Forces of Nature

by Professor Brian Cox

  Life on an orbiting planet

  The Seasons

  T he passage of the seasons is a gentle experience with powerful resonance. I can recite the words of hymns memorised decades ago that celebrate the great cycles of life in the North; ‘In the bleak midwinter, frosty wind made moan. Earth stood hard as iron, water like a stone’. A handful of out-of-time voices drifts in the dark depths of a winter snow painted by yellowed light that falls through stained glass. ‘We plough the fields and scatter the good seed on the land.’ The quiet of autumn woodland in September, faded green splashed with berry red. The daily transitions are gentle, the reddening leaves and cooling of the streams subtle, but the seasonal shifts mask jarring celestial violence.

  I love simple questions; they provide the opportunity to learn a lot, if not dismissed too lightly. They are also traps for the overconfident. Scientists are sometimes described as possessing a childlike quality when contemplating Nature, which I take to mean that scientists don’t simply wave away questions that appear to have obvious answers without checking whether the obvious answer has content and meaning. Perhaps children have a better-developed sense of intellectual honesty. The answer to the question ‘Why do the seasons pass?’ has a superficial answer: ‘because the Earth goes round the Sun’. But what keeps the Earth in orbit around the Sun? That also has a deceptively simple answer: gravity. But gravity is a force that acts between the Earth and the Sun, pulling them together, so why does the Earth keep orbiting and not just simply fall in? That’s a deeper question.

  The seasons are obviously something to do with the Earth’s orbit around the Sun, which has something to do with gravity. Newton was the first to write down a mathematical model for the force of gravity. He published it in 1687 in The Principia Mathematica, alongside his laws of motion. Newton’s law of universal gravitation states that there is a force of attraction between all massive objects which is inversely proportional to the square of the distance between them.

  The first thing to notice is that the force of gravity acts directly along a line drawn between the centres of the Earth and the Sun, pulling them together. You may remember Newton’s second law of motion from school. It is usually written as an equation:

  F = ma

  This says that an object will accelerate in the direction in which the force acts, and the acceleration is proportional to the strength of the force and the mass of the object. This is intuitively obvious; if you want a bus to accelerate you have to push harder than if you wanted a feather to accelerate. The force of gravity therefore accelerates the Earth directly towards the Sun. This would seem to suggest that the Sun and Earth should get closer together over time, but this doesn’t happen. Why? The Earth must also obey Newton’s first law of motion – the law of inertia; if no force acts on it, it will continue to move in a straight line forever. If the Sun is nearby, the force of gravity acts along a line between the centre of the Sun and the centre of the Earth. Since F = ma, this will cause the Earth to be deflected from its straight line so that it accelerates towards the Sun in the direction of the force. It will still continue happily on its way in the direction of the ‘straight line’, though, because no forces are acting in this direction. The Earth is therefore accelerating towards the Sun, but also flying along in a direction at right angles to the acceleration, and the net effect is that it orbits around the Sun forever. Think of the Earth falling towards the Sun but continually missing because it’s also got some speed at right angles to the force that’s making it fall.

  The quiet of autumn woodland in September, faded green splashed with berry red. The daily transitions are gentle, the reddening leaves and cooling of the streams subtle, but the seasonal shifts mask jarring celestial violence.

  The Earth’s orbit around the Sun is an ellipse, with the Sun at one focus. The Earth’s spin axis is tilted at an angle of 23.5 degrees to the plane of its orbit, and it is this tilt that gives us our seasons.

  The annual migration of caribou herds in the Arctic is a key marker in the changing of the seasons. The animals will travel around 200 kilometres to avoid the harsh windy conditions of their grazing area as winter approaches.; George F. Mobley/National Geographic Creative

  There is a great deal of beautiful subtlety in the analysis of orbits. Newton discovered the family of all paths that objects will take if they move under the influence of a force proportional to the square of the distance between them. These curves are known as the conic sections, because they are the shapes you get if you cut through a cone at different angles (see illustration).

