Have you ever played with a spinning top? Those round wooden toys with a point on the bottom and a little stick handle on the top? You hold the handle with your thumb and forefinger, twist as hard as you can, and let the top loose on a table or floor. It spins fast and for a long time. Tops wobble around a lot and often move around the table in a haphazard way.

Astronomers think of the planets much like these wooden tops. Centuries ago, they thought of planets as spinning in space forever, in perfect balance, with an unchanging motion, like a perfectly-set spinning top. In reality, whatever started the planets spinning did not do a perfect job of it. The planets wobble all over the place in space much like the spinning tops do on the table. To have a full understanding of planetary motion, we must take these wobbles and tilts into consideration.

8a. Axial Tilt: A Wonky Spinning Top

If you have ever set a top spinning, you will know that even if you are careful placing it down, it sometimes will lean to the side so the handle does not point straight up. Nevertheless, it will keep spinning merrily away.

We can understand how the Earth spins in much the same way. If we think of the Earth as a spinning top, then the North Pole would be like the handle on the top, pointing in a direction in space. We know that the Earth is not like a perfectly-set spinning top; instead, the Earth tilts whilst it spins at an angle of 23.5 degrees. This tilt is known as an axial tilt; the Earth is tilting on its axis of rotation. Even though the Earth is orbiting the Sun, the direction in which the North Pole points is (near enough) constant. For astronomers on Earth, it appears that the North and South Poles are always pointing at the same patch of sky - the Northern and Southern Celestial Poles (the points on the celestial sphere around which all the stars seem to orbit). For half the year, the North Pole is pointing towards the Sun, and for the other half, it is pointing away. This change relative to the Sun gives the Earth its seasons.

Earth is not the only planet with an axial tilt. In fact, it is more common for a planet to have an axial tilt than to have none at all. Venus’s axial tilt is so large that, whilst all the other planets rotate on their axes and orbit around the Sun in a counter-clockwise direction, Venus appears to rotate clockwise, a different direction to its orbit. For all intents and purposes, it seems that Venus is upside-down. It is thought that Venus’s axial rotation started out counter-clockwise, the

same as all the other planets, but the gravitational tidal forces from the Sun have tugged on its thick atmosphere, causing the planet’s rotation to slow and eventually reverse.

Uranus is another planet with an odd axial tilt; the planet seems to be lying on its side. To anyone watching Uranus for long enough, it would appear that Uranus was rolling and skittering around the Sun. This leads to some strange effects on Uranus’s seasons and days, which are explained in the chapters devoted to that planet.

It is well understood that as a planet appears to be approaching us, the positive or active magical aspects of the planet (healing, enhancing elemental effects, etc.) will be boosted. When the planet is moving away from us, however, negative or passive aspects (dangerous or unwieldy elements, better defensive spells) will be strengthened. Using information primarily from Mercury (which has practically no axial tilt), Venus, and Uranus, astronomers have been able to conclude that this attribute-boosting effect due to planetary motion is amplified when the axial tilt is very small (when the planet is rotating and orbiting in the same direction, like Mercury), and the effects are reduced when there is a larger axial tilt. For Venus’s extreme tilt, the boosting effect is reduced so much that there is little change in Venus’s magical attributes felt on Earth, whichever way Venus moves.

8b. Axial Precession: Spinning Whilst Spinning

Paying close attention to the spinning top again, no matter how hard you try, the top eventually will gain an axial tilt. But if you are lucky enough to have a spinning top that is at least staying in the same position, you can watch the tilt itself start to spin. The top’s handle will keep the same axial tilt of a few degrees, but the direction in which the handle points will start to rotate very slowly, taking a few seconds to spin once during the same amount of time the top itself is spinning several times. This rotation of the axial tilt is known as axial precession.

In the previous paragraphs, it was mentioned that the Earth’s North Pole always points to the same patch of sky whilst the Earth rotates and orbits the Sun. This is not strictly true. Like the spinning top, the Earth’s North Pole rotates very slowly - much, much slower compared to a day or a year. For astronomers on Earth, this means Polaris (sometimes called the ‘North Star’) will not always be near the North Celestial Pole (the point in the sky towards which the North Pole points). Instead, due to this axial precession, the North Pole is moving slowly around in a rough circle, with the circle centred on ‘straight up.’ This keeps the Earth’s axis tilted at around 23.5 degrees at all times. It would take 25,772 years for the North Celestial Pole to travel across the sky and get back to where it is today. That is a one-degree movement across the celestial sphere per 72 years.

