Wonders of the Universe - Brian Cox, Andrew Cohen (2011)
Chapter 3. FALLING
For all its scale and grandeur, the Universe is shaped by the action of just four forces of nature. Two of these, the weak and strong nuclear forces, remain hidden from everyday experience inside the atomic nucleus. The third force, electromagnetism, is perhaps most familiar to us, as it is the one we marshal to power our lives – electric currents flow because of the action of this force. Finally, there is gravity, the great sculptor – the force that acts between the stars. Gravity shapes the cosmos on the largest distance scales. From the formless clouds of hydrogen and helium that once filled our universe, gravity forged the first stars, sculpted the first planets and arranged them into the exquisite shapes of the galaxies. Having assembled countless billions of solar systems, gravity drives their cycles and rhythms. It is the invisible string behind the revolution of every moon around every planet and every planet around every star. Gravity keeps our feet on the ground and the Universe ticking over.
Gravity is more than a mere gentle presence; it is relentless, and for the largest agglomerations of matter in the Universe – the stars – it is both creator and destroyer. Stars shine in temporary resistance to gravitational collapse, but when they run out of nuclear fuel and the other three forces can no longer rearrange the matter in their cores in order to release energy and resist its inward pull, gravity crushes the most massive of them out of existence. In doing so, it creates the least understood objects in the Universe.
Before embarking on the voyage of their lives, astronauts are prepared for the flight and the sensation of weightlessness in aircrafts such as this C-131 at Wright Air Development Center, which flies at a ‘zero-g’ trajectory. These flight simulators are dubbed ‘vomit comets’ because of the nausea they often induce.
Soviet cosmonaut Gherman Titov is perhaps not the luckiest of men. In 1960 he was selected alongside Yuri Gagarin for the Soviet manned space programme. Out of the twenty men who started the programme, only these two made it through a fierce selection process that tested their physical and psychological resilience to the limit. Throughout training the two fighter pilots matched each other point for point, but someone had to be first, and Gagarin was given the ticket into the history books. On 12 April 1961, Gagarin became the first human to travel into space, completing a single orbit in 108 minutes before returning to Earth first in Vostok 1 and then by parachute. In one of those interesting bits of space trivia, Gagarin actually arrived back on Earth after his spacecraft, because he ejected at an altitude of 7,000 metres (23,000 feet) due to worries about the safety of the capsule on landing. Vostok 1 arrived safely on the ground 10 minutes before he did.
This bus ride to the Vostok launch on 12 April 1961 was the first part of the journey that was to make Yuri Gagarin a Soviet hero and worldwide celebrity.
On his return, Gagarin became a Soviet hero and a worldwide celebrity, leaving Titov to become the second man to orbit our planet. Titov’s name will be unfamiliar to most, although to this day he remains the youngest man ever to make the journey into space, at just under 26 years old. He piloted Vostok 2 on 6 August 1961, completing 17 orbits of Earth. Titov also claimed a rather less glamorous place in the history books; on the 25.3-hour mission, he not only became the first man to sleep in space (snoozing for a couple of hours as his spacecraft orbited the planet), but also the first to suffer the symptoms of a condition that has affected almost half of those who have experienced weightlessness for an extended period of time. Titov was the first victim of Space Adaption Syndrome. Known more usually as space sickness, this condition includes a variety of symptoms such as nausea, vomiting, vertigo and headaches as a common reaction to the odd sensations of space travel. Although weightlessness remains one of the great thrills of being an astronaut, it is also one of the most difficult to prepare for. Since Titov introduced medics to Space Adaption Syndrome, space agencies around the world have employed the only method they can of creating weightlessness here on Earth. How is it possible to remove the effects of gravity? The answer is by doing the same thing that Gagarin and Titov did: by falling towards Earth.
The American response to the Vostok programme was Project Mercury, a series of six manned launches which included the historic flights of Alan Shephard, the first American in space, on 5 May 1961, and John Glenn, the first American to orbit Earth. The astronauts selected for the programme, known as the ‘Mercury Seven’, became celebrities in the United States, and all of them eventually flew into space. The final flight of the Mercury Seven was John Glenn’s Space Shuttle mission in 1998, which he completed at the age of 77. The Tracy brothers in the TV series Thunderbirds were named after five of the Mercury Seven: Scott (Carpenter), Virgil (‘Gus’ Grissom), Alan (Shephard), Gordon (Cooper) and John (Glenn). Wally Schirra and Deke Slayton missed out. (I think Wally and Deke would have been great names for Thunderbirds pilots. The days when astronauts were bigger than rock stars are sadly missed.)
Astronauts prepare for Extravehicular Activity by practising techniques on a Hubble Space Telescope mock-up in the Neutral Buoyancy Laboratory. Underwater conditions simulate the weightlessness experienced in space.
During training for Project Mercury, perhaps after hearing about the experiences of Titov, NASA developed a way of flying a regular military aircraft to take would-be astronauts on an unusual ride. Using a C-131 aircraft, weightlessness was achieved by flying an unconventional flight path. This parabolic path creates a brief period of around 25 seconds during which all the occupants of the plane experience the sensation of weightlessness. This is because they are actually weightless; it may be brief, but when repeated twenty or thirty times in succession, the physiological effects are just as intense as those felt in space. This led to the C-131 being named the ‘Vomit Comet’, a name that has stuck with every plane used for this task ever since.
