# GEK1506 Heavenly Mathematics & Cultural Astronomy, Sun Homework

## Goals of the Homework

There are three goals of the Sun homework.

• Observe the setting (or rising) position of the Sun over the course of two months
• Estimate the date of the zenith passage around September 20 or March 24
• Study the changes in the shape of the shadow path of a vertical sundial over the course of three months
 Sunset in August Sunset in September

## Detailed Description

On a day in August (January), determine the rising or setting position of the Sun. Take a picture showing the Sun rising/setting, and use a compass (the magnetic declination is negligible in Singapore) to estimate how many degrees the rising/setting point is from due East/West. If your compass doesn't have a degree scale, you can use a protractor or use your hand as explained in the links on the Moon homework.

On a day in August (January) suspend a ring-shaped object vertically in the East-West plane. What does the shadow of the ring look like on the ground? Where does the shadow of the half of the ring closest to the Sun fall with respect to the other half of the ring? Take a picture of the ring that illustrates this. Indicate north in your picture. You do not have to do this on the same day as you take the picture of the Sun. You can take this picture any time of the day. You can take this picture anywhere. It is important that the ring is in the East-West plane. Please include a compass in your picture. You may want to think about what is a good size and thickness for the ring. You may want to fasten an object to the bottom half of the ring, so that it is easier to distinguish between the shadows of the two halves.

On a day in August (January) put a stick in the ground. Take at least five photos of the shadow of the stick in the course of the day. (This of course depends on the weather. You may want to take more than five pictures at various times of the day, and then at the end pick the best five. In order to get a nice curve, you need a reasonable spread.) Mark the shadow points on the ground, and draw a curve on the ground estimating the path of the shadow. Take a photo of this path, too. I want pictures of both the individual marks and the overall path. It is easy to fake the overall path, but unless you have some fancy lighting equipment, it is hard to fake the individual mark pictures. You do not have to do this on the same day as either the Sun or the ring pictures. This part requires the whole day. Remember to pray for sunny weather, and think about what is a good length for the stick.

Repeat the sunrise/sunset picture and shadow path experiment near the September equinox around September 23 and in October (in February and near the March equinox around March 21). Repeat the ring experiment on the zenith passage around September 20 and in October (in February and on the zenith passage around March 24). For the zenith passage picture, you can take the picture any time of the day, so I want a picture that looks like it is taken on the day of the zenith passage. For the sunrise/sunset picture and the shadow path picture, you may not be able to do them on the day of the equinox, but I want them close to the equinox. Compare the observations and explain the differences.

You can chose sunrise or sunset depending on what is most convenient for you, but please use the same for all three observations. It is important that the sunrise/sunset pictures are taken from the same place (and preferably with the same camera), so that the pictures are easy to compare.

You will be graded on the clarity of your presentation. The pictures must clearly illustrate the concepts.

Please do this in your project groups and submit both soft copy and hard copy.

## Links

Helmer Aslaksen
Department of Mathematics
National University of Singapore
helmer.aslaksen@gmail.com

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