Precession

or

The Battle of the One True Zodiacs

I seem to get into one of these "discussions" about this particular problem at least once or twice a year. Frankly, it gets a little tiring, since the exchanges are usually very heated and take a lot out of me. This is because the issues are terribly technical and I have studied them in detail and the person approaching me usually has not. Too many people think a simple question should have a simple answer. Actually, a good simple question almost always has a long, open ended answer with lots of twists and turns. This problem also has to do with the "hot button" question of whether astrology is valid or not, and if so, which brand of astrology is the correct one. For some reason, astrology is a real intellectual whipping boy with many "reasonable" people (including many so-called scientists) and they love nothing better than to use this problem as a way to "prove" the field is bogus. Meanwhile, astologers of various persuasions use this issue as a way to prove themselves right. Rather than repeat this argument every time it comes up, let me put the discussion online once and for all.

"The problem" is due to a motion of the Earth known as precession, which causes the positions of the Earth's poles, the equinoxes and the solstices to drift relative to the positions of the "fixed stars" -- or vice versa, depending upon your point of view -- in grand cycles of about 26000 years. Also, depending upon your point of view, you can use either the Earth's framework of poles, equinoxes and solstices as your "frame of reference" for measuring positions in the sky, or you can measure against the backdrop of the stars. But because of precession, these two ways of measuring give differing answers and the discrepency between them gets bigger with each passing century. So who's right in this matter and who is wrong? Or is that even an appropriate question to ask? And what does this say about the nature of the zodiac?

My questioner usually poses the question of precession in one of three ways. The first form of the opening salvo (and this often comes from people wishing to "disprove astrology") goes some variation of:

How come astrologers say the Sun is in Aries on the first day of spring when it's really in Pisces? Aren't you guys 2000 years out of date?

How come you tropicalists say the Sun is in Aries on the first day of spring when it's really in Pisces? Don't you know all the planets in your charts are in the wrong zodiac signs? How can you even call this astrology?

So, like when does the Age of Aquarius start?

Having given the topic of precession a lot of consideration over the years, let me lay out some of the gems I've dug up (and a few pointed opinions). They may surprise you...

What is Precession?

Astronomers have identified three distinct motions of the Earth that play an important role in their calculations and observations. These motions are the daily rotation of the Earth about its axis, the annual movement of the Earth in its orbit around the Sun, and the precession of the rotation axis. Let's look at them in turn. (Mind you, I'm glossing over a large number of fine details in this section.)

The easiest motion to visualize is the daily rotation. Quite literally, the Earth is like a spinning top or a gyroscope. Every 24 hours, the Earth rotates once about an axis through the north and south poles. For people living on the surface of the globe, this causes the Sun, Moon, planets, stars and other cosmic bodies to rise in the east and set in the west every day. Even though it's "obviously" the Earth that is rotating, we still talk about objects rising and setting. ("Obviously" means for modern people raised with western scientific ideas; prior to the time of Copernicus, the preceding sentence would have been "obviously false".) I think it was Bertrand Russell who said something like: how can you teach logic to anyone who thinks the Sun is rising when it's actually the horizon that is setting?

The plane of the Earth's orbit around the Sun is called the plane of the ecliptic. Our planet moves in an elliptical path around the Sun within this plane once each year. However, as seen by people on the Earth's surface, what we see is the Sun moving against the background of the stars in a circular path each year. We talk about the Sun moving around the Earth, about the Sun being high in the sky in summer or low in the sky in winter, and the sunrise point moving north and south along the horizon. We talk about "sun signs", not "earth signs", and call the ecliptic the path of the Sun in the sky. Back when people believed the Earth to be the center of the universe, such geocentric talk was obviously true. Nowadays, we "know" it's "really" the Earth that moves.