I’ve known about the Vomit Comet since I was a child, because I was, and still am, passionate about the space programme. Imagine my delight when I heard we were going to ride in it for our film on gravity. Who cares if it makes you feel rough, if the Mercury Seven could face it, so could I.
The Vomit Comet is the perfect place to experience the two related aspects of the force of gravity that hold the key to understanding what gravity actually is. Firstly, it is possible to completely cancel out the effects of gravity by simply falling towards the ground. This sets gravity apart from all the other forces of nature; it is not possible to negate the effect of electric charge, other than by adding more electric charge of the opposite sign. The Comet achieves the removal of gravity simply by flying along the trajectory that a cannon ball would take when fired out of a gun. The plane doesn’t just drop to the ground like a lift with a severed cable, of course (because then it would be impossible to control), but the acceleration of the plane towards the ground is exactly the same as the acceleration you would experience in a falling lift or a parachute jump (if you neglect air resistance). In numbers, the plane must accelerate towards the ground at 9.81 metres per second squared to cancel out the force of gravity. In order to keep the plane under control, it also flies forward at its usual flight speed. This results in the plane flying along a parabolic path. The fact that the effects of gravity are completely removed in freefall is very interesting, and the converse is also true: it is also possible to add to Earth’s gravitational pull by accelerating.
The race for space was on in the 1960s, as the US and Soviet nations battled to be the first to launch a human being into space.
Everyone knows that astronauts in space are weightless and float around inside their spacecraft, but not everybody knows why. It is not because they are a long way from Earth that gravity is absent (they are in fact only a few hundred miles above Earth’s surface, and the strength of Earth’s gravitational field in near-Earth orbit is not too different to the strength on the surface), it is that the effects of gravity are removed by falling, which is important point number one.
We flew in a modified Boeing 727-200, which is still used today for training shuttle astronauts. During the flight I was also able to demonstrate another strange but equally important and related aspect of gravity. Isaac Newton knew it when he wrote down his theory of gravity in 1687, as did Galileo many decades before him. The strange thing is this: all objects fall at the same rate under the force of gravity, even though gravity acts on objects in proportion to their mass. Newton and Galileo knew this to be the case because they did experiments and noticed that it was true, but they had absolutely no idea why. If you think about it for a moment, it is very odd indeed. Newton found that the gravitational force between two objects, such as Earth and you, is proportional to the product of their masses. So the force you feel due to the pull of Earth’s gravity is proportional to the mass of Earth multiplied by the mass of you. If you were to double your mass, the force between you and Earth would double. But, the rate at which you accelerate towards Earth because of its gravitational pull is also proportional to your mass, and when you work everything out it turns out that your mass completely cancels out, so therefore all things fall at the same rate under gravity. This looks very strange and was famously demonstrated by Apollo 15 Commander Dave Scott on the surface of the Moon in 1971. Scott dropped a feather and a hammer to the ground and, of course, both hit the ground at the same time. The reason you can’t do this on Earth is because air resistance slows the feather down, but in the high vacuum of the Lunar surface the only force acting on the falling objects is gravity. No matter how much physics you know, this is entertaining to watch because it isn’t in accord with common sense! Surely a cannon ball should fall to the ground faster than a single atom? The answer is, no, it doesn’t, and here is something to think about for later on: even a beam of light falls to the ground at the same rate as a cannon ball. Understanding this concept is key to understanding gravity.
As we accelerate away from Earth we experience a gravitational pull 1.8 times the strength of Earth – so I weigh nearly twice as much as I do back down on the ground.
I was able to demonstrate this for myself in the Vomit Comet armed with a model of Einstein. When we were weightless, I let a little plastic Albert float beside my head. One way of understanding why we floated next to each other is to simply state that we were both weightless, so we floated, but think about what this looks like from outside the plane. To someone on the ground looking up at us, the plane, myself and plastic Albert are all falling towards the ground under the action of Earth’s gravity, and obviously we are falling at the same rate. If I fell faster than Einstein, he wouldn’t float next to my head. Indeed, if the much more massive plane fell faster than both plastic Albert and myself, we’d both bump into the ceiling! The fact that we all floated around together is a beautiful demonstration of the fact that all objects, no matter what their mass, fall at the same rate in a gravitational field.
This simple fact inspired Albert Einstein to construct his geometric theory of gravitation, called General Relativity, which to this day is the most accurate theoretical description of gravity that we possess. We shall get to Einstein’s beautiful theory later on, and in doing so we’ll arrive at a very simple explanation of why everything falls at the same rate, and why gravity can be removed by the act of falling
Gravity holds the water in our oceans and hugs the atmosphere close to the planet. It’s the reason why the rain falls and the rivers flow; it powers the ocean currents and drives the world’s weather; it’s why volcanoes erupt and earthquakes tear the land apart. Yet gravity also plays a role on an even grander stage. Across the Universe, from the smallest speck of dust to the most massive star, gravity is the great sculptor that created order out of chaos.
THE INVISIBLE STRING
Everything in the Cosmos is subject to the force of gravity. From the manmade satellites that rotate around our planet creating the technological infrastructure of the twenty-first century, to the orbit of our only natural satellite – the Moon – which journeys around Earth every 27.3 days, it is gravity that provides the invisible string to guide them on their path. The journey of every planet, moon, ball of rock and mote of dust in our solar system is guided by gravity; from the 365-day trip our planet takes around the Sun to each of the orbits of the seven planets and 166 known moons in our neighbourhood. Beyond our solar system, gravity continues to conduct the flow of the Universe, with everything affected by the gravitational pull of something else, no matter how tiny or how massive.
