GEK1506 Heavenly Mathematics & Cultural Astronomy, Tutorial 3

1. What's the etymology of the following words?
   • Solstice
   • Equinox
   • Tropic of Cancer
   • Tropic of Capricorn
   • Tropics
   • Arctic
   • Antarctic
2. If you live in the tropics, how often will the Sun be in zenith? What time of the year will it happen?
3. How long will there be midnight Sun at the North Pole? At the arctic circle? At other points in the Arctic?
4. How does the distance between the northernmost and the southernmost rising position of the Sun depend on the latitude?
5. What is the Sun's altitude when it crosses the meridian in Singapore at the solstices or equinoxes?
6. Describe how you can construct a coordinate system on a sphere. Describe in detail
   • Terrestrial latitude and longitude
   • Altitude and azimuth
   • Declination and right ascension
   • Celestial latitude and longitude

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