3.13 The sun sets in the West – does it?

A daily walk is one positive to be salvaged from this grim year of lockdown. One of our readers who’s taken to this has been watching the Sun, observing its shifting place in the landscape. This is one of his photos. In the deep winter he noticed how close the place where the sun rises is to the place it sets, compared to the equivalent in summer.

He wrote to ask about this, pointing out that, “whilst the sun notionally rises in the East and sets in the West, there is a massive difference over the course of the year”.

Before going into detail about this, however, it’s worth recalling how the Earth and the Sun are actually positioned in space – something that was worked out in stages during the 16th century by Copernicus and refined by Kepler in 1609.

The Earth and the Sun

This highly simplified diagram reminds us not only that the Earth rotates around the Sun in the course of a year, but also that its axis is distinctly tilted rather than “upright”.

As the bright blue illuminated parts demonstrate, the northern half  of the globe is tilted towards the Sun in June and the Southern half tilted that way in December.

This  video of the Earth from NASA, shows the motion of the Earth taken from space over a whole year, compressed into twelve seconds. It imagines the Earth to be spinning on a vertical axis with the angle the Sun makes rising and falling. It shows very clearly how the tilt of the Earth means people living well away from the equator see the Sun more directly overhead and for longer in the summer months, when the Earth is tilted towards the Sun. This is why there are seasonal differences away from the equator and why they are opposite in the southern and northern hemispheres.

Of course, we on Earth do not sense that we are hurtling through space, careering around the Sun once a year. Nor do we usually appreciate that we are on a spinning globe. We certainly have no direct experience of the Earth’s axis being tilted. What we see in the sky is relative: it’s how it all looks to us when we imagine we are stationary.

We imagine the sun to be rising and falling in the heavens above us over the course of a day, rather than us spinning around every twenty four hours. This clever photograph taken by Danilo Pivato, an enthusiast from Rome, uses a fixed camera. It shows snapshots of the sun taken throughout the course of a day.

Image courtesy of Danilo Pivato https://www.danilopivato.com

This remarkable photographic image goes a step further: it shows the course of the Sun each day over a six month period, starting from the summer solstice on June 21st and running to  the winter solstice on December 21st. The photographer, Kevin Sharman, has given permission to reproduce his image taken just outside the small town where he lives in British Columbia.  He tells us that the sharper continuous lines occurred on sunnier days.

The image shows how the trajectory of the sun falls ever lower towards winter while, at the same time, the location of sunrise and sunset get closer to each other.

This graph presents the path of the Sun at three times in the year more formally. The red line shows it at midsummer, the blue at midwinter, the black line at the equinoxes.

Image courtesy of Deditos

The peak height the Sun reaches is depicted up the graph and its East-West position along the horizontal axis. Exact East is at 90 degrees and exact West 270 degrees. It’s only on the black line (equinoxes) that the Sun truly rises in the East and sets in the West.

The strange timings of sunset and sunrise

With his curiosity aroused by what he observed on his country walks, our reader went on to look up the timing of the latest sunrise of the year in his neck of the woods. It was 08.06 precisely. He also noticed, to his surprise, that this timing remained the same for four days in a row from 28th December to 2nd January. This seems strange as, intuitively, you might expect the timing of sunrise to creep forward and back the same amount each day. The same was true at the other end of the day too: sunset remained steadfastly at its earliest time of 15.51 for several days.

This graph explains all. It was compiled by a diligent amateur called Bob who was “pondering the rate at which sunrise and sunset times are changing”, to quote his website.

He decided to look up the timing of sunrise (blue) and sunset (red) in New York City over the course of a year and used a simple Excel Spreadsheet to plot them. The days are numbered off along the horizontal axis and the time of day indicated upwards.

The curve is repeated twice to emphasise its sinuous shape. For completeness the length of each day, from dawn to dusk, was also calculated and plotted (green). The effect of putting the clocks forward and back an hour each year was removed.

It’s immediately obvious that each graph is smooth, with no abrupt changes. In the steeper stretches of the graphs, the line rises and falls steadily, but at the turning points – where the graph peaks or bottoms out – you’ll notice the line is almost flat, it hardly shifts up or down over several days. So the static timing of sunrise and sunset near the solstices is simply due to the smoothness of the changeover. Rather like a car slowing down and then reversing, it has to go through a period of very little change of speed at the point of transition. The same is true of most natural processes – they tend to be smooth rather than abrupt at a moment of transition.

A closer look at the graph also shows another quirk of the calendar: the earliest sunset (the dip in the red line) occurs a little earlier than the latest sunrise (the peak in the blue line).  The shortest day (the dip in the green line) lies in between the two.

This curiosity had also been noticed by our reader. In his area, the earliest sunsets occurred between 8th and 16th December – well before the dates of the latest sunrises. So, not only do the rising and setting times of the Sun seem to remain static for a few days in midwinter, but sunsets bottom out well before Christmas and sunrises peak after it. “It’s all to do with the angle apparently” he surmised vaguely as he asked for further explanation.

Tilts and orbits

By good fortune an enterprising student in Trondheim, Norway, called Steffen Thorsen, set up a website over twenty years ago, timeanddate.com which describes the causes of these strange timings around the shortest and longest days. The main one is a slight variation in the length of the solar day over the course of the year.