Our solar system orbits around the centre of the Milky Way Galaxy, a place dominated by a supermassive black hole, the heart of a swirling system of over 200 billion gravitationally bound stars. And even this vast, rotating structure isn’t where the merry-go-round of the Universe ends, because even the galaxies are steered through the vast Universe by the action of gravity.
The Virgo Supercluster of galaxies is a good example of how gravitational pull exerts itself. This cluster of galaxies has a gravitational pull on the Local Group of galaxies that surround our Milky Way Galaxy.
NASA / SCIENCE PHOTO LIBRARY
The supermassive black hole at the centre of the Milky Way Galaxy, Sagittarius A*, is the heart of a swirling system of over 200 billion stars which are gravitationally bound.
The elliptical galaxy M87 is located at the centre of the Virgo Cluster. This huge galaxy includes several trillion stars, a supermassive black hole, and a family of 15,000 globular star clusters which may have been graviationally pulled from nearby dwarf galaxies.
Beyond our solar system, gravity continues to conduct the flow of the Universe, with everything affected by the gravitational pull of something else, no matter how tiny or how massive.
Our galaxy is part of a collection of galaxies called the Local Group – a cluster of over 30 galaxies named by the American astronomer Edwin Hubble in 1936. Over ten million light years across, this vast dumbbell-shaped structure contains billions and billions of stars, including the trillion stars that make up our giant galactic neighbour, Andromeda. Just as the Moon orbits Earth, Earth orbits the Sun, and the Sun orbits the Milky Way, so the Local Group orbits its common centre of gravity, located somewhere in the 2.5 million light years between the two most massive galaxies in the group: our Milky Way and Andromeda. But even this giant community of galaxies isn’t the largest known gravitationally bound structure. As you sit reading this book, gravity is taking you on an extraordinary ride. Not only are you spinning around as Earth rotates once a day on its axis, not only are you orbiting at just over 100,000 kilometres (62,137 miles) per hour around the Sun, not only are you rotating around the centre of our galaxy at 220 kilometres (136 miles) per second, and not only is the entire Milky Way tearing around the centre of gravity of the Local Group at 600 kilometres (372 miles) per second, but we are also part of even an grander gravitationally driven cycle.
The Local Group is part of a much larger, gravitationally bound family called the Virgo Supercluster – a collection of at least 100 galaxy clusters. Nobody is sure how long it takes our Local Group to journey around the Virgo Supercluster; vast beyond words, stretching over 110 million light years, it is, even so, only one of millions of superclusters in the observable Universe. It is now thought that even superclusters are part of far larger structures bound together by gravity, known as galaxy filaments or great walls. We are part of the Pisces-Cetus Supercluster Complex.
Gravity’s scope is unlimited, its influence all-pervasive at all distance scales throughout the entire history of the Universe. Yet, perhaps surprisingly, given its colossal reach and universal importance, it is the first force that we humans understood in any detail
THE APPLE THAT NEVER FELL
The history of science is littered with examples of circumstance and serendipity leading to the greatest discoveries, which is why curiosity-driven science is the foundation of our civilisation. Among the most celebrated is the convoluted story of Newton’s journey to his theory of gravity – the first great universal law of physics.
The Great Plague of 1665 was the last major outbreak of bubonic plague in England, but also the most deadly. Over one hundred thousand people are thought to have died the hideous death that accompanied the rodent-borne illness. London was the epicentre of the outbreak, but even then the matrix of connections between the capital and the rest of the country caused the disease to spread rapidly across England. Extreme and often useless measures were taken to prevent its spread, from the lighting of fires to cleanse the air to the culling of innocent dogs and cats. Infected villages were quarantined and schools and colleges closed. One place affected was Trinity College Cambridge, and one of the students to take a leave of absence in the summer of 1665 was Isaac Newton.
Newton was twenty-two years old and newly graduated when he left plague-ridden Cambridge to return to his family home in Woolsthorpe, Lincolnshire. He took with him a series of books on mathematics and the geometry of Euclid and Descartes, in which he had become interested, he later wrote, through an astronomy book he purchased at a fair. Although by all accounts he was an unremarkable student, his enforced absence allowed him time to think, and his interest in the physical world and the laws underpinning it began to coalesce. Over the next two years his private studies laid the foundations for much of his later work in subjects as diverse as calculus, optics and, of course, gravity. On returning to Cambridge in 1667 he was elected as a fellow, and became the Lucasian Professor of Mathematics in October 1670 (a post recently held by Stephen Hawking and currently held by string theorist Michael Green – both of whom continue to work on the problem of the nature of gravity). Newton spent the next twenty years lecturing and working in a diverse range of scientific and pseudo-scientific endeavours, including alchemy and predictions of the date of the apocalypse. The economist John Maynard Keynes said of Newton that he was not ‘the first in the age of reason, but the last of the magicians’. This is not entirely accurate, but then what can one reasonably expect from an economist? Newton lived on the cusp of pre-scientific times and the modern age and did more than most to usher in the transition. His greatest contribution to modern science was the publication in 1687 of the Philosophiæ Naturalis Principia Mathematica, otherwise known as the Principia. This book contains an equation that describes the action of gravity so precisely that it was used to guide the Apollo astronauts on their journey to the Moon. It is beautiful in its simplicity and profound in its application and consequences for scientific thought.
