# GEK1506 Heavenly Mathematics & Cultural Astronomy, Tutorial 10, Solutions to Selected Questions

1. If it is noon on Sunday at Greenwich it will be late Sunday night if we move 179° east from Greenwich and early Sunday morning if we move 179° west from Greenwich. What if we move 181° east? Then it will be early Monday morning or early Sunday morning depending on our point of view. For most time zones it will be one hour earlier to west and one hour later to the east, but in order to avoid inconsistencies, there must be a jump somewhere where two neighboring time zones are one day appart. It is convenient to have that jump in the Pacific, since there are few people living there and since it is opposite from Greenwich.
2. 2min/40=3s.
3. If you were at the equator on the June solstice, the altitude of the Sun would be 66.5° in the north. Your latitude must therefore by (90-66.5)°+(90-68.5)°=45° north.
4. On Valentine's Day, February 14, the equation of time reaches its minimum of about -15m. That means that true noon at Greenwich is at about 12:15. Your longitude is therefore 105°.

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