I guess pretty much all of us know that December 21st this year marked the winter solstice, and so – in the northern hemisphere – the shortest day and longest night of the year. But comparatively few people seem to know that this day is not the one when the sun rises latest and sets earliest. The exact dates of those events are, at the latitude of London, just over a week different from the solstice. Specifically, the latest sunrise this year is not until January 1st 2017, and the earliest sunset was on December 12th.

It turns out that the times when the sun rises and sets are governed by a moderately complicated algorithm called the Equation of Time. This obviously varies with your latitude and longitude, but also takes into account the small differences between the solar day and the sidereal day (the day length as measured against the distant and essentially fixed stars), seasonal variations in the earth’s distance from the sun, the apparent size of the solar disk, and a host of other relevant pieces of information. Strictly speaking, one’s height above sea level, and the details of the surrounding terrain also make a difference, but not in a way that’s easy to quantify here. Finally, there are several different definitions of what angle counts as the zenith line, and I have taken the civil definition as opposed to nautical or astronomical.

Once upon a time the calculations would have taken a very long time and lots of paper, but nowadays we can throw the calculation steps into Excel and find out the information for anywhere we want, and for a reasonably long span of time into the past or future. For the curious, a step by step description can be found at this link.

Out of curiosity, I plotted the changes for a series of latitudes from that of Reykjavik in Iceland (just over 64 degrees north) via Orkney, Penrith and London in the UK, through Rome and the Tropic of Cancer to the Equator. For simplicity I just took everything on the zero longitude line (through Greenwich) since I was only interested in changes in latitude. If you wanted to do this for yourself then you would need to adjust for your actual longitude east or west from Greenwich, and your official time zone.

Here’s the corresponding chart for sunset.

A few things stand out at a quick glance. First, the time of sunrise varies considerably at some times of the year even between London and the north of Scotland. Secondly, you don’t have to go all that far north to get to the ‘land of the midnight sun‘. Thirdly, the total range of variation of sunrise is very small at the equator – about 1/2 an hour, as compared with London’s 4 1/2 hours, or Iceland’s 8 1/2 hours. The places where all these lines cross over is at the spring and autumn equinoxes, where night and day are each 12 hours long across the whole globe.

Going back to where we started, and looking carefully at the early part of the year, you can see that the day of latest sunrise happens after the solstice. The further north you go, the closer the two days are together. So in Reykjavik the latest sunrise is on December 26th. Come down to Orkney and it’s the 28th. In London you have to wait until January 1st. In Rome, January 5th. If you lived on the Tropic of Cancer (say in parts of the Sahara, roughly on a level with Kolkata, India) you’d be waiting for the 8th.

If you live right on the Equator something else comes into play. You get not just a simple days-get-longer then days-get-shorter cycle. Instead there is a more complex curve. Something similar happens in the whole belt of the tropics. This is because there are times when the sun at noon is to the south (as always happens in the northern hemisphere north of the Tropic of Cancer(, but then times when the noonday sun passes overhead and is, for a while, to the north. As it swings over and past you, the day length lengthens and then shortens again – as you can see in the graph.

OK, that’s enough of the Equation of Time for this week. Next time – another oddity about solar movements through the year, together with some thoughts about what this all means for us humans as we have observed the sun through the years. I am convinced that our remote ancestors knew about these patterns (though probably didn’t dress them up in the sines and cosines used by modern maths) and incorporated this knowledge into their monuments and observatories. But more of that next time…

Today’s topic is – once again – inspired by an experience on the Scilly Isles. It has to do with how things look different from one point of view than they do from another. If you were going to navigate between the islands – say from Bryher round to St Martin’s – then the chances are you’d pull out a map. If you were feeling particularly cautious, or you were going in a larger boat which drew more water, maybe you’d go up a grade and get yourself a chart with underwater depths plotted. Coupled with some knowledge of the tide, you could then plot out a course.

Now if you also had a GPS navigation system, in principle you could then hand over the course to that, sit back, and enjoy the journey with no more effort. But if you didn’t have that, and you were reliant on personally converting all that map work into movements of the tiller, you’d find that it is rather more tricky than it looks.

A map is a top-down view of the world – the sort of thing you would see if you were flying. But out on the water you get a completely different perspective. You are looking along the (reasonably) flat surface of the water, seeing the sides of islands and rocks as they project up from that surface. Some things – perhaps your destination – are hidden behind other ones. Some things which look close together are actually far apart, having been brought together by visual accident. A passage between two rocks might appear wide and easy on your chart, but narrow and problematic on the water, since it calls for careful wiggling at key moments.

Now, of course, this was the norm for navigation throughout our history until very recently, and goes a long way to explaining why the profession of pilot was so important. The pilot knew his waters, and how to navigate ships of different sizes through them at different states of the tide – or indeed not to make the attempt until the tide turned.

Now, maps and charts to help navigation have been around for quite a long time – several centuries, at least. But a pilot in action was not so interested in the top down view given by a chart. What he wanted – needed – to know was the direction to steer in at any point. And this was done, by and large, by means of lines of sight. Certainly pilots necessarily built up a vast store of information of local conditions in all kinds of weather and tide. But the key to their navigation was the index of knowledge which knew that by lining up particular landmarks one behind the other, and trusting these remote guidelines over local phenomena, a difficult voyage could be broken down into a series of simple legs.