This time-lapse image neatly illustrates the concept of gravity. The feather and ball are here seen falling at the same speed in a vacuum, proving that any two objects of different mass will accelerate at identical rates when at the same gravitational potential. The reason that this does not happen on Earth is because of the air resistance that is present, which is, of course, absent in a vacuum. This principle was also proved correct when an Apollo astronaut dropped a feather and a hammer on the Moon (which has no atmosphere) and saw them fall at the same rate.
This is the mathematical expression of Newton’s Law of Universal Gravitation. In words, it says that the force (F) between two objects is equal to the product of their masses (m1 and m2), divided by the square of the distance between them. G is a constant of proportionality known as the gravitational constant; its value encodes the strength of the gravitational force: The force between two one-kilogramme masses, 1 metre (3 feet) apart, is 6.67428 x 10-11 newtons – that’s 0.000000000667428 N, which is not a lot. For comparison, the force exerted on your hand by a 1kg bag of sugar is approximately 10 N. In other words, the gravitational constant G is 6.67428 x 10-11 N (m.Kg)2. The reason why G is so tiny is unknown and one of the greatest questions in physics; the electromagnetic force is 1036 times stronger – that’s a factor of a million million million million million million.
There are many reasons why Newton’s Law of Universal Gravitation is beautiful. It is universal, which means it applies everywhere in the Universe and to everything not in the vicinity of black holes, too close to massive stars or moving close to the speed of light. In these cases, Einstein’s more accurate theory of General Relativity is required. For planetary orbits around stars, orbits of stars around galaxies and the movements of the galaxies themselves, it is more than accurate enough. It has also applied at all times in the Universe’s history beyond the first instants after the Big Bang. This is not to be taken for granted, because the law was derived based on the work of Johannes Kepler and the observations of Tycho Brahe, who were concerned only with the motion of the planets around the Sun. The fact that a law that governs the clockwork of our solar system is the same law that governs the motion of the galaxies is interesting and important. It is the statement that the same laws of physics govern our whole universe, and Newton’s law of gravitation was the first example of such a universal law.
It is also profoundly simple. That the complex motion of everything in the cosmos can be summed up in a single mathematical formula is elegant and beautiful, and lies at the heart of modern fundamental science. You don’t need to sit down with a telescope every night and use trial and error to find the positions of the planets and moons of the Solar System. You can work out where they will be at any point in the future using Newton’s simple equation, and this applies not just to our solar system, but also to every solar system in the Universe. Such is the power of mathematics and physics.
Newton found that gravity is a force of attraction that exists between all objects, from the tiny immeasurable force of attraction between two rocks on the ground to the rather larger force that each and every one of us is currently experiencing between our bodies and the massive rock upon which we are stood. With a mass of almost 6 milllion million million million kilogrammes, the force between all of us and our planet is strong enough to keep our feet on the ground. On the scale of planets, however, gravity can do much more than simply keep them in orbit and hold things on the ground; it can sculpt and shape their surfaces in profound and unexpected ways
The Fish River Canyon in southern Namibia is one of the world’s greatest geological sites, and a spectacular example of how the effects of climate and gravity can impact on the structure of Earth’s surface.
ERICH SCHREMPP / SCIENCE PHOTO LIBRARY
THE GRAND SCULPTURE
Fish River Canyon in the south of Namibia is one of the world’s great geological features, second only in scale to the Grand Canyon in Arizona, at over 160 kilometres (99 miles) long, 26 kilometres (16 miles) wide and half a kilometre (a third of a mile) deep in places. Like the Grand Canyon, the movement of tectonic plates or volcanic action did not create this scar in Earth’s crust; instead it stands testament to the erosive power of water. The Fish River is the longest river in Namibia, running for over 650 kilometres (403 miles). Despite only flowing in the summer, over millennia it has slowly but forcefully gouged the canyon out of solid rock. This takes energy, and that energy ultimately comes from the Sun as it lifts water from the oceans and deposits it upstream in the highlands to the north. Once the rain begins to fall, gravity takes over. The highlands around the source of the Fish River are at an elevation of over a thousand metres above sea level. When the rain lands on the ground at this elevation, every water droplet stores energy in the form of gravitational potential energy. There is a simple equation that says how much energy each drop has stored up:
U is the amount of energy that will be released if the drop falls from height (h) above sea level down to sea level, m is the mass of the drop and g is the now-familiar acceleration due to gravity – 9.81 m/s2.
Every droplet of water raised high by the heat of the Sun has energy, due to its position in Earth’s gravitational field, and this energy can be released by allowing the water to flow downwards to the sea. Some of this energy is available to cut deep into Earth’s surface to form the Fish River Canyon.
