by Marcus Chown
In 2013, the Hubble Space Telescope detected jets of water spouting 200 kilometres into space from cracks in the Europan ice. They can be coming only from a sub-surface ocean. NASA scientists believe that if they fly JUICE through these icy plumes and sample them, they may be able to detect Europan microorganisms.
Another moon with fountains spewing ice into space is Saturn’s moon, Enceladus. At barely 500 kilometres across, nobody expected such a tiny moon to be active. But tidal stretching appears to have liquefied its interior. Enceladus may contain the smallest ocean in the Solar System. And, like the ocean of Europa, it may also contain life.
That the Jovian and Saturnian moons are heated by tidal interaction with their parent planets may also have implications for finding life elsewhere in our Galaxy. The reason is that Jupiter and Saturn are outside the ‘Habitable Zone’ of the Sun. A planet in the Habitable Zone of its parent star is close enough to the star that water does not freeze and far enough away that water does not boil. Jupiter and Saturn are so far away from the Sun that water, essential for ‘life as we know it’, should freeze. But, as can be seen in the case of Europa and Enceladus, this has not happened. Gas giant planets, many of which are larger than Jupiter, appear to be common around nearby stars. They might very well be orbited by moons bigger than Io and Europa and kept warm by tidal heating.
Precession of the equinoxes
The tides are not the only way that gravity affects the Earth, because it is an extended rather than a point-like object. There is another way discovered by Newton: the precession of the equinoxes.
The seasons occur because the spin axis of the Earth is tilted relative to the plane of its orbit around the Sun. Specifically, as already mentioned, the axis is tilted at 23.5 degrees to the vertical, which means the equator is also tilted at 23.5 degrees to the plane of the Earth’s orbit. Summer in the northern hemisphere occurs when the northern hemisphere is tipped towards the Sun and winter when it is tipped away. A similar thing happens in the southern hemisphere. Consequently, it is summer in the southern hemisphere when it is winter in the northern hemisphere, and vice versa.
Spring and autumn are of course the in-between seasons. But astronomers like to be a bit more technical than that. They say that spring and autumn occur when the plane of the Earth’s orbit – known as the ‘ecliptic’ – crosses the plane of the equator. These times during the Earth’s journey around the Sun are known as the spring and autumn equinoxes.
All the planets orbit close to the ecliptic because they formed out of a common pancake-like disc of rubble circling the Sun. Consequently, they are confined to a narrow band around the night sky, something that was recognised even in antiquity. In fact, the stars in the band were grouped into twelve constellations, corresponding to the twelve ‘signs of the Zodiac’. In 2000 BC, when the Babylonians created the system, the spring equinox was in the direction of Aries. But the spring equinox moves through the signs of the Zodiac at about one sign every 2,000 years. At the time of Christ, the spring equinox was in the direction of Pisces. Today, the spring equinox is beginning to move into Aquarius – it will officially get there in AD 2600 – which is why people talk of the ‘coming of the Age of Aquarius’.
This peculiar movement of the Zodiac constellations around the night sky is known as the precession of the equinoxes. It is the third of the Earth’s motions – after the planet’s rotation on its axis and the planet’s circling of the Sun – and it is the most mysterious. Its discovery is credited to Hipparchus, a Greek who lived and worked on the Mediterranean island of Rhodes and who is often described as ‘the greatest astronomer of antiquity’.
In 129 BC, when Hipparchus was compiling the star catalogue which made him famous, he noticed an odd thing: the positions of the stars did not match up with the Babylonian measurements. Furthermore, the stars seemed to have shifted their positions in a systematic way. Hipparchus was led to speculate that it was not the stars themselves that had moved but the Earth.
Using Babylonian observations, Hipparchus accurately estimated the speed at which the positions of stars shifted. It seemed that the axis of the Earth changed its orientation in space by about 1 degree every 72 years. This ‘precession’ causes the planet’s spin axis – still maintained at 23.5 degrees to the vertical – to rotate about the vertical once every 26,000 years. Because of this motion, the star immediately above the north pole of the Earth’s spin axis – the pole star — is not the same one that the Egyptians saw. We see Polaris in the constellation of Ursa Minor, the Little Bear. But 5,000 years ago the Egyptians saw Thuban, a relatively faint star in the constellation Draco the Dragon.
