Today’s post is in celebration of the summer solstice and all things solsticey.

If someone asked you to define a year, what would you say? Probably a lot of people would opt for “the length of time it takes the earth to go round the sun”. If asked to be more precise, these people might suggest the interval between successive alignments of the sun and a particular star, where hopefully that star would be chosen so as to have a small proper motion – in other words, as near as dammit a “fixed” star.

But if we did define a year in such a way, over a long period of time we would notice something rather odd happening. Summer (and indeed all the seasons) would come slightly earlier each year; after two thousand years, midsummer would be a whole month earlier, and after just under 13,000 years midsummer would be in December.

The above definition is actually that of the sidereal year, and its length is given in the Oxford Dictionary of Astronomy as 365.25636 days. But our calendars – or rather, the pattern of leap days that keep the calendar synchronised – are based on the tropical year, which is all of 20 minutes shorter, at 365.24219 days. (Hence a century of tropical years is 36,524.219 days, whilst a constant pattern of one leap year every four years would make a century about a day longer at 36,525.636 days – which is why century years are not leap years, except for the extra day every four centuries, which keeps the tally about right).

But what is a tropical year? Well, it’s defined as “the interval between successive passages through the mean equinox”, and if we ignore for the time being the concept of a mean equinox, that can be re-phrased as “the interval between successive vernal equinoxes”, although it could equally be the interval between successive autumnal equinoxes, or summer or winter solstices. In other words, it is the interval on which the seasons repeat, and that is not quite the same as the time it takes for one orbit of the sun.

The discrepancy is due to the precession of the equinoxes, and this phenomenon is connected with a slow change in the direction of the earth’s axis of rotation. Naively, one might assume that if the planets formed out of a spinning disc of material left over after the formation of the Sun, all the planets would spin on their own axes in exactly the same direction as their motion round the Sun – so that the axes of rotation would be perpendicular to the orbital plane. But that isn’t generally the case – certainly not for the Earth, which is tilted at an angle of 23.5 degrees to that perpendicular. Hence each hemisphere of the earth gets a warm season (when it is pointing towards the sun, days are long and the sun beats down on us from on high) and a cold season (when it is pointing away from it, days are short and the sun’s heat is attenuated by the long oblique passage of the rays through the atmosphere) and times between these extremes when climates are more equable.

What’s more, the direction in which the axis points is slowly changing; it is “wobbling”. This is usually described by analogy with a spinning top. If you set a top spinning and then push the top of the top, as it were, to one side it will start to “wobble”: the axis of spin will slowly rotate around a vertical line drawn through the point of contact between the top and the surface it rests on. The technical word for this is precession. Tops eventually run down, but an isolated, virtually frictionless system like a planet spinning in space will just keep spinning and wobbling indefinitely.

What starts the top wobbling in the first place is not the act of pushing it to one side, but the fact that by doing so one causes a couple, or torque, to be exerted on the top in the horizontal plane; this is due to the fact that the weight of the top and the equal-and-opposite reaction of the surface it rests on are no longer collinear, and hence produce a torque or twisting effect. It is a piece of fairly standard dynamics that a torque T acting on a body spinning with angular momentum L will cause it to precess with an angular velocity w such that T = L x w, where the “x” here is vector multiplication (and so, maddeningly, you can’t rearrange the equation into one that looks more causal by dividing both sides by L). [By the way, I know that is true, because it is in my PhD thesis, on page 10.]

Precession also occurs when a spinning particle, such as a neutron, is placed in a uniform magnetic field; the neutron has a magnetic dipole moment (i.e. it’s like a tiny magnet) and hence the effect of the field on the neutron is to produce a torque. In the case of the earth, it’s not so easy to understand what causes the torque; I’m pretty sure it’s not a magnetic effect, and in fact the good old Oxford D. of A. tells me it is “due to the combined gravitational attractions of the Sun, Moon and planets”. (It does not elucidate; if I took the time to find out how this happens, I’d miss the solstice; but my guess is something  like this. The Earth bulges out around the equator due to its rotation, and at any one time part of this bulge sits above the equatorial plane and part below; if we can treat these parts of the bulge as separate objects, we can deduce that the gravitational forces due to all the matter in the orbital plane (Sun, Moon, planets) have equal and opposite components perpendicular to the plane and towards it; hence we have a couple trying to pull the Earth back to an upright position, which is what we need to explain precession).

