Time, Sun and Longitude

I have just returned from Scotland, where I have been doing some more research for the book I’m working on. In Edinburgh, I had the almost surreal experience of ducking into buildings to take shelter from the intensity of the midday heat.

During my time in the city sun, I took the time to look at the relationship between time in the city and the sun. Do not adjust your mind, that sentence makes some sense.

It has been known for thousands of years that there is a direct relationship between your longitude, time and the height of the sun. The challenge has always been to find a way to measure time sufficiently accurately to tie the pieces together, particularly at sea. This was effectively solved by John Harrison and his chronometers.

The sun rises in the morning and sets in the afternoon. When it is rising, the sun is east of you. When it is setting, the sun is west of you. When it is neither rising, nor setting it is neither east nor west of you, it has the same longitude as you do. This means that at this exact moment that the sun is highest in the sky, it is overhead the line that runs from the North Pole, between your feet all the way down to the South Pole.

This line moves west as the Earth spins towards the east. Therefore the sun will reach its highest point in the sky later relative to your starting point the further west you go.

The word ‘relative’ is very important in that last sentence. This is because wherever you are in the world the sun will appear highest in the sky at midday, that is the middle of the day. It is only the comparison of that time with the time at another place that gives any clue to how far east or west you are. This can quickly become confusing, so here is a simple imaginary experiment that will explain how it works, using a little modern technology to help simplify things.

Let’s say a friend told you that they were going on a touring holiday of the world, but you then said, ‘Don’t tell me exactly where yet. What I’d like you to do is this…

Put a stick in the ground and mark the end of the shadows.

When the shadow reaches its shortest length each day, this means the sun has reached its highest point and I’d like you to give me a telephone call.

Now on the first day they kindly give up their holiday plans to mark shadows and your telephone goes at 11.00am GMT.

You quickly do the mental arithmetic. Where your friend is the sun reached its highest point one hour before it did in Greenwich. One hour is 1/24th of a day, therefore they must be 1/24th of the way round the world from you, in the direction of the sun rising. 1/24th of 360 degrees is 15.

“You’re 15 degrees east of Greenwich.” You reply.

A week later their call comes at 10.00 GMT,

“Now you’re 30 degrees east of Greenwich.”

A week after that, their call comes in at 09.00 GMT,

“Now you’re 45 degrees east of Greenwich.”

A week later, it comes in at 15.00 GMT

“Now you’re 45 degrees WEST of Greenwich.”

A week after that, their call comes in and they ask if they can stop marking shadows and get on with the world’s longest holiday.

If we measure the exact moment the sun appears highest in the sky and we can compare this to the time at home, we can easily work out our longitude, that is how far east or west we are of home.

The sextant is just a fancy shadow stick in reverse. It may be quite a bit more accurate, but it is not much more complex in principle. All a sextant does is measure angles. Once the angle between your horizon and the sun stops growing, you know the sun is highest where you are, therefore it is your local midday.

A chronometer keeps track of time at your home, or traditionally Greenwich for most navigators. By looking at the time on the chronometer when the sun is highest in the sky, there is no need to ‘phone a friend’. You can therefore work out your longitude on a ship at sea.

The picture at the top shows the visible time signal that ships moored near Edinburgh used to set their chronometers. The ball on the Nelson Monument is raised halfway at 12.55, to give a warning to the ships’ navigators to get ready. It is raised all the way at 12.58 and then drops at 13.00 precisely. When it was foggy, the ships would listen to the gun fired at the Castle each day. Sound is not a bad second option, but it travels so much more slowly than light that it is prone to greater inaccuracies. (The gun has traditionally been fired at the Castle, not to keep tourists happy, but because the vibrations would harm the instruments at the Observatory.)

Tourists take the time to come to Edinburgh, they take the time to listen out for the Castle gun and some even watch the ball drop from the Nelson Monument. But very few take the time to understand the relationship between the sun, time and the place they are.

Tourists visiting this website take a slightly different journey.

My trip to Edinburgh reminded me of one more valuable lesson about time and the sun. In future, I just need to remember that the correct time to apply suntan lotion is when the shadows are still getting shorter, not two hours after they’ve started getting longer again.

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