The wobble, or precession, of the Earth’s spin axis is behind the ‘precession of the equinoxes’. No one had ever guessed at a reason for this motion. Until Newton.
Newton realised that the shape of the Earth is distorted not only by the gravitational pull of the Moon and Sun but by its own rotation. This causes material on the equator to fly around at 1,670 kilometres an hour. The Earth’s gravity has difficulty providing the centripetal force necessary to keep stuff moving around at such a tremendous speed. Consequently, it flies outwards. In fact, the Earth bulges outwards by about 23 kilometres more than it would if the planet were a perfect sphere.
Newton realised that the gravitational pull of the Sun and the Moon on this ‘equatorial bulge’ causes the spinning Earth to wobble like a top. Indeed, the direction in which the spin axis points moves in a circle. From the forces acting on the Earth’s equatorial bulge, Newton calculated that this precession would take 26,000 years, precisely as observed.
Newton’s law of universal gravity, it turns out, is a gift that keeps on giving. It has a multitude of consequences. And there are yet more.
In proving the inverse-square law of gravity, Newton assumed that the Sun pulls on each planet as if the Sun and planets are point-like masses. He assumed the Earth pulls on the Moon as if the Earth and Moon are point-like masses. But the Earth and Moon are extended bodies, and this is at the root of other phenomena such as the tides and precession of the equinoxes.
But Newton made another approximation to crank out predictions from his theory of gravity. He assumed that the Sun alone pulls on the Earth, and the Earth alone pulls on the Moon. The breakdown of this assumption can be seen in the case of the tides, where both the Moon and the Sun affect the Earth. And this is a general feature of the real world: bodies are pulled on by more than one other body. This not only leads to bodies such as planets not moving in exact elliptical orbits but to the possibility of deducing from the perturbed motion of known bodies the existence of new ones.
Further reading
‘The Severn Bore: A natural wonder of the world’ (http://www. severn-bore.co.uk/).
Ekman, Martin, ‘A concise history of the theories of tides, precession-nutation and polar motion (from antiquity to 1950)’, 1993 (http://www.afhalifax.ca/magazine/wp-content/ sciences/vignettes/supernova/nature/marees/histoiremarees. pdf).
Shu, Frank, The Physical Universe, University Science Books, Mill Valley, 1982.
Simanek, Donald, ‘Tidal Misconceptions’, 2003 (https://www. lhup.edu/~dsimanek/scenario/tides.htm).
4
Map of the invisible world
How Newton’s law of gravity not only explains what we see but also reveals what we cannot see
Kepler’s laws, although not rigidly true, are sufficiently near to the truth to have led to the discovery of the law of attraction of the bodies of the Solar System. The deviation from complete accuracy is due to the facts, that the planets are not of unappreciable mass, that, in consequence, they disturb each other’s orbits about the Sun.
Isaac Newton1
Pick a flower on Earth and you move the farthest star.
Paul Dirac2
They had been searching for almost an hour now and had already slipped into a trance-like automatic rhythm. Johann Galle peered through the giant brass refractor at the night sky above Berlin, adjusted the fine control knobs of
the telescope until a star appeared in the crosshairs, and barked out its coordinates. His younger assistant, Heinrich d’Arrest, seated at a wooden table across the stone floor of the dome, ran his finger over a star map by the light of a shielded oil lamp, and shouted back, ‘Known star’. Galle twiddled the brass knobs again, lining up another star. Then another. In the chilly night air, he was already getting a crick in his neck and beginning to wonder whether they might have embarked on a futile search.
They were at the Royal Observatory, Berlin, because of an extraordinary letter that had arrived that afternoon. It was signed by Urbain Le Verrier, a mathematical astronomer at the École Polytechnique in Paris. Galle had sent Le Verrier a copy of his thesis the year before but had received no reply. Le Verrier, evidently regretting this omission now he needed a favour, had peppered his letter with belated and pointed praise of the Prussian astronomer’s work.