As for precession, let's go back to that spinning top again. If the axis of the top is slightly off vertical, it's seen that the axis slowly rotates in a circle around the vertical point. You'd expect that an object tilted to the side like this would simply fall over due to gravity, but since it's rotating quickly, the axis "precesses" instead. The physics of this is kind of complicated, but it has to do with something called "angular momentum" which has some unusual and counterintuitive properties at times. The situation with the Earth is a perfect analogy to this spinning top. As the Sun and Moon (and to a lesser extent, the other planets) pull on the Earth's equatorial bulge (another by-product of our rotation), the rotation axis, the line between the north and south poles, slowly precesses in a circle every 26000 years or so. This causes the poles to wander in a big circle against the stars over the centuries. We call the star pointed to by the north pole at any given time "the north star" or "the pole star" (e.g., alpha Ursa Minor is commonly called Polaris, meaning pole star). So the clear fact of precession can be described as the pole star changes with time. The north star of one era is not the same star as the next era. The ancient Egyptians saw the star Thuban (in Draco) at the hub of the sky, while we now see Polaris at this hub. The sky appears to change.

Recall that the circle on the Earth's surface halfway between the poles is the equator. If the poles change their tilt in space over time, the equator must also change its tilt as well -- it's really the same tilt, by definition. When we on the Earth's surface look at the sky, this shift in the equator is experienced as a complicated movement of the stars over the centuries. In some areas of the sky, the stars move away from the equator, in other areas they move towards the equator. This has some important ramifications for measuring star positions, as we'll eventually see.

Actually, the motion of the stars due to precession (as seen from Earth) is most easily understood in terms of the ecliptic. To a good first approximation, stars precess in circles in the sky that are parallel to the ecliptic, all centered on the ecliptic poles. These poles are the points at right angles to the ecliptic plane, just as the Earth's north and south poles are at right angles to the equator. The north ecliptic pole (NEP) is in the constellation of Draco the dragon, while the south ecliptic pole (SEP) is in the constellation Dorado the swordfish, very near to the Large Magellanic Cloud, curiously enough.

"Stars precessing"? But didn't we just say that the Earth's axis is the thing that precesses? What's going on?

You may want to skip to the next section at this point, because some picky technical details are about to follow. Feel free to skip them, at least on the first reading.

A Detailed Breakdown of Precession

The preceding "textbook version" of precession is hopelessly inadequate for working astronomers. When the level of detail and precision of measurement they require is of interest, it's necessary to talk about a number of separate motions of the Earth that are generally lumped together as "precession". Let's tease some of them apart.

The so-called "luni-solar precession" is roughly what was described above in the spinning top analogy. This particular motion is caused by the gravity of the Sun and Moon on the Earth's equatorial bulge. In this particular motion, the Earth's mean north pole ("mean" indicates an average position with the more chaotic fluctuations smoothed out) rotates around the north ecliptic pole (NEP). The angular distance between the mean pole and the NEP, which is the same angle as between the equator and the ecliptic, is called the obliquity of the ecliptic. The 2003 mean value of the obliquity is approximately 23 degrees, 26 minutes and 20 seconds.

The second major component of this motion is known as "planetary precession". When the other planets in the solar system pull gravitationally on the Earth, one of their effects is to cause the entire plane of the Earth's orbit to rotate in space. Currently, the ecliptic is rotating towards the equator at roughly 47.11 seconds of arc per century; the "hinge points" of this rotation are at 24 degrees of (tropical) Virgo and Pisces. Not only does the plane of the ecliptic move in space, but the ecliptic poles (NEP and SEP) also move relative to the stars, and the angle of the obliquity changes over time as well (currently decreasing at a rate of 46.85 seconds of arc per century). Hence, the circular motion of luni-solar precession is actually a shrinking circle as the obliquity (i.e., the radius of the circle) decreases -- it's really a spiral. Over the very long term, on the scale of tens of thousands of years, this rotation of the ecliptic is actually more of an oscillation: the obliquity varies (more or less) sinusoidally between 22.1 and 24.5 degrees with a period of about 40000 years.

You can see visible evidence of this change in obliquity at Stonehenge. Back around 1700 BCE, the summer solstice Sun would rise and stand on top of the famous "Heel Stone". Today, when the Sun reaches that height above the horizon, it's somewhat to one side of the top of the Heel Stone. That's because the ecliptic is now at a shallower angle causing the Sun to rise at a different spot at the eastern horizon.