The strength of Earth’s gravitational field therefore has a powerful influence on its surface features. This is not only visible in the action of falling, tumbling water, but in the size of its mountains. On Earth, the tallest mountain above sea level is Mount Everest; at almost 9 kilometres (5.5 miles), it towers above the rest of the planet. But Everest is dwarfed by the tallest mountain in the Solar System which, perhaps at first sight surprisingly, sits on the surface of a much smaller planet. Around 78 million kilometres (48 million miles) from Earth, Mars is similar to our planet in many ways. Its surface is scarred by the action of water that once tumbled from the highlands to the seas, dissipating its gravitational potential energy as it fell, although today, the water has left Mars. The planet is only around 10 per cent as massive as Earth, though, so its gravitational pull is significantly weaker, and this is one of the reasons why Mars was unable to hang on to its atmosphere, despite being further away from the Sun. The possibility of liquid water flowing on the Martian surface vanished with its atmosphere, leaving the red planet to an arid and geologically dead future, but Mars’s lower surface gravity has a surprising consequence for its mountains.
Towering over every other mountain in the Solar System is the extinct volcano, Olympus Mons. Rising to an altitude of around 24 kilometres (15 miles), it is almost the height of three Mount Everests stacked on top of each other. The fact that a smaller planet has higher mountains is not a coincidence; it is partly down to environmental factors such as the rate of erosion and the details of the planet’s geological past, but there is also a fundamental limit to the height of mountains on any given planet: the strength of its surface gravity. Mars has a radius approximately half that of Earth’s, and since it is only 10 per cent as massive, a little calculation using Newton’s equation will tell you that the strength of the gravitational pull at its surface is approximately 40 per cent of that on our planet. This changes everything’s weight.
Here on Earth we don’t often think about the difference between mass and weight, but the distinction is very real. The mass of something is an intrinsic property of that thing – it is a measure of how much stuff the thing is made of. This doesn’t change, no matter where in the Universe the thing is placed. In Einstein’s Theory of Special Relativity, the rest mass of an object is an invariant quantity, which means that everyone in the Universe, no matter where they are or how they are moving, would measure the same value for the rest mass.
Weight is different. For one thing, it is not measured in kilogrammes, it is measured in the units of force – newtons. This is easy to understand if you think about how you would measure your weight. When you stand on bathroom scales, they measure the force being exerted on them by you; you can see this by pressing down on them – the harder you push, the greater the weight reading. The force you are exerting on the scales is in turn dependent on the strength of Earth’s gravity. This should be obvious; if I had taken the scales up in the Vomit Comet and tried to stand on them, they wouldn’t have read anything because I would have been floating above them – hence the word ‘weightless’. In symbols, the weight of something on Earth is defined as:
The immense Olympus Mons can exist on Mars because the planet has 40 per cent of Earth’s gravitational pull. However, move this extinct volcano to our planet and it would sink into the ground because of its enormous weight.
W is weight, m is the thing’s mass, and g is the familiar measure of Earth’s gravitational field strength – 9.81 m/s2 – with a couple of caveats that we’ll get to below! (For absolute accuracy, the correct definition of weight is; the force that is applied on you by the scales to give you an acceleration equal to the local acceleration due to gravity – i.e. the force the scales exert on you to stop you falling through them.) So, here on Earth a human being with a mass of 80kg weighs 785 newtons; on Mars, the same 80-kg person would weigh approximately 295 newtons.
So your weight depends on a few things; one is your mass, another is the mass of the planet you are on. Your weight would also change if you were accelerating when you measured it, which is another manifestation of the equivalence principle. So, if you took Olympus Mons and stuck it on Earth, then as well as dwarfing every other mountain on the planet, it would also weigh around two and a half times as much as it does on Mars. This enormous force would put its base rock under such intense pressure that it would be unable to support the mountain, so it would sink into the ground. A planet the size of ours cannot sustain a mountain the size of Olympus Mons – it would weigh too much. The highest mountain on Earth, as measured from its base, is Mauna Kea, the vast dormant volcano on Hawaii. It is over one kilometre (half a mile) higher than Everest, and it is gradually sinking. So Mauna Kea is as high as a mountain can be on our planet, and this absolute limit is set by the strength of our gravity.
The definition of weight can get a bit convoluted, and we mentioned that there are caveats to the rule of thumb that your weight on Earth is 9.81 times your mass. One problem is that the strength of Earth’s gravity varies slightly at every point on its surface. The most obvious effect is altitude; on the edge of the Fish River Canyon I would weigh slightly less than I would if I stood on the canyon floor. That’s because at the top of the canyon I am further from the centre of Earth than I would be at the bottom, so the gravitational pull I feel is weaker. Earth is also not uniformly dense – some areas of Earth’s surface and subsurface are made of more massive stuff than others, which also affects the local gravitational field. To complicate matters further, Earth is spinning, which means that you are accelerating when you stand on its surface, which means that the strength of gravity you feel changes in accord with the equivalence principle; this acceleration increases as you go towards the Equator, reducing the gravitational acceleration you feel there. Earth bulges out at the Equator because it is spinning, which weakens the gravitational pull there still further. The upshot of all this is that you weigh approximately 0.5 per cent less at the North and South Poles than you do at the Equator. The effects of the varying density of Earth’s subsurface and the presence of surface features on Earth’s gravitational field have been measured to extremely high precision and presented as a map known as the geoid
If you took Olympus Mons and stuck it on Earth…it would weigh around two and a half times as much as it does on Mars… A planet the size of ours cannot sustain a mountain of this size – it would weigh too much.
