GEK1506 Heavenly Mathematics & Cultural Astronomy, Homework

Goals of the Homework

Picture Picture
Sunset in August Sunset in September

Detailed Description

On a day in August (January) take a picture showing the rising or setting position of the Sun. You don't need to take it just when the Sun is rising or setting, just make sure that you get both the Sun and the horizon (or whatever you see instead of the horizon at your place) in the picture, and that the picture gives a sense of where the Sun is rising or setting. 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 described in the links at the bottom of the page.

On a day in August (January) suspend a ring-shaped object vertically in the East-West plane so that is represents the celestial equator. What does the shadow of the ring look like on the ground? Take a picture of the ring that illustrates this. 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. Include a compass in your picture and indicate north. Hint: It is easier to get good pictures if the ring is fairly large, but narrow. You may want to indicate the East-West line on the ground directly below the ring. That makes it easier to see which half the shadow falls in. You may also want to attach a mark (paper clip, for instance) on the ring, so that I can see which part of the ring corresponds to which part of the shadow.

Repeat the sunrise/sunset picture 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). You may not be able to take pictures 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, so that the pictures are easy to compare.

Small crescent in the top middle: Evening of second day of the Chinese month, start of first day of the Muslim month

Take a picture showing the view from the room of one of your group members. I also want an aerial photograph (using for instance Google Earth). Draw on the picture where you estimate the path of the Sun to be at the solstices and the equinoxes. Try to estimate what time during those days you can see the Sun from your window. Depending on the view from your window, not all the three paths may be visible, but I want a picture that gives a reasonable impression of when the Sun will be visible from your room on those three dates. I'm not expecting exact values, just reasonable estimates that shows that you have learned the key concepts about the motion of the Sun. Please choose a window where there is some clear sky visible. I would like to see the frame of the window, so that I have a frame of reference.

You will be graded on the clarity of your presentation. The pictures must clearly illustrate the concepts and confirm that you made the observations.

Please submit both soft copy and hard copy.

More Details of the Homework

How to Estimate Angles in the Sky

Links about the Sun and the Moon

Links about Crescent Visibility

Helmer Aslaksen
Department of Mathematics
National University of Singapore

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