Of course, when I earlier said "mean north pole" as an average position, the implication is that the "true north pole" (the true axis of rotation at any given moment) can deviate from this average. In fact, the solar system is a messy place that only vaguely resembles the simple textbook models. When you take into account all these funny details, there are a lot of wobbles between the mean and true poles. All these wobbles are summed together into a motion called "nutation", which is simply a corrective fudge-factor applied to the mean pole. The most important of these nutational motions is due to the fact that the Moon's orbital plane is tilted about 5 degrees relative to the ecliptic. Further, this tilted plane rotates backwards around the ecliptic (with the ecliptic poles as an axis). Astologers are very familiar with this backwards drift. The crossing points of the Moon's orbit and the ecliptic are the well-known "lunar nodes", which move backwards around the zodiac every 18.61 years. Thus the Moon's gravitational pull on the equatorial bulge is variable over this 18.61 year period, causing the true pole to wander around the mean pole in an elliptical path with this same period. The size of this ellipse is small, only 9.21 seconds of arc, which in distance terms on the Earth's surface corresponds to roughly 285 meters or the length of three football fields, but it's enough to make life difficult for the astronomers. There are many other nutational motions of smaller size and lesser duration; the reference book I'm looking at lists 69 such terms, though many more have since been identified. For most practical purposes, astrologers can easily ignore nutation.

I found mention of several other precessional motions. One important term in the equations is due to the entire solar system rotating around the galactic center every 230 million years or so. Another recent addition to the equations is "geodesic precession", probably an obscure phenomenon of general relativity known as "frame dragging". Apparently there are others as well, but all these miscellaneous motions are very small and mostly ignorable.

I've also glossed over a number of motions of the north pole (the rotation axis of the Earth) relative to the land masses of the planet. For starters, there's always plate techtonics, the slow (on the order of centimeters per year) drift of the continents around the globe. There are also a number of cyclical wobbles of the pole due to motions of the Earth's core and annual weather patterns. Even if you subtract off these cycles, producing a "mean pole", there's still a slow drift (11 centimeters per year) of the mean pole in the direction of Newfoundland. Over time, these various motions affect the latitude and longitude of every point on the globe.

As you're going to find many times in our discussion, things are never as simple as they first seem. Precession is extremely complex in its details. Viewed from a distance, it looks like a smooth, stately promenade in a big circle. Up close, however, it resembles a drunkard's stagger.

Precession of the Equator and Ecliptic

It's not just the poles that move because of precession. The equator (both the circle around the Earth's belly and the corresponding plane in the sky) is affected by luni-solar precession, defining the mean equator for a given time. Similarly, planetary precession will change the ecliptic plane as time passes, defining the mean ecliptic for that date.

Both the equator and ecliptic are affected by nutation as well. When nutation is being taken into account, the true equator is somewhat displaced from the mean equator, and the true ecliptic also deviates from the mean ecliptic. These deviations are not terribly significant, unless you're doing precise astronomical calculations.

The Length of the Precessional Cycle: the Great Year

An important question is how long it takes the Earth to go through one precessional cycle. This period is known in astrology as the Great Year and is one of the longest cycles that most astrologers ever deal with. The Great Year is typically divided into 12 Ages corresponding to each of the 12 zodiac signs, giving us this "Age of Pisces" and "Age of Aquarius" business.

Unfortunately, precession occurs at a variable rate, making a simple answer to this question impossible. Astronomers best estimate of the speed of precession (2003) is that the mean poles rotate around the ecliptic poles about 50.28 seconds of arc each (tropical) year. This speed is increasing about 0.0222 seconds per year each century. Hence, the period of precession is currently about 25776 years and decreasing slightly. That would make an Age roughly 2148 years; it takes 71.6 years to precess one degree. For general discussions, the approximate value of 26000 years is close enough. Also note that various authors will quote different values for the Great Year. A length of 2160 years for an Age is commonly kicked around, giving a Great Year of 25920 years. This traditional value for the length of an Age has the "advantage" of making one degree of precession exactly 72 years, with no leftover fraction. Be careful of numbers that are more exact than they can possibly be!

Issues of Measurement

Few people in our culture really understand where "facts" come from, especially in the scientific field. We all indulge in some very sloppy ways of thinking about the world that help us "get by" in life. But when these common sense ideas are examined carefully, they completely fall apart and are seen to contradict the way the physical world works. Both of the major advances of 20th century physics, namely relativity and quantum mechanics, are based on looking very carefully at how we "know" something about the physical world.