  A conic is a curve that is created as the intersection between a plane and right circular conic surface. The four basic conics are the circle, ellipse, parabola and hyperbola, depending on the angle of intersection.

  Isn’t that a beautiful thing? Perhaps you can see that a circular orbit is a very special case – it only happens when the cone is sliced parallel to its base. At shallow angles the orbits are elliptical, and at steeper angles the orbits are known as parabolic or hyperbolic.

  The Earth’s orbit around the Sun is an ellipse. The closest approach, known as perihelion, occurs near the beginning of the calendar year around 3 January, when Earth passes within 147 million kilometres of the Sun. Six months later, our orbit carries us 5 million kilometres further out. The most distant point, known as aphelion, occurs around 3 July. The particular details of the orbit – the angle of the slice through the cone – are determined by what physicists call the initial conditions. In our description of the Earth’s motion we broke things down into two parts; the Earth’s straight-line motion without the Sun, and the deflection caused by the gravitational force if we put the Sun down somewhere near it. This isn’t how it happened! But in this imaginary case, the initial conditions would be the initial speed of the Earth relative to the Sun, the relative positions of the Earth and Sun when we dropped the Sun in, and the mass of the Sun.

  Can you see why the details of the orbit don’t involve the mass of the Earth? That’s an exercise for the interested reader. All the planets move in elliptical orbits. Some comets move in parabolic or hyperbolic orbits, which means that they will only visit the inner Solar System once before escaping off into space. Halley’s Comet is in an elliptical orbit, otherwise it wouldn’t return every 76 years. We’ve built five spacecraft that are travelling on hyperbolic trajectories away from the Sun, which means that they will journey into interstellar space, never to return. They are Pioneers 10 and 11, Voyagers 1 and 2, and New Horizons. All these different paths are a consequence of Newton’s law of gravitation and his laws of motion, and the particular initial conditions that started the whole thing off.

  The Earth’s orbit is half the explanation for the gentle passage of the seasons. To see why it isn’t the whole story, consider the climate in Tasiilaq, southeastern Greenland, one of the locations we filmed in for Forces of Nature. Tasiilaq is a remote settlement sitting approximately 100 kilometres south of the Arctic Circle. The two thousand residents of the town experience extreme seasonal fluctuations. It’s rarely what one might call warm, with summer temperatures rising to around 10 degrees Celsius on the average July afternoon. Winters, on the other hand, are brutal. The average high temperature in December is -4 degrees Celsius, and temperatures regularly approach -30 degrees Celsius. That’s mild compared to northern Greenland, where a temperature of -70 degrees Celsius has been recorded. Compare that to the coldest temperature ever recorded on Earth, in Antarctica on 10 August 2010, which was -93 degrees Celsius. That’s chilly.

  The Voyager probes were launched in 1977, destined never to return from their mission to explore the outer reaches of the Solar System. In their travels around interstellar space they have sent back images of Jupiter and Saturn.

  Notice that winter is at its harshest in Tasiilaq in January when the Earth is closest to the Sun, and warmest when the Earth is furthest away. That is, of course, because the timing of winter in the northern hemisphere has nothing to do with the distance be
tween the Earth and the Sun; it’s because the Earth’s spin axis is titled at an angle of 23.5 degrees to the plane of its orbit around the Sun, as shown in the illustration on here. In January, the North Pole and virtually all of Greenland are pointing away from the Sun and experiencing near-perpetual night. This is why it’s cold. Why is the Earth’s axis tilted? That’s a good question.

  Pioneer 10, launched on 3 March 1972, completed the first mission to the planet Jupiter and became the first spacecraft to travel through the asteroid belt.

  This illustration shows the current positions of four spacecraft which are leaving the Solar System on escape trajectories – our first emissaries to the stars. On this scale, the nearest star to the Sun would be approximately 100 metres away, and it would take Voyager 1 about 70,000 years to cover that distance (view from 10 degrees above ecliptic plane).