Each sight line gives you a stage in your journey: each journey consists of a chain of such guidelines. Arthur Ransome used this idea in Swallows and Amazons, where a navigation line was set up by visible marks in daytime, or lanterns after dark. John says: “This [stump marked with white cross] is one of the marks, and the other is that tree with a fork in it… come into the harbour without bothering about the rocks by keeping those two in line”. In this way they could easily get in and put of the harbour on Wildcat Island. The pilot’s job was basically the same, but upscaled to a much larger region and a hugely more complex set of navigation tasks.

But it is not just navigation on the water which has this difficulty. When we look up at the night sky, at stars and planets, we are looking at objects scattered through a vast three-dimensional space, as though they were arranged on the surface of a sphere. Extremely distant objects are pressed together, and small nearby ones can hide much larger further-away ones – as in this solar eclipse. And although changing tides are not a problem in space, things are moving at different speeds, and if you are trying to navigate – say – from one of Jupiter’s moons down to Mars, you have to take into account the change of location which will happen in the meantime. Human pilots still ply their trade in many parts of the world, and although they are usually supported by electronic backup, it still calls for in-depth familiarity with their coast, and day-by-day assessments of change. I wonder if the same will be true if and when we move into space?

I’ve been reading quite a lot recently about prehistoric sites in the British Isles in particular two short books by Aubrey Burley covering stone circles and henges (Prehistoric Astronomy and Ritual, and Prehistoric Henges)

A definition from an archaeology text book is:

“Henge: a type of ritual monument found only in the British Isles consisting of a circular area, anything from 150 to 1700 feet across, delimited by a ditch with the bank normally outside it”.

So I thought I’d add to my blog of a few weeks ago with some others through the rest of this summer. The research into these monuments is quite fascinating, especially the leaps and bounds in understanding their orientation which have been achieved in the last few decades. To cut a long story short, the main choices are between alignment with some nearby feature on the land, or some far away feature in the heavens.

Local ground features include prominent hills or mountains, especially where their shape is unusual or striking. Several Scottish sites are oriented towards hills which look like breasts, and it is not hard to imagine a belief that these were visible signs of an Earth goddess. So when you’re looking at a site, the first thing to do is look out beyond it to the skyline.

Astronomical alignments include both sun and moon, typically at key calendar points such as midsummer, midwinter, or the equinoxes. Plus the cardinal compass points. The evidence suggests that earlier sites were often aligned with respect to the moon, and were subsequently adapted by a later generation to a solar orientation. More of this another day, but the point here is that we often need to think twice about sites. It is easy from to imagine that the site was put together as a single coherent whole. The historical reality may be of a series of changes over many years, with new settlers reusing and repurposing older places. Stonehenge is a particularly good example of this.

Our own appreciation of lunar alignments has grown dramatically in recent years. Even as a casual tourist, it is quite easy to work out where the sun will rise at the calendar festivals using nothing more complicated than a compass. It remains predictably the same every year, so even without a compass it does not take long to mark out the cycle.

However, the moon’s movement is considerably more complicated, varying over a cycle lasting about 18.6 years. This is primarily because of the complex relationship between the earth’s orbit round the sun, and the moon’s orbit round the earth. Also, because the solar 365 day cycle contains almost exactly 13 lunar 28 day months, the quarterly solar festivals cannot all mesh neatly with the same moon phase. It takes a long time of regular watching to spot the patterns, and be able to understand and predict where the moon will rise and set.

The key observations over this 18.6 year cycle are of the most extreme northerly and southerly limits of rising and setting, called the Major and Minor Lunar Standstill points. These vary from place to place, partly because of changing latitude and partly through the accidents of the terrain. At latitude 55°, not far north of the cluster of henges near Penrith, the rising point of the full moon varies in its cycle by 12.5° either side of the place where the sun rises – a big shift along the landscape as seen from the centre of a henge! Even if the basic pattern is known, each region must carry out its own observations of where the moon will rise and set at these stationary points. This is where the local and distant alignment issues interact with each other. If you have recognised the exact direction to look in, what more natural impulse is there than to place your circle where that direction lines up with a prominent hill or valley?

It’s worth mentioning here that although henges may be restricted to the British Isles, lunar alignments are not. All over the world people have found places where the 18.6 year cycle is shown off to good advantage.

The astronomy of the moon’s movements is now well understood, and over the last few decades has been applied to stone circles and henges. It is not an easy task, given the considerable damage done to sites over the years by natural wear and tear together with human acts such as ploughing over ditches and banks, or robbing stones for building work. But aerial photography has provided huge insights into layout no longer visible on the surface, and some careful archaeology has uncovered items placed in particular locations.

Astonishingly, given the difficulties of observation and long baseline required, our remote ancestors have showed themselves to be well aware of the intricacies of the moon’s movement, and able to codify it in their monuments. Often these key directions are pinpointed by buried items. While there may well have been some visible signal such as a banner, it seems that the real importance was a sacred one. Apparently it was important to signal to the invisible world that you knew these patterns. In the absence of written texts from this era, we can only speculate.

To close this blog post with a striking but only very loosely related picture, here is the first image of Jupiter and a few of its moons, sent back by NASA’S Juno probe…