The Theory Behind Longitude

Your coordinates while at sea depend on two dimensions, Latitude and Longitude. Latitude is your position on the surface of the Earth based North/South, while Longitude is your position on the Earth based East/West.  Previously, we have discussed the math and simple calculations to find your Longitude without going into the theory behind the calculations.

Longitude is time dependent, and longitude will also make time zones make sense as well. As with before, a Earthcentric view of the solar system makes longtitude easier to explain, but do remember that it is the Earth that revolves around the sun (Heliocentric Solarlarsystem). So, back to the Earthcentric view:  The sun revolves around the Earth in 24 hours, and the Earth is a sphere.

As a sphere, the earth can be divided into degrees, and we all know from geometry class that a sphere (and a circle) is divided into 360 degrees. 

This means that the sun revolves around the entire Earth in 24 hours, and therefore makes the journey of 360 degrees in 24 hours. This can be simmered down to a speed of 15 degrees per hour, and 0.25 degrees per minute of time. This is where the "Hours x 15" and the "Minutes x 0.25" comes from.

Now, the sun, while visible from sunrise until sunset over a vast expanse of the Earth, is only actually directly overhead in one very particular position. This position is called the "Meridian" and it is where the sun is directly overhead, also known as "Local Aparent Noon". Noon is a very important part in this story, and leads to the reason that the sighting is called a "Noon Site"

When viewed from the suns perspective, the Earth is slowly turning beneath it, and there is only a small sliver of Earth that is located directly under the sun. This small sliver is called the Meridian and it is the small segment of Earth that is currently experiencing "Noon". Every minute, this meridian moves 0.25 degrees to the West, slowly making its way around the Earth until it reaches its starting point for the day.  

The starting point, which is degree 0 and known as the Prime Meridian, is located over Greenwich, which gives the reason behind the name of that time zone of Greenwich Mean Time, also abbreviated as GMT. In the name of science, and to move away from any places name, this very same meridian and timezone is also called UTC which stands for Universal Time Coordinated.  

Now, you are not standing on the sun looking down on the Earth slowly rotate under you. Instead you are standing on the Earth, watching the sun slowly rise in the East, move directly overhead, and then set in the West. At some point in the day, the sun will be located directly overhead, and that very moment will be when the sun's meridian is shining down on your little sliver of Earth. At this point, the sun is at it's zenith (highest point) in the sky and this time is your local noon.  

You don't need a sextant to figure out your longitude, only a clock and a shadow, but a sextant does help. 

When your shadow is pointing directly at True North (not magnetic North) the sun has made its journey from 0 degrees to be directly overhead of you. The time it took to reach you is proportional to the number of degrees you are from 0 degrees. So, if it took exactly 1 hour for the sun to be directly overhead, then you are exactly 15 degrees to the West of 0 degrees. This would mean that your longitude is 15W.  You would also be located in the next timezone, known as UTC-1.

If your local noon occurs at 1 hour and 1 minute after the sun has left 0 degrees, then you would be located at 15.25 degrees West of the Prime Meridian. Now, you won't see coordinates listed as decimals, instead they are listed in the format that is Degrees:Minutes:Seconds; where 60 seconds is 1 minute, and 60 minutes is 1 degree.  (it's easy to think of it in the same format as time, Hours:Minutes:Seconds, but since its coordinates, the Hours are called Degrees). 0.25 degrees can be multiplied by 60 to convert it into minutes: 0.25 x 60 = 15 minutes. This means that if your local apparent noon occurs at 1 hour and 1 minute after the sun has left 0 degrees, then your longitude would be 15 degrees and 15 minutes West (also written as 15*15'W).

Now, thinking of the time as "Time since the sun has left 0 degrees" may be helpful at first, it doesn't help with the actual calculations. To make the math easier, simply have a 24 hour clock set to UTC time and look at that clock at your local apparent noon. 1 hour and 1 minute after the sun left 0 degrees would be 13:01. If you are located further West, local noon will occur later on the clock. If you are located in the Eastern Hemisphere, then your local noon will occur before the clock says 12:00.

I know this might seem rather simple, and that is because it is. The sun moves across the sky at a set and specific speed of 15 minutes of longitude every 1 minute of time. If you check the time of your local noon, you can easily find your longitude. 

All you need to do is measure the time difference from your local noon and Noon of UTC. The difference in hours is multiplied by 15, and the difference in minutes is multiplied by 0.25.  

If your local noon occurs at 16:55, then your difference from 12:00 is 04:55.  
04 x 15 = 60 degrees
55 x 0.25 = 13.75 (the whole numbers are degrees, the decimal is going to be minutes) 

13.75 = 13 degrees, 0.75 x 60 = 45 minutes

60 degrees + 13 degrees + 45 minutes = 73*45' W


If your local noon occurs at 08:47, then your time difference from 12:00 is 3 hours and 13 minutes (03:13). 
03 x 15 = 45 degrees
13 x 0.25 = 3.25

3.25 = 3 degrees, 0.25 x 60 = 15 minutes

45 degrees + 3 degrees + 15 minutes = 48*15'E


Just that easily, with an accurate measure of time, you can find your longitude on this large round Earth. 

There was mention of timezones earlier, and this is how they come into play. Every hour, the sun is generally overhead an area of 15 degrees. So, at 12:00 UTC, the sun is over the area of 0*W to 14*59'W.  
At 13:00, the sun is over the area of 15*W to 29*59'W
At 14:00, the sun is over the area of 30*W to 44*59'W

Every hour, the sun has moved over 15 degrees, so the Earths 24 timezones are divided up into 15 degree increments. Every hour, the sun has moved 15 degrees West, and a new timezone is experiencing their Noon.  

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