GEK1506 Heavenly Mathematics & Cultural Astronomy, Tutorial 3, Solutions

  1. Arctic comes from the Greek work “Arctus”, meaning bear. The reason is that in the Arctic the constellations Big Bear and Little Bear are prominent.
  2. Twice, unless you oive right on one of the two Tropics. For the time, use the applet.
  3. At the North Pole there will be six months of midnight Sun. At the arctic circle there will be one day of midnight Sun. At other points in the Arctic the length of the midnightsun period will be somewhere between these two values.
  4. In Singapore, the difference between the northernmost and the southernmost rising position of the Sun is 47°. As we move away from the Equator, the angle between the daily path of the Sun and the horizon decreases, and the distance increases. When we approach the Arctic Circle, the distance approaches 180°.
  5. The Sun's altitude when it crosses the meridian in Singapore at the June solstice is 66.5° (or 67.5°) in the north, at the equinoxes it is 90° (or 89° in the south) and at the December solstice it is 66.5° (or 65.5°) in the south.
  6. See the notes.
Helmer Aslaksen
Department of Mathematics
National University of Singapore

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