# GEK1506 Heavenly Mathematics & Cultural Astronomy, Homework

## Goals of the Homework

• Take three pictures showing the change in the setting (or rising) position of the Sun in the course of the semester
• Take three pictures showing the changes in the shadow cast by a ring
• Take pictures of the Western horizon on the first three days of the lunar month to determine the day of the first visibility of the lunar crescent, i.e., the first day of the Muslim month
• Take a picture of the first daytime visibility of the Moon
• Estimate the tilt of the Moon when it is a crescent close to the horizon
• Estimate where and when the Sun can be seen from your window in the course of the year
 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
• I want photos of the Moon on each of the first three days of the Chinese lunar month that starts after September 1 or February 22. (I don't want to ruin Chinese New Year for you!) However, if the new Moon occurs after sunset on the first day, I want pictures of day two and three. If we have an evening lecture, we will either skip the picture if we are not likely to see the Moon, or take a "field trip" to take pictures.

There is a new Moon on Wednesday 8 September 2009 10:30 UTC (18:30 Singapore time), but this is close to the time of sunset in Singapore, so there is no chance of seeing the Moon that evening. According to Khalit Shaukat there is a borderline chance of us seeing the crescent on Thursday 9/9/20. MUIS, using the MABIMS criteria, starts Hari Raya Puasa that evening.

So to simplify, let us just take pictures of the second and third days, that is 9/9 and 10/9. I realize that this may be a problem for Muslims and people going away for the long weekend. In that case, I hope you can get somebody else from the group to take pictures on those days or alternatively you can take pictures at the start of the next lunar month on Friday 8 October 2:44 Singapore time. I would then like to see pictures on Friday 8/10 (not likely to see the Moon), Saturday 9/10 and Sunday 10/10.

• I want a picture of the Moon on the first day it is visible during daytime (before sunset). I do not know which day this will be. You may have to try several days. This picture can be taken anywhere and any time. However, I want a "real" daytime picture. I don't want one taken just before sunset, where you can clearly see that the sky is beginning to change color.
• For each observation include the following.
1. Photo of the Moon. For the three crescents I want a photo showing the horizon and the Moon. (Or a building or something else that indicates where the horizon is.)
2. Time of the photo.
3. Age of the Moon by indicating the day of the month in either the Chinese, Islamic calendar or an Indian lunisolar calendar. (But please don't use an Indian solar calendar!)
4. Approximate azimuth using a compass.
5. Approximate altitude using your hand as described in the links at the bottom of the page.
6. If you can see the Moon in the pictures from the first three days of the month, use a protractor to measure the approximate tilt of the Moon with respect to the horizon. By the tilt I mean the angle between the line between the two "horns" and the horizon. Discuss briefly whether the angle of the tilt matches the theory.
7. Time of sunrise, sunset, moonrise and moonset for that day.

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

• You may not be able to see the Moon because of the weather. In that case, I want pictures of the Western horizon at times when you could have seen the Moon, i.e., between sunset and moonset. However, if you claim that you couldn't see the Moon on a certain day, and several of your classmates get nice pictures, you have a problem.
• The most crucial observation is the one for the day that starts the Muslim month, usually the second or the third day of the Chinese month. Use Khalid Shaukat's Moonsighting.com, MoonCalc or Accurate Times to predict when the crescent will first be visible. Make a serious effort to see it that night. Don't give up before the time of moonset. If you can't see it, I want at least a picture of the western part of the sky between sunset and moonset.
• This is a major exercise in team management! You can do it while on trips, dates or whatever! On the crucial first day of the Muslim month, you may want to divide your group into several teams in case one part of the island is cloudy or one one team has picked a bad spot. For the other observations, you may schedule different people in your group to attempt to make observations on different days.
• It is very hard to take good pictures of the Moon. Please don't despair; it's just as hard for everybody else! Please don't try to impress me with photos from the web or past homework!