a vertical stick at Syene (now Aswan) cast no shadow. Check that out using a flat head nail. Then place another one at Eratosthenes' hometown of Alexandria. Notice that they are not parallel.

6. Orient the globe corresponding to the angle with the sun for September 21. Repeat question 4.

7. Place a nail on the globe at Charlottesville to see how the shadow moves throughout the day. Which way does it point at midday? Describe in words how the shadow on a similar sundial would move in Capetown, South Africa, then check out your prediction with the globe. What would a sundial designed to be used at the north pole in summertime look like?

8. Use the globe in the appropriate orientation to find the angle the sun makes with the vertical at midday on June 21? On December 21?

What we found when we did these exercises:

We had six globes (12" from Barnes and Noble, also at Toys R Us, \$20 each) and had a group of four working with each globe. This is much more effective for learning than one globe in front of the whole class, and globes are not that expensive. For globe stands, we used inverted plastic buckets, which worked fine. All the globes were illuminated by a bright light placed carefully at just the height above the classroom floor of the centers of the globes.

One problem was that using a single bright light for the sun, reflected light from the walls was bright enough to make the difference between "day" and "night" on the globe rather small (although not difficult to see). For a class using a single globe, this can be solved by using a projector, with the slide replaced by something with a round hole in it just big enough to fully illuminate the globe. There is then little reflected light. This is not practical for several groups in the room, of course. We could have put black material to shield the backs of the globes a bit. It would be dramatic to do the experiment outside after dark.

We used roofing nails, because they have a large flat head, so when the head is placed in good contact with the globe, the nail is definitely vertical. However, holding the nail  between the fingers, it's difficult to see its shadow. Holding the nail with a pair of nail tweezers or a bent paper clip works pretty well, but then you have to be careful to check that its head is really flat against the globe. The nail can also be just taped against the globe, for example using two nails for question 7.

We went on to demonstrate phases of the moon as observed from earth. For this demonstration, we had a single setup. We used a three inch styrofoam ball to represent the moon (thus approximately the right size for our 12 inch globe earth). We illuminated the moon with the projector mentioned above, then viewed it using a small video camera placed on the surface of the earth, being sure to have the video camera "upright" as would be understood by someone standing on the earth at the corresponding point. It was the easy to see how the angle of the crescent moon was quite different viewed from different places on earth at the same time.

We did not put the moon the correct scaled distance from the earth, which would have been thirty feet.