# GEK1506 Heavenly Mathematics & Cultural Astronomy, Tutorial 4, Solutions

1.  Equatorial Ecliptic Horizontal Polaris 90°, undef. 66.5°, 90° 0°, 0° Vernal equinox 0°, 0h 0°, 0° -90°, undef. Summer solstice 23.5°, 6h 0°, 90° 0°, 293.5°
2. Longitude is related to the revolution of the Earth around the Sun. When the longitude of the Sun is x degrees, we are x days after the vernal equinox. Right ascension is related to the rotation of the Earth, so it runs from 1 to 24 hours.
3. The horizon coordinates are easy to use, but they depend on time and place. The equatorial and ecliptic coordinates require that you know where the celestial equator, ecliptic and vernal equinox are.
4. The daily paths of all the stars are parallel to the celestial equator because their apparent motion is caused by the rotation of the Earth around its axis.
5. When a celestial object it is at its highest position above the horizon, it is on the meridian. Hence the azimuth is 0°, 180° or undefined.
6. The altitude of the pole star is equal to your latitude.

Helmer Aslaksen
Department of Mathematics
National University of Singapore
helmer.aslaksen@gmail.com

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