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Baiju Mathew

Pre-GPS Navigation & Geometry of the Sun-Earth Waltz

Updated: Feb 23

reading time 6 minutes, 1200 words



Humankind has always been wanderers and explorers. We can imagine that as hunter-gatherers our ancestors would go in search of food and then return home with the help of markers like trees, waterbodies or mountains. Even other animals and birds do have their means of locating themselves. These animals and birds may have direction instincts in-built in them. Instinctive knowledge has limits; our ancestors developed navigation to much beyond instinct, and founded it on firm knowledge based footings that could be passed down the generations. The meticulous recording of patterns in the night sky, by our ancestors, helped us get an orientation of our location. This was further aided by the way we devised, in modern times, an imaginary grid of latitudes and longitudes crisscrossing the Earth, these are called the ‘Coordinates’. These Coordinates allow us to specify any particular location on Earth. Fortuitously, in the sky over the north hemisphere there is a star that appears stationary, and thus always lets us know which direction is north. Every other star can be then located in relation to this star. This is the North Star, also called Polaris. This star appears stationary because it is roughly in the direction to which the axis of rotation of Earth points.  We need to understand that this orientation of the axis is maintained while the Earth revolves around the sun. Therefore, whatever be time of the day, or day of the year, Polaris remains at the same location. Our ancestors observed that the position of Polaris does not change allowing it to be used for finding our bearings. It may be noted that since this axis or rotation changes over thousands of years, our ancestors used a different star as their north star, now this star is Polaris.


Let us now understand the ingenuity of how a coordinate is assigned to a location. The following figure shows how the Coordinate Grid:



Determining the Latitude of a Location:


There are 180 latitudes, 90 in the northern hemisphere and 90 in the southern hemisphere. Each latitude is evenly spaced from one another. Similarly, the longitudes are equidistant from each other at the equator.


The geometry of this system, superimposed on Earth, operates in a way that, when observing Polaris from any location, Latitude of a location is the angle that the line-of-sight to Polaris makes with the horizon. Horizon can simply be understood as the horizontal. For example, from Mumbai, Polaris is at 19.08deg angle from the horizon, thus indicating the latitude of Mumbai to be 19.08deg north.


Determining the Longitude of a Location:


There are 360 longitudes, 180 to the east of the main meridian, shown as a red line in figure 4, and another 180 of them to the west of the main meridian. Kindly refer to figure 5 below:


During equinoxes, at dawn, sun illuminates the Earth along a singular meridian at any given time. This implies that if we take two locations on the same meridian, on equinox the two location will experience sunrise, noon and sunset, or any other time for that matter, will be synchronous. This phenomenon is instrumental in determining longitude of a location. The ‘Prime’ meridian, assigned as 0deg longitude, runs through Greenwich observatory. Over the course of 24 hours, Earth spins one complete rotation, which is 360deg of geometry (comprising of 180deg East + 180deg west totalling 360deg longitudes.) Given that 24 hours has 24X60= 86,400 minutes, the time difference between each longitude will be 86,400 minutes divided by 360deg longitude equal to 4 minutes per longitude.

 

 

Navigation Method:


Navigation requires two essential elements, location of one’s position and location of the destination. Therefore, navigation is essentially finding the coordinates of a particular location.

Determining Latitude

Look at the position of Polaris and calculate the angle between Polaris and the horizon formed at the eye of the observer. This angle is the latitude of the observer. The instrument used for this is a sextant.

Determining Longitude

Carry a reference clock that shows time at a known location. Determine local time of one’s present location by reference to the celestial bodies including the sun. Divide the difference in time between the known location and present location by 4 minutes per longitude to derive the longitude of one’s location.

Throughout history, astronomers have charted the celestial bodies that appear at specific times at specific locations of the sky, as seen from various locations on Earth. This compilation, known as, the almanac, serves as a valuable reference for the navigators, to determine their location. They look at the sky and identify a celestial object. Then, they refer to the almanac of a known place and note the difference in their present sky to figure out their present coordinate. Notably, Polaris is not visible from the southern hemisphere, hence other celestial objects from the almanac is used to determine the latitude, in the southern hemisphere.


In situations where navigators do not have access to a reliable clock or a clear sky to observe celestial bodies, the ‘dead reckoning’ method is used. In dead reckoning, the present location is derived from the last known location by adding the course taken by the traveller to the coordinates of the last known location. Hence, it is important for the navigators to record a proper log of movements, like the log of a ship’s voyage. The Star Trek fans would remember Captain Kirk recording his log on USS Enterprise!


The reader will be wondering, why the magnetic compass is not even mentioned? After all, even the photo above shows Jack Sparrow looking at his Compass! Well, the compass is used to get the orientation i.e. north, when the Polaris is not there.

I had started this post to explore how GPS works, and thought it would be interesting to also look at the traditional navigation method. Next post will be on how GPS system works

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