Time – The Key To Navigation On Planet Earth

 

Time – The Key To Navigation On Planet Earth

Measuring time started by measuring the movement of the planets.  The movement of the earth in relation to the Sun was where measuring time had its beginning. People did not understand the earth circled the Sun back then, but that was not an issue.  Ancient people first measured time by the rise and fall of the Sun on the horizon. The sundial was invented, and then water clocks to improve accuracy.

What Is At The Center?

Skip forward a bit to 1650, and it became generally acknowledged that the earth orbits the Sun. I deliberately chose the word “acknowledge” because Copernicus, who first proposed that the earth orbits the Sun, published his theory in 1543, just before his death.  Due to politics and religious powers at that time, the wider public did not widely accept his theory until approximately 100 years later.  Time was now understood in reference to the spin of the earth and its orbit of the Sun.

The original theory from Nicolaus Copernicus that laid out for the first time that the earth orbited around the Sun.  A very politically contentious idea at the time.  Nicolaus Copernicus, CC BY-SA 4.0, via Wikimedia Commons

Time Measurement – The Drive For Accuracy

Measuring time and conveying between people periods of time and specific times of the day became more important.  This allowed for the coordination of efforts between groups of people.  As the groups became larger, being able to coordinate effort accurately was the holy grail for the timekeeper.   

It was the ancient people who first grappled with these problems. Even today, all our concepts for measuring and communicating time have their genesis in ancient history.  I have covered the development of the time indexes in a prior blog.   The key driver of the development of the measurement of time was very practical, what can be measured from the periods of the Sun, and how can these be easily segmented.

This practical, scientific approach to time continued until very recently.  As recently as the 1970s, prior to the advent of the quartz movement, a large number of the Swiss watch brands that we admire today described themselves as the makers of scientific instruments. One name that springs to mind, in particular, is Heuer.

Advantages Of Time Measurement

Time measurement developed from the necessity to coordinate between ever-larger groups of people.  It became particularly important for armies looking to coordinate efforts between disparate groups and manage the guard watches.

Today the world coordinates in an unprecedented way. We are very comfortable moving between time zones across the world.  As we travel around the world, we pass certain points on the earth and change the time on our watch almost without thought.  This means we know the time wherever we are, and we can coordinate between multiple people across the world. 

It Was Not Always Like This

But back 200 years, there was no central control (or should I say guidance) over the time that different towns and cities operated on, never mind across continents.  Each city or town clock would be set to midday by reference to the Sun; noon was when the Sun was at its highest point in the sky.  Greenwich Mean Time was in use, but travel west to Bath (in the UK) and its clocks would be 9 minutes 26 seconds slower than those in London.  Another example would be Paris, which is 9 minutes and 21 seconds ahead of Greenwich Mean Time, not the 1 hour that is customary these days.   You can see that the time we work to today is a construct of convenience rather than the rhythm the earth moves to around the Sun.

Time Is Standardized

The system for telling the time was centralized and standardized in the UK by an act of Parliament in 1880, and this introduced a single legal time in the UK.  The whole of Great Britain was to follow Greenwich Mean Time, which was the standard that all the railways had adopted to coordinate all trains.

Time And Location

So why should we care about all this today, in the world of digitization and watches for fashion? The fact is that wherever you are standing on the surface of the earth, provided you are not exactly on a meridian, your watch will tell you it is midday when it is not.  Or, to think of it another way, there is an error between the measured time on your watch and the time indicated by the Sun.

In theory, by measuring the difference between the solar noon and the time on your watch, it should be possible to calculate your longitudinal position on the earth. 

Errors Bring Accuracy

The technique for calculating your longitude was particularly important for sailors, especially when they were not able to see the coast.  For early explorers, it was imperative that they could chart their position as the winds took them across the oceans.  This technique allowed early explorers to chart their movements across the oceans to a good degree of accuracy, typically within 4 ~ 5 nautical miles. 

How To Harness The Error

So how can this be done? It is done through a technique called “noon sight.” As the name indicates, you can only verify your position once a day, at noon.  As a starting point, it is important to have a reasonable idea of when noon is in your location so that you do not miss the opportunity.  Thankfully the Sun can give us a reasonable indication of when it is getting close to noon. This process of marking the time of the solar noon is called sighting the Sun in celestial navigation. 