Facts are not something that you read in a book or (heaven forbid!) get from the television. To a scientist, a fact is a very specific answer to a very specific question posed to Mother Nature, known as an experiment. When a scientist designs and performs an experiment, he or she wants to know: "If I do this, this and this, what happens?" The "what happens" part is known as an observation, which consists of some kind of measurement. The results of an experiment are the facts of the situation. A theory is simply an intellectual framework of some kind (hopefully mathematical) that relates a wide variety of related experiments with their expected results, giving a wider, more general purpose answer to "if I do this, what happens?" Theories are never true, only useful to a greater or lesser degree. When the theory runs into situations where it gives wrong answers, we note its limitations and start seeking a better explanation.

Warning! I'm trying to jar you out of your intellectual complacency in this section. If we're going to make any sense of precession, we need to look closely at measurement.

Take a simple question: "What is my position in space?" We are so used to maps, globes and GPS devices, that we don't find anything remarkable about such a question. The western world has deeply internalized the universe of Issac Newton, especially the myth of "absolute space", even though physics abandoned that universe nearly a century ago. When Albert Einstein looked closely at how you could answer this question, he concluded it was totally meaningless! That's because Newtonian absolute space is featureless with no bumps, ripples, islands or signal flares to distinguish one piece of space from another in any sensible way. There is simply nothing about empty space to observe or measure. It was only when he changed the experiment that he came up with a question that made sense. He started with an observer somewhere in space, perhaps in a space ship of some kind. Maybe he's moving, maybe not (whatever "moving" means -- keep reading). He defines a "coordinate system" or "frame of reference" in his surroundings, maybe by using his own space ship as a "stable platform" or using a gyroscope or whatever, allowing us to discuss the X, Y and Z axes of the coordinate system. He sees me floating by in space at a certain time. Getting out his meter sticks, lasers, clocks, etc., he proceeds to measure the distances from himself to me in each of the X, Y and Z directions. Then and only then can he radio me a message saying "Your position relative to me at time T are the distances X, Y and Z."

Notice that we've changed the question! Instead of asking for "my position in space", I'm told my position relative to a specific observer. To be precise to an ungodly degree, you also need to specify the coordinate system, units of length and time, and types of measurement tools used by the observer to really make sense of this "fact". The most relevant issue, however, is that measurements are always relative to an observer and a frame of reference. If a different observer were to measure my position, I'd get totally different numerical values for my X, Y and Z coordinates. Two totally different answers and yet both are perfectly correct, relatively speaking. That's why Einstein's theory is called Relativity.

Similarly, if you ask "How fast am I moving?", you'll find that the answer depends on who's doing the observing. Like position, velocity can only be measured relative to a given frame of reference. To one observer, such as the person sitting quietly next to me, I may be standing still. To another flying by in his spaceship or on another planet, I may be whizzing through his neighborhood at high speed. Motion is also relative. In fact, the question "Am I moving or standing still?" is meaningless, since it implies a notion of absolute motion (or rather, motion relative to absolute space) that simply does not exist in our world.

Since this idea of relative motion seems to be intuitively repugnant for so many people, let me explain it from another angle. Imagine you are driving down the highway in your car. You see the stripes on the road, the road signs and the scenery all whizzing by you, you hear the sound of the engine, you feel the vibration of the road and you think "I'm really moving." Of course, it's possible that the Earth is speeding by you in the other direction and you need to hit the gas in order to just "stand still", but I don't think many of us would take that possibility seriously. Now imagine the road and the scenery (in fact, the entire Earth) should miraculously disappear and there's nothing but empty space outside your windows (you may want to trade in your car for a spaceship at this point). With nothing under your tires, you could even turn off your motor or slam on the brake pedal and nothing would change. With nothing to see "going past you" anymore, would you still have confidence that you were moving? If your car had originally been parked on the side of the road before everything disappeared, would you still be thinking you're standing still? Moving and standing still requires that there's some fixed terrain "out there" to measure you motion against. Without "out there", motion is meaningless.