Towering over every other mountain in the Solar System is the extinct volcano, Olympus Mons. It is almost the height of three Mount Everests stacked on top of each other. The fact that a smaller planet has higher mountains is not coincidence; it is partly down to environmental and geological factors, but there is also a fundamental limit to the height of mountains on any given planet; the strength of its surface gravity. Mars has a gravitational pull at its surface of approximately 40 per cent of that on our planet.
ESA / DLR / FU BERLIN (G.NEUKUM) / SCIENCE PHOTO LIBRARY
Data collected by the GOCE satellite between November and December 2009 is here used to create a map of the tiny variations in Earth’s gravity field across the globe. These maps provide invaluable information for oceanographers, hydrologists and geologists in order to create accurate climate models for our planet.
This picture of Earth’s gravitational field was taken by a European Space Agency satellite, GOCE, which was launched in March 2009. GOCE is equipped with three ultra-sensitive accelerometers, arranged so that they respond to very tiny changes in the strength of Earth’s gravitational field as the satellite orbits. Skimming the edge of Earth’s atmosphere at an altitude of 250 kilometres (155 miles), GOCE spent two months gathering the data to create this extraordinary image. It’s the first time the strength of gravity across the globe has been mapped this accurately. The blue patches indicate areas that have a weak gravitational field, the green are average and the red are places where it is stronger. The reason for these fluctuations is the density of the rocks below Earth’s surface and the presence of features such as mountains or ocean trenches. More technically, the picture is presented as an equipotential surface, which means that if Earth were entirely covered in a single ocean of water, this picture would correspond to the water height at every point.
Looking at this map, it is clear that Iceland has a higher gravitational field strength than that of England. These changes are imperceptible to us, but it means that I would weigh slightly less standing at the same altitude in Manchester than I would in Reykjavik. This map was not made to show the trivial distinctions in a traveller’s weight, of course; the unparalleled level of detail will enable a deeper understanding of how our planet works, because this data is a high-precision geological tool. One particular benefit will be for oceanographers; because the map defines the baseline water surface in the absence of tides, winds and currents, it is critical to understanding the factors that determine the movement of water across the oceans of our planet. This is a very important part of understanding and predicting the way energy is transferred around our planet, which is in turn an important factor in generating accurate climate models.
The geoid therefore reveals a vast amount of detailed information about the structure of our planet, just from measuring the strength of its gravity. As far as the actual height of the ocean surface is concerned, however, the most influential factor of all is not shown: the Moon
The geoid helps us to understand unseen structures on our planet, such as here in Iceland where magma is welling upwards from Earth’s mantle, affecting the gravitational field there. In this image, taken in May 2010 from a NASA satellite, the Icelandic volcano Eyjafjallajökull can be seen erupting.
THE TUG OF THE MOON
Many of the planets that exist in our solar system have families of moons; from the sixty-three satellites of Jupiter, to the thirteen moons of Neptune, and to the two tiny misshapen moons of Mars. Our planet has only a single moon; it is our constant companion, with which we have travelled through space for almost four and a half billion years.
The elusive far side of the Moon, which was eventually first photographed in 1959 by the Soviet Luna 3 probe.
No other planet in our solar system has a moon as large as ours in relation to its parent planet. Orbiting only 380,000 kilometres (236, 000 miles) from Earth, it is a quarter of the Earth’s diameter, making it the fifth-largest moon in the Solar System after Titan, Ganymede, Callisto and Io – although of course their parent planets, Jupiter and Saturn, are significantly larger than Earth. This makes the Earth and Moon close to being a double-planet system. The current best theory for the formation of our moon is that it was created around 4.5 billion years ago when a Mars-sized planet, which has been named Theia, crashed into the newly formed Earth, blasting rock into orbit which slowly condensed into the lunar structure that we see today. The evidence for this theory is partly that the Moon has a very similar composition to that of Earth’s outer crust, although it is much less dense because it has a significantly smaller iron core. This is what would be expected if the Theia/Earth collision was a glancing blow, leaving the Earth’s iron core intact and so reducing the relative amount of iron in the Moon. This in turn means that the Moon’s gravitational field is much weaker than ours. When Neil Armstrong took his small step onto the Moon, he weighed just 26 kilogrammes (58 pounds), despite the fact that he was wearing a space suit that had weighed 81 kilogrammes (180 pounds) on its own on Earth – this is all because the Moon’s gravitational field strength is approximately one-sixth of Earth’s. Despite this relatively weak gravitational pull, however, the Moon still has a profound effect on our planet.
The Moon has a visible effect on our oceans. The combination of the gravitational pulls of the Moon and of Esarth squashes everything, which in turn creates tides.
Because of the Moon’s proximity to our planet, its gravitational pull varies significantly from one side of Earth to the other. The illustration (right) shows the net gravitational force exerted at each point on Earth by the Moon, as seen by someone sitting at Earth’s centre, after Earth’s own gravitational field has been subtracted away. What remains is a net gravitational force pulling the side of the Earth that is facing the Moon towards the Moon, as you might expect. But there is also a net force pulling the opposite side of Earth away from the Moon. Notice also that at right angles to the position of the Moon, the lunar gravity actually adds to the Earth’s gravitational pull and squashes everything! This is the origin of the tides; because water is easier to stretch than the rock that forms the ocean floor, the water in the oceans bulges outwards relative to the ground beneath the Moon and on the opposite side of Earth to the Moon. The difference in water heights is only a few metres, but can be much higher depending on the shape of the shoreline. It’s worth mentioning that there are also tides in the rocks of Earth’s surface; gravity doesn’t just affect water! But rocks are very rigid, and so don’t stretch much. The surface of Earth does, however, rise and fall by a few centimetres due to tidal effects. As Earth rotates beneath the tidal bulge raised in the oceans, the distorted water surface sweeps past the shorelines and we experience two high and low tides per day.
