The Great Debate II: Longitude Latitudes and longitudes M.V.N. Murthy The Institute of Mathematical Sciences, Chennai

Co-ordinate Systems The most natural way of defining the position of any object on a surface, flat or curved, is to define an appropriate co-ordinate system. For example, x-y co-ordinates are useful when you want to talk about the size of a room. The length of the room is along the x-direction and the breadth (perpendicular direction) is along the y-direction.

You can use a scale to make measurements. The zero of the scale is the zero of the co-ordinate system from which all distances are measured. This is called the origin of the system.

If you want to measure, not just the length and breadth, but also the height of the room, then x-y-z co-ordinates are more useful.

For spherical objects, x-y-z co-ordinates are not convenient. For spherical objects like the Earth, where only surface distances are important, angles turn out to be more convenient.

You can understand this by cutting an apple (which is approximately round). You usually slice an apple from top to down, always going through the centre. This gives you wedges. Start by calling any one wedge as the first. Then you can specify any other wedge by counting off its ”distance” from the first one. Each wedge makes equal angles with the centre of the apple as you go around.

Suppose you instead cut the apple in horizontal slices (like with mosambi and lemons). You have a central big slice and then smaller slices as you go away from the centre in either direction. Each slice makes equal angles with the centre of the apple, but in an up-down direction.

So there are two ways of slicing the apple: up-down or sideways. If you cut it both ways, you get small pieces of apple. If you make the slices finer and finer, you get smaller and smaller pieces of apple whose suraface is so small it is like a point.

You can see that the wedges are just like lines of longitude and the horizontal slices are just the lines of latitude on Earth.

This is actually an ancient method and was proposed by Eratosthenes from Greece in 3rd century BC for the first time. By 150 AD, astronomer Ptolemy had already plotted these lines on the maps of the World.

Thus on any map of the Earth (flat projection of the spherical earth), the latitudes appear as horizontal lines though they are actually circular. The longitudes appear as curved lines joining the north and the south poles thus forming a grid-like pattern.

The equator that divides the Earth into Northern and Southern hemispheres is a natural choice for fixing the zero latitude whereas the poles correspond to 90 degrees north and 90 degrees south latitudes.

Latitude The Sun appears to drift a few degrees (23.5) north of the equator and a few degrees south over the year. (See article on Solstice in this issue). So the latitude of any place can be found rather easily from the height of the Sun in the sky at noon.

Small corrections have to be made for the time of year and the fact that the Earth is not a precise sphere but this is easily done.

At night there is no Sun, so the Pole star is used instead (in the northern hemisphere). The Pole star always points north. Also, its height in the sky depends on the latitude (it will be higher in the sky at Delhi than Chennai).

So sailors could calculate the latitude easily either in the day or at night.

Longitude However, the accurate determination of the ship’s position requires not just the latitude but also the longitude.

There were two difficulties: one was to fix a zero for the longitude (it was easy for latitude since the Earth is naturally divided into northern and southern hemispheres). But the zero degree longitude has no ready reference. The other difficulty is to actually determine the longitude with some instruments.

Longitude zero In principle the zero longitude can be any where. The Greek astronomer Ptolemy was free to put it along the longitude line running through the Canary islands off the northwest coast of Africa. Over centuries the zero line was moved through many places before it settled down at last on a line passing through Greenwich near London. The prime meridian, as it is called now, passes through the Royal Observatory at Greenwich.

Indian Standard Time is set with reference to the 82.5 degrees East longitude line running through Mirzapur near Allahabad in North India. It is exactly 5 hours 30 minutes ahead of Greenwich time.

Origin of the co-ordinate system

The intersection of the prime meridian with the equatorial (zero) latitude thus provides the origin of the coordinate system that describes the whole globe.

Graphics from Encyclopedia Britannica and plantwatch.sunsite.ualberta.ca end