  Antarctica is the coldest place on Earth, with an average temperature of -34.4C, beating Tasiilaq by a long way! The tilt of the Earth’s axis at its southernmost point means Antarctica has just two seasons: summer and winter.

  The timing of winter in the northern hemisphere has nothing to do with the distance between the Earth and the Sun; it’s because the Earth’s spin axis is tilted at an angle of 23.5 degrees to the plane of its orbit around the Sun.

  Tasiilaq, Greenland, one of our filming locations for Forces of Nature. This remote settlement sits about 100 kilometres south of the Arctic Circle. Summer temperatures peak at around 10 degrees Celsius, and winters are brutal – with temperatures ranging from -4 to -30 degrees Celsius. Dog sleds or snowmobiles are the only ways to traverse the frozen waterways and snow-covered trails.

  The formation of the Earth and Moon

  Four and a half billion years ago, when the Earth formed, there was no Moon. Our planet was a hostile, molten ball of rock travelling around the Sun. The young Solar System was a chaotic place, with crowded orbits and frequent collisions.

  Today the Earth orbits in an astronomical highway that is mainly clear of debris, which is good if you are travelling at 30 kilometres per second. A cleared orbit is one of the three definitions that the International Astronomical Union (IAU) uses to classify a planet. To clear its orbit the Earth had to go through a violent period of collisions and near-misses as smaller bodies were either thrown out of the orbit or added to the mass of the planet itself in collisions.

  Not all of the objects the Earth encountered as a young planet were small. It is thought that there were dozens of proto-planets orbiting the Sun in those days, swirling around in crowded orbits, and Earth would have experienced a number of significant collisions. Direct evidence of these planetary collisions has long been erased from Earth’s surface, but one particular collision left an indelible mark.

  The Giant Impact Hypothesis suggests that there was a glancing collision between the newly formed Earth and a Mars-sized planet around 4.5 billion years ago, resulting in a planetary merger. The colliding planet has been named Theia, after the Greek goddess who gave birth to Selene, the goddess of the Moon. Scientists love their Greek mythology, and there is a good reason for the choice of goddess in this case. Computer simulations suggest that the collision resulted in large amounts of material from both Theia and Earth entering orbit around the battered larger planet, and over time the debris combined under the action of gravity to form the Moon. The supporting evidence for this hypothesis is strong, although, as always in science, healthy scepticism remains. Without scepticism there can be no progress. Computer simulations certainly match the details of the spins and orbit of the Earth–Moon system, but there is also physical evidence of a common origin for the system from the lunar rock samples returned by the Apollo astronauts. In particular, the abundances of oxygen isotopes 16O, 17O and 18O in lunar rocks are near identical to those on Earth. For those who need a bit of chemistry revision, isotopes are atoms of the same chemical element but which have different numbers of neutrons in the nucleus. The most plausible reason for this similarity is that the rocks have a common origin – namely the collision 4.5 billion years ago. The Moon also has significantly less iron in its core than Earth. This is also consistent with the computer models describing such an impact. To get the spins and orbit right a glancing collision is required, and in such collisions the iron-rich cores of the colliding planets tend to merge together, leaving the iron-depleted rocks from the outer layers to form the Moon.

  The Giant Impact Hypothesis suggests that there was a glancing collision between the newly formed Earth and a Mars-sized planet around 4.5 billion years ago, resulting in a planetary merger.