It would have been easy for Galle to exact his revenge by accidentally losing the letter among the crowded papers on his desk. He would be doing no more than the French astronomers at the Paris Observatory, who, evidently, had also opted to ignore Le Verrier – otherwise why would he have had to write to Berlin? But Galle was a bigger man than that, and, anyhow, the favour Le Verrier was requesting had piqued his interest. Would Galle use the Observatory’s famous Fraunhofer telescope to scan the night sky in the area between the constellations of Capricorn, the goat, and Aquarius, the water carrier? Would he look for an object that did not appear on the star maps?
Joseph Franz Encke, the Observatory’s director, thought such a search a waste of time. But that night he would be celebrating his fifty-fifth birthday and so not using the 22-centimetre refractor. Against his better judgment, therefore, and because he could see no possible harm in it, he gave Galle permission to pursue Le Verrier’s ridiculous search. Galle quickly roped in an astronomy student, d’Arrest, and here they were, the pair of them, on the morning of Thursday 24 September 1846, scanning the skies with the great clock-driven Fraunhofer telescope, one of the most advanced instruments of its kind in the world.
They had started the search at midnight when the gaslights of Berlin sputtered off, plunging the city into primal blackness, and now it was coming up to one o’clock in the morning. Galle manoeuvred the crosshairs to the next star and called out its coordinates. His mind wandered to thoughts of the warm bed he would soon be in with his wife as he waited for a response from d’Arrest. And waited. What, he wondered, was his assistant doing?
The crash of a chair hitting the floor shocked Galle back to reality. Leaping back from the eyepiece, startled, he saw his assistant, silhouetted against the oil lamp, rushing towards him, flapping his star map like a demented bird. It was too dark to make out the expression on d’Arrest’s face but Galle would remember his words for the rest of his life: ‘The star is not on the map! It’s not on the map!’
Struggling to stay calm and, most importantly, to stop their hands from shaking, the two men took turns at the eyepiece until there could be absolutely no doubt. The object they had found was definitely not on the star map. And the reason for that was clear: it was not a star. Stars, because of their immense distance from the Earth, appear as mere pinpricks of light no matter how powerful a telescope’s magnification. But this object was no dimensionless pinprick. It was a tiny shimmering disc.
It was a planet. An unknown planet. Since the birth of the Earth it had been making its way around the Sun in the frigid darkness out at the periphery of the Solar System. And, until now, no one had known. For the moment, it had no name and they were the only two people in the world who knew of its existence. But soon everyone would know it as Neptune.
Pulled in every possible direction
That Galle and d’Arrest should have found the planet was impossible, a piece of magic. A man in Paris had written asking Galle to look for a new world. The man had been very precise about where to look. Intrigued, but not seriously believing he would find anything, Galle had followed the man’s instructions. And within an hour, incredibly, the planet had appeared, hovering slap-bang in the middle of the field of view of their telescope, exactly where the man had said it would be. It was a triumph for astronomy. It was a triumph for predictive science.3 But, most of all, it was a triumph for Isaac Newton and the theory he had devised almost two centuries earlier.
In order to predict things with his universal law of gravity, Newton had made approximations. As mentioned already, he assumed that the Earth pulls on the Moon as if all its mass is concentrated at its centre. In reality, of course, the Earth is an extended body, and differences in the pull of the Moon across its bulk distort its shape, thereby creating the phenomenon of the tides. But the assumption that the Earth pulls on the Moon as if its mass is concentrated at its centre is not the only approximation made by Newton. He also assumed that a planet experiences a gravitational pull from only the Sun. By making this assumption, he was able to prove that the path of a planet moving under the influence of a force that weakens with distance according to an inverse-square law is an ellipse, exactly as Kepler had found.