Also note that it can be very useful to change back and forth between different frames of reference. Sometimes a change in reference frame can change a messy answer to a very simple answer, just because we're approaching the question from a different point of view. A simple answer can make it easier to understand the more complicated situations. Besides, the crux of Relativity is that the laws of nature are the same for all observers, when these laws are expressed in the proper mathematics. There is no one observer that is more "right" than any other.

Let's take another example: "How long is a day?" How do you measure how long it takes the Earth to rotate once? For starters, to even recognize that the Earth is spinning, you need to look at some object distant from the Earth (that is presumably not rotating with us) and observe it moving in a "rotary fashion". For instance, the Sun rises in the east, reaches its greatest height in the sky in the south, sets in the west and then magically reappears in the east the next morning. If you measure the time from one noon to the next, you get (on average!) 24 hours. (Well really, "24 hours" are defined in terms of a mean solar day, and later by more precise definitions of time, but that's another big topic...) Notice that we measure the Earth's rotation by observing the motion of the Sun in our terrestrial reference frame, a rather odd twist of logic in my mind. But that's only a "solar day". If you observe the passage of a star due south from one day to the next, you get a "sidereal day" ("sidereal" means "pertaining to the stars") of 23 hours, 56 minutes and 4+ seconds, not 24 hours! A sidereal day does not equal a solar day. The "day" depends on which external object you observe. If you measure the position of the Sun relative to the stars, or the position of the stars relative to the Sun, you find there is a relative motion between them. If a star and the Sun are directly south at the same time one day, the star will beat the Sun to the midheaven by nearly 4 minutes on the clock the following day. (That's evidence for the Earth's orbital motion around the Sun, by the way.)

So we have evidence that celestial objects revolve around the sky when earthlings make the proper observations. However, it's somewhat ludicrous to think the rest of the universe revolves around us, at least since Copernicus -- scientific fashions of "what's real" do change with time. It leads to a complicated description of the universe. If you instead assume the universe stands still (whatever that means) and the Earth revolves, you get a very simple description. Simple explanations beat out complicated ones, all things being equal, a principle known as Occam's Razor. So we opt out for the sloppy, lazy man's description that the Earth rotates. Even worse, we think the Earth "really rotates" in some absolute, Newtonian sense. So much for an obvious fact...

"How long is the year?" also leads to such torturous details. A year is the length of time it takes the Earth to orbit back to the same position in its orbital path. But as we discovered earlier, "same position" is not a useful notion. The idea of "same position" can only be defined in terms of observations of the motions of the Sun or stars relative to the Earth's frame of reference. Depending upon our choice of external objects to watch and measure, we may get slightly different answers for the length of a "year". Again, solar years do not equal sidereal years or any of the other years that can be imagined. And while we express our results as "the Sun moves around the zodiac in 365.2422 days", the simpler explanation is that Earth revolves around the Sun in this period.

So, how do we know that the Earth precesses and the stars don't. Precession simply means the rotational axis of the Earth changes direction over time. As stated, this is an absolute space kind of description, so we should be suspect of it. First of all, we need to measure the positions of the poles relative to some observable objects outside of the Earth, an external frame of reference. Typically, this means we need to study how the daily paths of stars in the sky change over long periods of time (on the order of centuries). We observe that pole stars change over time, that the vernal equinox moves relative to the stars. We can explain this movement by saying the stars precess around the Earth in our frame of reference. Or we can say that our frame of reference, particularly our axis of rotation, precesses relative to the stars. The latter explanation is "simpler" (because everyone "knows" the stars stand still, at least in a Copernican world), though contrary to what we actually see in the sky, but both points of view are useful in their own way. Ergo, commiting the lazy man's oversimplification again, the Earth precesses. Simple, huh? Like mud...

In fact, the simplest explanation is that precession is the relative motion of the stars relative to the Earth's rotational frame (or vice versa), an observable fact -- no more, no less. Any notions of who is doing the moving and who is standing still is a matter of convenience, not observable truth.

Now I don't intend to beat this issue of measurement into the ground for no good reason. It just seems to me, however, that most of the confusions and paradoxes concerning the problem of precession are due to not understanding the details of measurement. In particular, whenever you see the words "really", "actually", "true", "correct", "absolute", etc., you should start questioning the details. Different points of view lead to different measurements, but only one view of nature's laws.

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