The cause of this precession is thought to be due to the shape of the planet. Earth is not quite a sphere, but bulges in the middle due to its rotation. The Sun’s and Moon’s gravitational forces tug on the bulge, causing the planet to wobble in this manner. The movement of the mantle under the Earth’s crust, earthquakes, the currents in the ocean, and even the wind can cause other wobbles on top of this, making the Earth’s axial precession very hard to predict indeed. All this wobbling means the constellations we see in the sky during certain seasons will not stay the same forever. Over thousands of years, some constellations we think of as being really near the Northern or Southern Celestial Poles one day will become constellations we can see easily from other hemispheres. The constellation Crux in the southern hemisphere, usually used to find the Southern Celestial Pole, used to be visible easily to the ancient Greeks.

Axial precession has some subtle effects on magic. For example, potions that are only effective when brewed outside overnight, under the steady light from a star, must be brewed in the northern hemisphere, under Polaris, which does not appear to move during the night. But in 7,000 years’ time, the Earth’s rotational axis will have precessed so much that Polaris will be nowhere near the Northern Celestial Pole, so it will be unable to provide a bright, steady light. Instead, production of these potions will need to take place in the southern hemisphere where, at that time, four stars from the constellations Velorum and Carinae will be circling the Southern Celestial Pole very tightly, providing the required steady light.

8c. Orbital Inclination: A Non-Flat Solar System

It would be nice to think of our solar system as a thin disk, with all the planets (even if they are all spinning oddly) orbiting in the same, flat way, and all the planetary orbits confined to a plane. As you must have guessed by now, this is not the case. Instead, the orbits of the planets are tilted, some more than others.

We consider Earth’s orbit to be ‘flat,’ and measure the inclination, or angle of tilt, of other planetary orbits relative to Earth’s. The dwarf planet Eris has such a large orbital inclination (44 degrees) that, if you were to travel outside our solar system and look back, Eris would appear to fly high above the main disk of the solar system on one side of its orbit, and then duck back down under the disk when on the other side.

The consequence of this for astronomers and wizards on Earth are two-fold. If all the planets had no orbital inclination and we had a completely flat solar system, all the planets would orbit along the ecliptic, appearing to take the same path across the sky as the Sun does, making the planets very simple to find. Unfortunately, this is not the case, so we have to look harder to find objects in our solar system. As a further consequence, it is extremely rare for planets to eclipse each other and align perfectly in this non-flat solar system. Thus, any magic that requires planetary alignments to work probably cannot be performed in your lifetime. Even if you are lucky enough to witness such an alignment, and to know of magic you could perform, the magic may never have been tested, and so may be very dangerous.

8d. Orbital Precession: Flowers in Space

Whilst early astronomers liked to think of the night sky as a perfect place where the gods lived, we now understand this is not the case. Even after the change in thinking from geocentrism (Earth at the centre of the Universe) to heliocentrism (the planets orbiting the Sun), it took may years to realise that the supposed ‘perfect circles’ planets trace out around the Sun are not perfect at all; they are, in fact, ellipses (covered in the chapter on 'Orbits'). Further, we think of these orbits as closed, with the planet orbiting back to exactly the same position each time. Instead, we find that the start and finish points of the orbits drift each time around, forming not a closed orbit, but a flower pattern or ‘rosette.’ This movement is a form of precession, but in the orbit rather than the axis. The Earth’s orbit has a pattern very much like this. The Sun also orbits the galactic centre as a rosette.

Most of these orbits can be accounted for and mapped, so budding astronomers need not fret. However, no orbital precession was more puzzling in times gone by than Mercury's. All measurements of Mercury's movements showed that the orbit was precessing around faster than predicted by a tiny 43 arcseconds (0.012 degrees) per 100 Earth years, distorting the rosette pattern. This was problematic at best, and the final stumbling block for the fundamental idea of Newtonian gravity at worst. Astronomers tried to adapt Newtonian gravity with nuances to explain the orbit, akin to the many additions that were made to explain the retrograde orbits of the planets in the sky when geocentrism was still in vogue. Wizard Siff McKenzie, an eminent planetary astronomer in the late 1800s, was so determined to reconcile this orbital anomaly with Newtonian gravity, he proposed that lost bludgers from an early-history Quidditch match were hitting Mercury off-orbit. Unfortunately, this explanation still was insufficient for the community, and McKenzie lost his academic position.

Like the epicycles were explained away by heliocentrism, eventually someone came along with a better idea entirely, throwing out Newtonian gravity as the ‘be all and end all.’ Albert Einstein, who already was making a name for himself in Muggle science with some high-profile papers re-writing Newton’s understanding of light and energy, developed a concept called General Relativity. Einstein was able to show that gravity actually was time and space bending around a massive object. In this particular example, the Sun’s mass curved spacetime enough to distort Mercury’s orbit. The orbits of the other planets are affected, as well; however the effect had been too small to notice previously. General Relativity also was able to explain all the same motions as Newtonian gravity. With this new information, astronomers were able to predict the motion of Mercury accurately, and more finely-tune their predictions of peak magical potency.