Next time someone starts trying to tell you that we are made of water and therefore the Moon must have an influence on us, you will now be justified in having a strange, blank and perhaps slightly pitying expression on your face for two reasons. One is that because the tides are a differential effect (that is to say they depend on the change in the strength of the Moon’s gravity across the diameter of Earth), the tidal effect on you is utterly insignificant and makes no difference to you at all because the difference in the Moon’s gravitational force across something the size of your body is negligible. Secondly, it has got nothing at all to do with water in any case!
Gravity is always a two-way street – just as the Moon raises tides on Earth, so Earth must cause tides to sweep across the surface of the Moon.
The relationship between the Earth and the Moon is not just a one-way street; just as the Moon’s gravity has transformed our planet, so in turn Earth has transformed its neighbour.
Throughout human history, half of the Moon’s surface remained hidden from view, and it wasn’t until 1959, when the Soviet Luna 3 probe photographed the far side of the Moon for the first time, that we caught our first glimpse of this hidden landscape. Nine years later, the astronauts on board Apollo 8 became the first humans to leave Earth’s orbit and the first human beings to directly observe the far side of the Moon with their own eyes. The reason only one side of the Moon faces Earth, appearing frozen in time and unchanging in the seemingly ever-moving night sky, is down to the tidal effects.
Billions of years ago, the view of our satellite from Earth would have been very different. In its childhood, the Moon rotated much faster, and both sides of its surface would have been visible from Earth. From the moment of its birth, the Moon felt the tug of Earth’s gravity – a force that would have been even greater than it is today because the Moon was also closer to Earth.
LUNAR GRAVITY DIFFERENTIAL FIELD
The lunar gravity differential field at Earth’s surface is known as the tide-generating force. This is the primary mechanism that drives tidal action and explains two equipotential tidal bulges, accounting for two daily high waters.
THE EFFECT OF TIDAL LOCKING ON THE EARTH AND MOON
As the Earth–Moon system moves towards being perfectly tidally locked, the Moon is gradually drifting away from Earth.
A glance at Newton’s Law of Universal Gravitation will tell you that gravity is always a two-way street – just as the Moon raises tides on Earth, so Earth must cause tides to sweep across the surface of the Moon. These tides are not in water, of course, but in the solid rock of the lunar surface. In an amazing piece of planetary heavy lifting, the Moon’s crust would have been distorted by up to 7 metres (22 feet)!
This giant tidal bulge sweeping across the Moon had an interesting effect. As the Moon turned beneath the giant parent planet hanging in the lunar sky, the rock tide was dragged across its surface, but the rising of the tide isn’t instantaneous; it takes time for the surface of the Moon to respond to the pull of the Earth. During that time, the Moon will have rotated a bit, carrying the peak of the rock tide with it. The tidal bulge will therefore not be in perfect alignment with Earth, but slightly ahead of it. Earth’s gravity acts on the misshapen Moon in such a way that it tries to pull it back into sync; in other words, it works like a giant break. Over time, this effect, known as tidal locking, gradually synchronizes the rotation rate of the Moon with its orbital period, effectively meaning that the tidal bulge can remain in exactly the same place on the Moon’s surface beneath Earth and doesn’t have to be swept around.
The Moon is now almost, but not quite, tidally locked to Earth, which means that it takes one month to rotate around on its axis and one month to orbit Earth. So there’s no dark side of the Moon – the side we can’t see gets plenty of sunlight, it’s just a side that perpetually faces away from Earth. The Earth– Moon system is in fact still evolving towards being perfectly tidally locked, and one interesting consequence of this is that the Moon is gradually drifting further and further away from Earth at a rate of just under 4 centimtres (1.5 inches) per year.
The power of gravity is not just in its ability to reach across the empty wastes of space and shape the surface of planets and moons; gravity also has the power to create whole new worlds, and we can see the process of that creation frozen in time in the sky, every day and every night
THE FALSE DAWN
It is one of the strangest lights that appears in our night sky; a light that for centuries has puzzled those who have witnessed its glow, fooling them into thinking that a new day was arriving. The Prophet Muhammed called it the false dawn and warned the followers of Islam not to confuse it with the real dawn when setting the timing of daily prayers.
This magical glow that appears on the horizon just before sunrise and just after sunset has nothing to do with the arrival or departure of our star; instead it is a ghostly reminder of our world’s origins and the power of gravity. It is the Zodiacal light; a wispy, whitish glow that appears to form a rough triangular shape rising from the horizon. The Italian astronomer Giovanni Cassini first investigated this strange phenomenon in 1683. The ethereal light perplexed many scientists of the age, and a common explanation was that the light came from the atmosphere of the Sun as it rose above the horizon before the Sun itself. It was Nicolas Fatio de Duillier, one of Cassini’s students, who finally explained its origin, and in doing so he provided a first glimpse of the origin of the planets and moons in our solar system.