Since the equinoxes are those intermediate times when the Earth’s axis, or rather its projection onto the orbital plane, is tangential to the orbit – so that everywhere on the planet gets 12 hours of day and 12 hours of night – you can see that since the axis is wobbling slowly you will get a slight difference between the two interpretations of the word “year”: the slight change in position of the axis between one equinox and the next means the equinox comes a bit earlier than it would without the wobble – 20 minutes earlier, in fact. Despite the fact that this is a relatively small effect – it takes 25,800 years for the axis to come back into line with its initial direction – precession has been known about since the time of the Greeks, and both Ptolemy and Copernicus had to allow for it in their models of the cosmos.

Of course a side-effect of the wobble is that the apparent position of the sun against the background of fixed stars (visible only during eclipses) at equinoxes and solstices will move around the heavens on a 25,800 year cycle. Since these four times in the year have always been significant, not just to astronomers but also to astrologers, the 25,800 year period has been divided up into twelve “ages” defined by the constellation the sun is in when the vernal equinox occurs, in exact analogy to the division of the year itself into astrological periods. Historically, the vernal equinox was considered to be in the constellation Aries, which is why the corresponding astrological period begins on that day, March 21st. But because of precession, it is now (according to the authoritative tome referred to earlier) in Pisces. Those of us “of a certain age”, however, will remember a popular song from the 1960s rock musical “Hair” which announced that

This is the dawning of the Age of Aquarius …

which surprised me a bit when I heard it way back then (I was keen on astronomy as a child) … “what happened to Pisces?”, I thought. Sure enough, from Wikipedia we learn that

in 1929 the International Astronomical Union defined the edges of the 88 official constellations. The edge established between Pisces and Aquarius technically locates the beginning of the Aquarian Age around 2600 AD. Many astrologers dispute this approach …

Perhaps the writer of that song consulted the wrong astrologer, or maybe This is the dawning of the Age of Pisces just didn’t sound right …

Anyway, all of that is but a preface to today’s topic. I was reminded of the whole subject of precession when visiting the wonderful Neolithic tomb at Maes Howe on Orkney recently; the long, narrow entrance passage only allows sunlight to shine on the rear wall of the tomb at sunset, during a limited period around the winter solstice, and has been doing that for 5000 years. It made me ask myself whether I’d understood things properly, as I thought it would go “out of tune” over that timescale, but of course it doesn’t – it’s the background stars that change.

What it all made me wonder, though – and here at last we come to the main point – was, what would life be like if the earth’s axis wasn’t tilted? If it were perpendicular to the plane of the ecliptic (so even the wobble would not happen)?

There would be no seasons. The climate would be the same throughout the year; in the UK it would be cooler than the average summer but warmer than the average winter, every day. No part of the earth would have 6 months of darkness or light, as happens at present around the poles; presumably the temperature would vary less with latitude.

Life would most probably still have evolved, but very differently – there would be no springs or autumns, no deciduous trees, no mating seasons. I am no expert on ecology or climatology, and there might be all sorts of complications I have not thought of, but at any rate we can be sure that life would be very different.

And our reckoning of time itself would be different, too. We would probably not count our ages in years; sure, we’d be aware of the annual apparent motion of the stars with respect to the sun, but it would be regarded as a purely astronomical phenomenon. The longest natural time period we’d have would be the lunar cycle, or month.

Let’s go even further for a moment and imagine there was no moon either. Some astronomers such as Simon Goodwin have theorised about the various factors necessary to life, and Goodwin gives the moon a mention in that context in relation to its role in producing the tides, and possibly even some effect on plate tectonics (though I may have remembered that wrong). But let’s just assume for now that life could happen without the moon.

Then we’d only have days. We’d probably have metric time, and measure our lives in kilodays (1000 days, or about three of our current years), with the average life expectancy being around 25-30 of these. There would be fewer birthdays as we’d probably only celebrate kilodays.

What about the week? Where does that come from? Well, we might still have it, but there again it too may be related to the phases of the moon (new, first quarter, full, last quarter) so with no moon we might instead have 10-day “weeks”, possibly with 3-day weekends. But with no easy, natural way of visualising long time periods, perhaps we would tend to “live for today” more, and plan less for the future. This might have good or bad implications, although overall, I can’t help thinking that a world with even more short-termism would be a pretty unpleasant one.

I’ll leave the reader to speculate on how else things might be different. Meanwhile, enjoy the solstice, spare a thought for whatever it was that tipped the earth over in the first place, and don’t ever, ever, even think about the days getting shorter …

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