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
• Estimate the date of the zenith passage around September 20 or March 24
• 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
• Determine 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. 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.

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). For the zenith passage picture I want a picture on the day of the zenith passage, since you can take it any time during the day. (Strictly speaking, seeing that the shadow of the top part falls on the bottom part only shows that the Sun is on the celestial equator, but it follows that on that day it will cross the meridian close to zenith.) For the sunrise/sunset 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, so that the pictures are easy to compare.

Small crescent in the top middle: Second day of the Chinese month, 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 through four. 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 19 September 2009, but we are not likely to see the crescent that evening, even though 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 20/9 and 21/9. I realize that this may be a problem for Muslims. In that case, I hope you can get somebody else from the group to take pictures on those days. If not, please come and see me, and I will work out something.
• 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.
• 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. For the three crescent Moons close to the horizon, use a protractor to measure the approximate tilt of the Moon. 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 want a picture that shows the horizon, or at least buildings on the ground. 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.

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!

How to Estimate Angles in the Sky

• Measuring Angles in the Sky.
• Astronomy Note on estimating angles.
• Austin Astronomical Society -- How to Estimate Angles in the Sky.

Links about the Sun

• The National Environment Agency on Singapore has a number of interesting pages, like Sunrise and Sunset Times, Moonrise and Moonset Times and Tide Times for Singapore.
• The Astronomical Applications Department of the U.S. Naval Observatory has a lot of interesting pages on their Data Services and FAQ, like Virtual Reality Moon Phase Pictures, Phases of the Moon, Phases of the Moon and Percent of the Moon Illuminated, Rise, Set, and Twilight Definitions, Earth's Seasons Equinoxes, Solstices, Perihelion, and Aphelion 1992-2020, Sun or Moon Altitude/Azimuth Table for One Day and Sun or Moon Rise/Set Table for One Year. You can use the last one to print out a table of rising and setting times for the Sun and the Moon in Singapore. The coordinates of Singapore are 104 east and 1 north. Our time zone is UTC + 8.
• If you need to do computations, there is a handy table of the equation of time and the Sun's declination on the Daily Sun Data at Tony Helyar's Home Page. The table of declinations can be used for estimating the azimuth of the Sun in Singapore, since we are almost on the Equator.
• A nice Table of the Declination of the Sun.
• Sun, Moon & Earth Applet and Sun Declination & Equation of Time from Juergen Giesen's GeoAstro Java Applet Collection.

Links about the Moon

• The National Environment Agency on Singapore has a number of interesting pages, like Sunrise and Sunset Times, Moonrise and Moonset Times and Tide Times for Singapore.
• The Astronomical Applications Department of the U.S. Naval Observatory has a lot of interesting pages on their Data Services and FAQ, like Virtual Reality Moon Phase Pictures, Phases of the Moon, Phases of the Moon and Percent of the Moon Illuminated, Rise, Set, and Twilight Definitions, Earth's Seasons Equinoxes, Solstices, Perihelion, and Aphelion 1992-2020, Sun or Moon Altitude/Azimuth Table for One Day and Sun or Moon Rise/Set Table for One Year. You can use the last one to print out a table of rising and setting times for the Sun and the Moon in Singapore. The coordinates of Singapore are 104 east and 1 north. Our time zone is UTC + 8.
• Moon info at John N's web site for Astronomy and Meteorology.
• Moon Phases.

Links about Crescent Visibility

• Khalid Shaukat's Moonsighting.com.
• Dr. Monzur Ahmed is the author of MoonCalc, which for many years was the leading lunar visibility and Islamic calendar software. He has pages on Astronomy and Islam and Ramadhan (Ramadan) and Eid-al-Fitr.
• The web page of the Islamic Crescents' Observation Project (ICOP) has a number of interesting articles. They also host the software Accurate Times by Mohammad Odeh. It is a Windows program for the Islamic calendar, Qiblah direction, and prayer times. There are samples of the lunar visibility charts on Visibility of Ramadan Crescent.
• Islamic calendar for Singapore by Majlis Ugama Islam Singapura (MUIS), the Islamic Religious Council of Singapore. MUIS seems to move the location of their calendar around from year to year. If the link doesn't work, go to their homepage and look under "Downloads" or do a search for Takwim (or Taqwim). This will give you MUIS's prediction for first visibility of the lunar crescent. But it is based on a dubious method, so you will often not be able to see the Moon on the day when MUIS claims that you will. Please see my page on The Islamic Calendar.
• Islamsk Råd Norge, Hilalkomiteen (in Norwegian) explains the policies of the Islamic Council of Norway.
• HM Nautical Almanac Observatory in the UK makes very nice lunar visibility charts. Their Websurf contains a wealth of information, including Global First Sighting of New Crescent Moon information for the last couple of years. The charts for the current month are also available at Moon Watch.
• Moon Watch.
• Crescent Moon Visibility and the Islamic Calendar from the Astronomical Applications Department of the U.S. Naval Observatory.
• Moon Research Centre (U.K). The article on Policies Adopted in Britain by Muslims in Celebrating Islamic Festivals is essential reading! They also have a copy of the RGO Astronomical Information Sheet No. 6.
• Predicting the First Visibility of the Lunar Crescent, The Umm al-Qura Calendar of Saudi Arabia, Islamic-Western Calendar Converter (Based on the Arithmetical or Tabular Calendar) and Internet sites over de islamitische tijdrekening (in Dutch) by Robert H. van Gent.
• Crescent-Sighting and Islamic Calendars and Islamic Astronomy: Questions, Comments and Correspondence by David McNaughton.
• CrescentWatch Australia is a nice site, but they have a bad moon rising on the top. Can you tell what's wrong with the pictures?

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