Just to confirm, noon at any given location is the moment when the Sun is at its highest point in the sky. Identifying this exact time can be done reasonably easily by using a sundial. If you do not have a sundial at hand, you can use a picnic table’s shadow against the ground, a pole, or really anything outside that casts a shadow.  The moment the cast shadows starts to reverse direction is the moment of celestial noon.

Timing Is Everything

At that moment, read the time on your watch and note the time difference between the celestial noon and the meridian noon. For example, let’s say celestial noon is 3 minutes earlier than the noon on my watch. In 3 minutes, the world will rotate 0.75 degrees. This is calculated as follows, 3 minutes x 360 degrees the earth rotates in a day / (24 hours in a day x 60 minutes in an hour).  At first glance, it would appear that this is the answer, that we are 0.75 degrees ahead of the meridian to which our watch is set, but alas, things are not quite that simple.

It Is Never Easy

A further complication of the equation of time   When people see the term “equation of time,” they tend to expect a mathematical equation. In this case, the word “equation” is used in its medieval meaning of “to reconcile.” The equation of time reconciles the actual rotation of the earth around its axis at an angle and the mean rotation that is calculated as if the earth orbited the Sun around its equator.  The lines of longitude are calculated on the earth by reference to the mean solar time or mean solar orbit, so a correction between the observed time and the mean solar time also needs to be considered. 

Thankfully the equation of time is a constant for the day of the year, regardless of the specific year, so provided you know the date, the correction for the equation of time can be read from a graph or a data table.

The equation of time – above the axis, a sundial will appear fast relative to a clock showing local mean time, and below the axis, a sundial will appear slow. Pedro Sánchez, CC BY-SA 3.0, via Wikimedia Commons

The graph for the equation of time provides the correction in minutes in advance or behind the observed celestial noon.  You can change this time adjustment to an adjustment to the longitude by multiplying the number of minutes of adjustment by 360/1440. This is calculated by multiplying the number of degrees the earth rotates in 24 hours (360) and dividing it by the number of minutes it takes to rotate the full 360 degrees. There are 24 hours in a day and 60 minutes in each hour, so every minute, the earth rotates 360/1440 degrees or 0.25 degrees.

Let’s Put It Into Practice

Now we have all the information required to calculate our longitude on the surface of the earth. Here is the process:

  1. Determine your time zone meridian (in degrees). 
  2. Determine the equation of time offset for the date of observation.
  3. At the moment of solar noon, observe the time, either before or following noon, on your watch.
  4. This is the tricky bit, subtract the offset and the equation of time from the meridian to obtain the longitude, be very careful with the negative signs!

Here I think an example is most useful.

For this example, I shall imagine that I am somewhere near Vladivostock. The time zone there is UTC +10, and the earth rotates 15 degrees in each hour, so the time zone meridian is 150 degrees.

Today, the date is 11 January 2022, so the equation of time is -8.01 minutes or -2 degrees. You can get an accurate value for the equation of time at THIS website.

Indicated time on the watch at solar noon is 11:43. This is -17 minutes (solar noon is before the meridian noon) or -4.25 degrees from the solar noon.

Adding It All Up

The calculation of the actual longitude is now quite simple as follows:

150 – – 2 – – 4.25, so the longitude at the point of observation is 156.25 degrees. As I mentioned before, be careful with all the negatives, and two negatives are equal to a positive – for those that need a gentle reminder.

This system of navigation was critical to early explorers and, in particular, sailors. Explorers would use this system to understand their direction of travel as they crossed the oceans and were not able to see any landmarks. Time has always been fundamental to and remains so even when navigating with GPS satellites today.  This manual method of calculating longitude is generally accurate to within 3 nautical miles if the equation of time is considered and within 8 nautical miles if the correction for the equation of time is ignored. 

Why are these distances important   On a clear day, at sea, it is generally possible to see for 3 nautical miles if the weather is reasonable.  Now, one day if your phone breaks and you have an automatic watch on your wrist, you will still be able to work out which longitude you are on! 

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