Mathematica 2015

Shackleton, Sextant and the…quadratic regression

----Jan Rybojad (Y12)

 A brief history of nautical navigation 10

Ever since the ancient times, sailors have been wondering about the way to navigate. Firstly, the travellers used maps – which are equally old as the scripture. However, it was impossible to make a map of a sea as the sailors could see there nothing but water. The 3 rd century BC brought 2 new inventions that have revolutionised the world of navigation. One of them is the magnetic compass, which was invented by the Chinese. 11 Firstly used by the fortune tellers, a magnetized needle suspended in a liquid was discovered to point always in the same direction. The other invention was the idea of the geographic coordinate system invented by Eratosthenes of Cyrene in the similar point in time. This unified system enables all travellers to communicate easily about any position on Earth. Later on, in 1884, the conference in Washington decided that the Prime Meridian (0°) is the one determined by the Greenwich Observatory. 12

Longitudes and latitudes 13

But how can one determine their longitude and latitude having no GPS available. Well, already in the past, scientists have discovered that some celestial bodies appear roughly in the same place on the sky every day on a particular hour or they even do not move at all! Thanks to the equal velocity of Sun’s rotation

around Earth (relative to us; as perceived by people on Earth), one can predict Sun’s position on the sky for every day of the year. The angle by which the sunlight shines on the equator is known as the declination. Knowing the declination at the noon for the particular day of the year, and the angle between the horizon and the

Figure 1: The declination of Sun [12]

10 A. J. Bratcher, “History of Navigation at Sea,” [Online]. Available: http://www.waterencyclopedia.com/Mi- Oc/Navigation-at-Sea-History-of.html. [Accessed 15 April 2015]. 11 M. Bellis, “The Compass and other Magnetic Innovations,” [Online]. Available: http://inventors.about.com/od/cstartinventions/a/Compass.htm. [Accessed 15 April 2015]. 12 “The Prime Meridian at Greenwich,” [Online]. Available: http://www.rmg.co.uk/explore/astronomy-and- time/astronomy-facts/history/the-prime-meridian-at-greenwich. [Accessed 15 April 2015]. 13 “How to navigate by the Sun?,” [Online]. Available: https://www.youtube.com/watch?v=CycmCFb-6VU.

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