But the central characteristic of gravity is that it is a universal force, which means every mote of matter in existence exerts a gravitational pull on every other mote of matter. This means that a planet as it travels through space is tugged not only by the Sun but also by every other planet. Take the Earth. The two other planets which exert the greatest pull on our planet are Jupiter, the biggest world in the Solar System, which weighs in at about 1/1,000th the mass of the Sun, and Venus, the closest world to our own. The pull of each on the Earth varies with time because Jupiter travels around the Sun more slowly and Venus more quickly than the Earth. But when Jupiter is at its closest, it exerts a pull which is about 1/16,000th that of the Sun. And when Venus is at its nearest, it exerts a pull about half of that.
That each planet experiences much smaller gravitational tugs from the other planets in the Solar System than it does from the Sun was the reason Newton was able to ignore them in his calculations. But, strictly speaking, a planet like the Earth moves under the influence of multiple bodies. And a consequence of this is that, actually, it does not orbit the Sun in a perfect ellipse. Kepler’s first law is only approximately true. The effect of all the other tugs is to cause the elliptical orbit of a planet gradually to change its orientation in space over a long period of time, with the closest point in the orbit to the Sun creeping, or ‘precessing’, around the Sun.
Say for some reason we are totally ignorant of the existence of the other planets of the Solar System. After monitoring the Earth’s orbit for a long time, we discover that it is deviating ever so slightly from a perfect ellipse. After considering the matter, we conclude that there are other massive bodies out in space tugging at the Earth as it flies along rather like children tugging at their mother’s coat as she hurries along a road. Employing enough computing power, not to mention a lot of ingenuity – the calculations are not easy – we deduce that the Earth is being tugged by seven other planets, each with a very particular mass and orbiting at a very particular distance from the Sun.4
Newton’s law of gravity has enabled us to make a map of the invisible world of our Solar System. And this technique is precisely the one Le Verrier used to map the outer reaches of known space and deduce the location of an undiscovered eighth planet, Neptune. This was because there was a planet whose orbit was deviating from a perfect ellipse.
A planet called George
Uranus had been discovered by William Herschel, a freelance German musician. In 1757, at the age of nineteen, he and his sister Caroline moved to Bath, a town in England founded by the Romans because of its hot springs.5 Herschel found work as a church organist. But his passion was for astronomy. And in the garden of his house, he built one of the best telescopes of his day. It was while scanning the night sky with this instrument, on 13 March 1781, that a fuzzy star popped into his eyepiece. At first Herschel thought it was a comet. But, over successive night
s, as it crept across the constellation of Gemini, Herschel realised it was not following the highly elongated orbit of a comet but the near-circular orbit of a planet.
The new planet caused an international sensation. From the beginning of recorded history people had known of only six planets. Now there were seven.
As an immigrant, Herschel’s greatest desire was to be accepted in his adopted country. So he christened the new planet ‘George’ after King George III (actually, he named it ‘George’s star’). This upset the French astronomers, who strongly objected to a planet named after an English king and instead referred to it as Herschel. In a rare instance of the Germans acting as peace-makers, the astronomer Johann Bode suggested Uranus, the father of the Roman god Saturn. The name stuck. If it had not, then, moving outwards from the Sun, we would today have Mercury, Venus, Earth, Mars, Jupiter, Saturn . . . and George.
Uranus had actually been seen almost a century earlier by English astronomer John Flamsteed. In 1690, mistakenly believing it to be a star, he had catalogued it as 34 Tauri, the thirty-fourth star in the constellation of Taurus. The historic records of Flamsteed and others of Uranus’s position, supplemented by new observations, meant that, by the early nineteenth century, the orbit of Uranus was known precisely enough that it could be compared with the prediction of Newton’s law of gravity.
But this threw up a puzzle.
The same elliptical orbit did not fit all of the observations. As soon as an orbit was determined for Uranus, the planet began wandering from its path. And as the decades passed and more observations were made, Uranus strayed more and more.
Few doubted that there could be anything wrong with Newton’s law of gravity. Its successes over the past couple of centuries had been so overwhelming and so comprehensive that it had achieved status akin to the word of God. Instead, the suspicion arose that there must be another world beyond Uranus whose gravity was tugging at the planet and causing it to veer from a neat elliptical orbit.