Exam Summary for GEK1506 Heavenly Mathematics & Cultural Astronomy

Here's a brief summary of some of the main points you should know for the exam. Good luck!

1. Define the following concepts.
   • Great circle.
   • Ecliptic.
   • Celestial poles.
   • Celestial equator.
   • Zenith.
   • Meridian.
   • Horizon.
   • Circumpolar stars.
   • Summer (June) and winter (December) solstices and spring (March) and autumnal (September) equinoxes
   • North pole, arctic circle, tropic of Cancer, equator, tropic of Capricorn, antarctic circle and south pole.
   • Tropics, temperate zones, arctic region and antarctic region.
   • Perihelion and aphelion.
   • Obliquity.
   • Eccentricity.
   • Co-latitude.
2. Know the following facts.
   • Direction of the Earth's rotation.
   • Direction of the Earth's revolution.
   • Direction of the Moon's revolution.
   • Direction of the precession of the equinox.
   • Period of the precession of the equinox. (About 26,000 years.)
   • Value of the obliquity.
   • Approximate dates for perihelion (early January) and aphelion (early July).
   • Approximate dates for the solstices and equinoxes. (Around the 21st of the respective months.)
   • Length of the synodic month.
   • Length of the tropical year. (A little less than 365.25 days.)
   • Length of the sidereal year. (A little more than 365.25 days.)
   • Length of the sidereal day. (23h56m.)
3. How does the length of the day and the rising position of the Sun change in the course of the year at the following places?
   • The north pole
   • The arctic region
   • The arctic circle
   • The north temperate zone
   • The tropic of Cancer
   • The northern part of the tropics
   • The equator
   • The southern part of the tropics
   • The tropic of Capricorn
   • The south temperate zone
   • The antarctic circle
   • The antarctic region
   • The south pole
4. How does the distance between the northernmost and the southernmost rising position of the Sun depend on the latitude?
5. What is the angle between the celestial equator and the horizon?
6. What's the etymology of the following words?
   • Solstice.
   • Equinox.
   • Tropics.
7. If you live in the tropics, how often will the Sun be in zenith? What time of the year will it happen?
8. Why is the tropic of Cancer called the tropic of Cancer? What about the tropic of Capricorn?
9. Explain how you can set up a coordinate system on a sphere once you have determined a great circle and a base point. Show how this works for the following coordinate systems.
   • The longitude/latitude system on the Earth
   • The horizon system on the celestial sphere
   • The equatorial system on the celestial sphere
   • The ecliptic system on the celestial sphere
10. Explain whether the new Moon will be a left, right, bottom or top crescent when seen from the northern hemisphere, the tropics and the southern hemisphere.
11. What are the two astronomical problems with the Singapore flag?
12. What's the difference between the sidereal year and the tropical year? What's the difference between the sidereal day and the solar day?
13. The length of the lunation changes between about 29.25 and 29.75 days. How can Kepler's 2nd Law help explain this? What time of the year do you expect the lunar months to be long?
14. How can you use the altitude of the pole star to find your latitude?
15. How can you use a sextant and a table of the declination of time to determine your latitude?
16. How can you use a sextant, a watch and a table of the equation of time to determine your longitude?
17. In order to win the £20,000 prize, Harrison had to determine longitude to within half a degree after a trip to the West Indies. If we estimate that it would take about 40 days to sail to the West Indies, what was the maximal daily error the clock could have?
18. What point is the origin for maps in Singapore?
19. What are the two causes of the equation of time?
20. Since we are almost on the equator, many visitors expect the Sun to rise around 6 a.m. every day of the year. Why doesn't it do that?
21. The equation of time is zero around the solstices and around April 16 and Sep 1. It takes on its extreme values (around 15 minutes) around November 3 and February 11.
22. At what times of the year do the earliest and latest sunrises occur in Singapore? You don't need to know the exact dates, it's enough if you can give a rough indication using the analemma.
23. What are the definitions of solar, lunar, and lunisolar calendars? Give an example of each.
24. What is the leap year rule in the Gregorian calendar?
25. Explain the change in leap year rule and the skipping of days in the Gregorian calendar reform. When did it happen in souther Europe? When did it happen in the UK?
26. Why was the Mid-Autumn Festival in 1978 was celebrated one day earlier in Hong Kong and Taiwan than in China?
27. What's the rule for determining Vesak Day?
28. What are the dates for Eid ul-Fitr (Hari Raya Puasa) and Eid ul-Adha (Hari Raya Haji) in the Muslim calendar?
29. What's the rule of thumb for determining Easter Sunday?
30. What is the earliest possible date for the following holidays and festivals?
    • Chinese New Year. (January 21.)
    • Mid Autumn Festival. (September 8.)
    • Deepavali. (October 15.)
31. How can you predict the date of next year's Chinese New Year, Mid Autumn Festival, Eid ul-Fitr (Hari Raya Puasa), Eid ul-Adha (Hari Raya Haji) and Vesak Day if you know this year's dates?