To explain this it’s easiest if we imagine what would happen if the Earth were not tilted and its orbit round the Sun were a perfect circle. Because the Earth spins on its axis at roughly the same speed all the time, every solar day would be exactly the same length, in this imaginary situation. It would simply be the time that elapses between the Sun reaching its peak one day and the next. This we would define as the 24 hour period. But in reality the Earth has an axis that  is tilted and it follows a path round the Sun that is slightly elliptical. As a result, the length of time that elapses between the Sun’s highest point on two successive days varies slightly over the course of the year. This “solar day” lengthens slightly towards the two solstices and shortens slightly halfway between, at the equinoxes.

The full explanation is a bit mind-boggling, but essentially this anomaly arises because the Earth is orbiting as well as spinning. In the time it takes to spin once round its axis over the course of a day, it also moves on a little bit in its orbit round the Sun (1/365th of it orbit, to be precise). Adding these two movements together (the spinning and the orbiting) lengthens the solar day a little bit. The complication is that this slight lengthening of each day is not same all year round. It changes a small amount each day as a consequence of the tilt of the Earth and, to a lesser degree, the elliptical nature of the orbit.

As a consequence, at certain times of year the solar day is a little longer than the 24 hour day our clocks mark out and slightly shorter at others. To be specific, it’s longer around solstice times – and shorter around equinox times.

In our modern highly organised world, we need our clocks to stick to a standard 24 hour day everywhere. Imagine a world in which the 12.50 to Bristol Temple Meads connects nicely with the 12.55 to Exeter in the summer but just misses it in springtime. The standard 24-hour clock which defines the so-called “Calendar Day” has to work to the average length of the day over the course of the year. This means there’s a slight discrepancy between noon as recorded on our 24 hour clocks and the actual position of the Sun in its trajectory.

This remarkable image , taken by enthusiast Giuseppe Petricci near his home in Abruzzo, Central Italy shows this effect clearly. It combines thirty two pictures of the Sun taken with a fixed camera at noon throughout 2015. The figure-of-eight is known as an analemma.

It’s at only four times in the course of a year that the Sun reaches its high point exactly at noon by the clock. In the image this moment is captured by the Sun being on the centre line of the image.  At the bottom, it occurs in December at the winter solstice and at the top at the summer Solstice in June. It also occurs twice in between, at the equinoxes – the cross-over point of the figure of eight. At all other times, noon and the high point of the Sun do not exactly coincide.

      Image courtesy of Giuseppe Petricci

A further nuance is that our distance from the equator (latitude) also has an effect on the timing of the latest sunrises and earliest sunsets, due to the angle of the sun locally. Places closer to the Equator have their earliest sunset sometime in November; for those further north it comes a little later, closer to the winter solstice.

We have effectively answered our reader’s question. The fundamental point is that our 24 hour clock doesn’t quite match the actuality of the Sun’s apparent movement across the heavens. The period of time between the Sun being directly overhead and the same the next day varies slightly over the course of the year and with latitude as we have seen – by up to 30 seconds from one day to the next. Accumulated over several days this is enough to shift the timing of the Sun’s highest point away from noon by the clock by several minutes at some points of the year.

The simple questions raised by a stroll at sundown has led us, somewhat surprisingly, into a genuine brain teaser. It turns out the movement of the heavenly bodies is far from simple. The tilt of the Earth as it spins around its axis and the eccentricity of its orbit as it journeys around the Sun mean we struggle to relate what we see – the apparent movement of the Sun in its daily and yearly cycles –  from what is actually the case, as seen from outer space.

For my discussion group all this just begs deeper questions: why is the Earth spinning in the first place, why is it tilted, what keeps it in orbit, why is that elliptical? But we’ve had quite enough complexity for now; these deeper questions will have to await a later blog. For the insatiably curious, however, a little more detail follows.

© Andrew Morris 24th January 2021

Further information

To keep matters simple in the foregoing explanation, we have overlooked the fact that the Earth doesn’t go round the Sun in a perfect circle. This (exaggerated) diagram shows it’s more like an oval (or ellipse), being 147 million km away at its nearest point and 152 million km at its farthest – a difference of 5 million miles (3%) over the course of a year.

Kepler discovered in the early sixteen hundreds, using observational data from Tycho Brahe, that the Earth speeds up slightly as it gets closer to the Sun. It was soon shown theoretically that this is an inescapable feature of any orbit in which one body travels around another body under the influence of a force directly linking them. When the Earth speeds up as it gets slightly closer to the Sun, it will move a little bit further along its orbit in the time of one rotation of the Earth.

As a result the Earth has to rotate a little further round than 360 degrees for the Sun to be aligned exactly overhead again. So the apparent day is lengthened a tiny bit more than it would be due to the tilt alone.

This effect is strongest when the Earth is closest to the Sun (called the perihelion).

image courtesy of explainingscience.org

It turns out that it’s just a fluke that this closest approach (perihelion) occurs quite near to the shortest day (solstice). It’s because of the closeness of these two that the tilting effect and the orbiting effect add together to lengthen the Solar Day rather than cancel each other out. At some later point in geological time the two dates will no longer be so close.