  The Giant Impact Hypothesis is able to explain the composition of the Earth and Moon and the details of their orbits and spins. This includes the origin of Earth’s tilted spin axis, angled at 23.5 degrees to the plane of the Solar System, which gives us our seasons (see here). I find this a wonderful thing; there are few certainties in science, but I would contend that we wouldn’t be here today if our spin axis wasn’t tilted. The Moon was likely formed in the event that tilted our spin axis, but in any case her presence acts to stabilise the orientation of Earth’s axis, and a reasonable level of stability over geological timescales is a prerequisite for the evolution of complex life. Humans wouldn’t be here without the Moon; at the very least, evolution would have taken a different path, and it is a major understatement to say that the road to humanity was convoluted. In one sense that’s a superficial observation. There are a vast number of chance events in our past that could have happened differently, and changing any one of them would have meant that we wouldn’t be here. We shouldn’t fall into the trap of attaching particular importance to a single event; we’ll leave that to the sonorous voice-overs of badly made television documentaries. The deeper unarguable point, which does bear at least a thought, is that we are very lucky indeed to be here. There cannot be any cosmic significance to our existence, because our existence is far too contingent on a series of chance events stretching back to the formation of the Solar System and beyond. Does the fact that you’re lucky to be alive make you feel irrelevant or valuable? I’ll leave that to you. In his essay ‘Some Thoughts on the Common Toad’, George Orwell reflects on the simple and available delight of noticing things like the passage of the seasons, and that is really what this book is about: ‘The point is that the pleasures of spring are available to everyone and cost nothing’, he writes. ‘How many a time have I stood watching the toads mating, or a pair of hares having a boxing match in the young corn, and thought of all the important persons who would stop me enjoying this if they could. But luckily they can’t.

  Humans wouldn’t be here without the Moon; at the very least, evolution would have taken a different path, and it is a major understatement to say that the road to humanity was convoluted.

  ‘The atom bombs are piling up in the factories, the police are prowling through the cities, the lies are streaming from the loudspeakers, but the Earth is still going around the Sun, and neither the dictators nor the bureaucrats, deeply as they disapprove of the process, are able to prevent it.’

  Humans wouldn’t be on Earth without the Moon, a fact we are always reminded of as we look up and see its ever-changing face in the night sky as it orbits the Earth, moving through its eight distinct phases.

  You don’t need permission to do science, to think carefully and without preconception about what Nature is telling you. After all, Nature is a more reliable guide to the truth than the opinions of those incalculably lucky humans.

  Life on an orbiting planet

  Storms

  The passage of the seasons is a gentle reminder that we live on a planet in orbit around the Sun. Although we’re moving at close to 30km/second in orbit, we can’t tell that from moment to moment because we’re moving in a straight line at constant speed to a good approximation, so it feels as if we’re standing still. This is why we don’t feel as if we are flying through space very quickly on a ball of rock. But there is a very important caveat; we are also spinning arou
nd as the Earth rotates once a day on its axis, and this does have definite physical consequences that we experience on timescales of hours rather than months.

  How do we know we’re spinning?

  You don’t have to be particularly observant to notice that something is spinning. The Sun rises in the east and sets in the west, arching across the sky. When it sets, the stars follow suit. There is obviously something circular going on.

  This eight-hour wide-angle star trail photo, taken in New Hampshire, USA in October, shows an Iridium flare streaking down near the horizon.

  From the evidence available to us, we might offer two possible explanations. The first and perhaps most natural is that the Earth is stationary and the Sun and stars circle around us once a day. The other possibility is that it is we who are doing the rotating rather than the Sun and stars. Copernicus described a spinning Earth moving in orbit around a fixed Sun in De revolutionibus, published in 1543. He was motivated primarily by his distaste for the inelegant explanation of the observed motions of the planets against the stars laid down by the Greek astronomer Ptolemy in the second century. Observed over the course of months, the planets do not follow neat circular arcs across the sky. They perform occasional loops, reversing their motion against the starry background. We now know this happens when the Earth overtakes a planet as it orbits the Sun. If you don’t accept that the Earth is in orbit you have to come up with some other mechanism for the planetary loops, and Ptolemy’s Earth-centred model, whilst delivering accurate predictions for the motions of the planets, is a terrifically messy affair. If you accept that the Earth goes around the Sun, on the other hand, you also have to come up with an explanation for day and night, which is separate from the yearly orbital motion. This is why Copernicus proposed that the Earth spins around on its axis once every 24 hours.