The story of the Zodiacal light can be traced back five billion years to the origins of our solar system. Back then, there was no Sun, nor any planets or moons; there was only a cloud of gas and dust, the building blocks of everything we now call home. Everything that makes up our solar system was contained in an enormous irregular cloud floating through space. It is thought the explosion of a nearby star sent a shockwave through the cloud, creating small fluctuations in density. It also imparted rotation. The denser regions had slightly more gravitational pull than the less dense regions, so they began to grow, and the largest one became the Sun. In its earliest days the Solar System would have been planet-less; surrounding the young Sun was a spinning disc of matter, a protoplanetary disc. Over time, the minute particles of dust in the disc collided and clumped together, and large objects the size of small asteroids, known as planetesimals, would have formed by chance. Once the larger planetesimals were big enough to have significant gravity, they began to sweep up the matter close to them and their growth accelerated. Roughly one hundred million years later, the largest planetesimals evolved into the planets and moons we see today.
However, not all this matter from the primordial cloud became a planet or moon. Out in the solar system beyond Mars there should be another planet, but a gravitational tug of war between Jupiter and the Sun stops it forming. Now, instead of a ninth planet, there is a band of dust and debris – the asteroid belt. Normally there is no way of seeing the asteroid belt from Earth with the naked eye – it’s just too far away and the asteroids are too small – but collisions within the asteroid belt produce dust, and that is the secret behind the false dawn. The faint glow of the Zodiacal light after sunset and before sunrise is caused by sunlight reflecting off the debris of a failed planet; a remnant of the early Solar System and a beautiful, glimmering reminder of our origins
The wispy, whitish glow that appears on the horizon before sunrise and just after sunset was a subject of great debate among scientists for centuries. This Zodiacal light, as it is known, is in fact the debris that remains after collisions within the asteroid belt caused by a gravitational tug of war in the Solar System.
© Tony Hallas/Science Faction/Corbis
Normally there is no way of seeing the asteroid belt from Earth with the naked eye – it’s just too far away and the asteroids are too small – but collisions within the asteroid belt produce dust, and that is the secret behind the false dawn.
Theoretically, another planet should have formed from the primordial dust in the Solar System beyond Mars; however, the conflicting gravitational forces between the Sun and Jupiter prevent this happening, resulting in a band of dust and debris known as the asteroid belt.
THE BLUE MARBLE
Even the most dogmatic flat-Earther would have a problem explaining away ‘The Blue Marble’. This photo, taken by the astronauts on board Apollo 17 during its journey to the Moon on 7 December 1972, has caused some to speculate that this beautiful picture of our fragile world is perhaps the most distributed image in human history. But why is Earth a sphere? Actually, why are all planets and all stars spherical?
As we’ve discussed, we know that planets and stars are formed by the gravitational collapse of clouds of dust. You could say that the force of gravity pulls everything together, which is one way of looking at it, but another way of saying the same thing is that all the little particles in the primordial cloud of dust had gravitational potential energy, because they were all floating around in each other’s tiny gravitational fields. Just like the water droplets that fell as rain high up in the mountains above the Fish River Canyon, these particles would all try to fall ‘downhill’ to minimise their gravitational potential energy. This leads us to a very general and very deep principle in physics, and you can pretty much explain everything that happens in the Universe by applying it: things will minimise their potential energy if they can find a way of doing so. So, you could answer the question ‘why does a ball roll down a hill?’ by saying that the ball would have lower gravitational potential energy at the bottom of the hill than the top, so it rolls down. You could also, of course, say that there is a force pulling the ball down the hill. Physicists often work with energies rather than forces, and the two languages are interchangeable.
‘The Blue Marble’…photo has caused some to speculate that this beautiful picture of our fragile world is perhaps the most distributed image in human history.
With a collapsing cloud of dust, the shape that ultimately forms will therefore be the shape that minimises the gravitational potential energy. The shape must be the one that allows everything within the cloud to get as close to the centre of it as it possibly can, because anything that is located further away from the centre will have more gravitational potential energy! So, the shape that ensures that everything is as close to the centre as possible is, naturally, a sphere, which is why stars and planets are spherical
‘The Blue Marble’ is perhaps one of the most famous photographs ever taken of Earth, and has inspired numerous images since. The photograph, taken by the Apollo 17 crew on their 1972 journey to the Moon, made history as the first true-colour image of our planet which showed Earth in unprecedented detail.
VERY LARGE ARRAY
A very large array indeed – the 27 dishes on the Plains of San Augustin are an impressive sight, stretching into the horizon. Through these, the radio astronomy observatory can take some even more impressive images.
In the US state of New Mexico, on the Plains of San Augustin between the towns of Magdalena and Datil, lies one of the most spectacular and iconic observatories on the planet. The Very Large Array (VLA) is a radio astronomy observatory consisting of 27 identical dishes, each 25 metres (82 feet) in diameter, arranged in a gigantic Y shape across the landscape. Although each dish works independently, they can be combined together to create a single antenna with an effective diameter of over 36 kilometres (22 miles). This allows this vast virtual telescope to achieve very high-resolution images of the sky at radio wavelengths.
Radio astronomy has a history dating back to the 1930s, when the astronomer Karl Jansky discovered that the Universe could be explored not just through the visible part of the electromagnetic spectrum, but also through the detection of radio waves. Over a period of several months, Jansky used an antenna that looked more like a Meccano set than the VLA to record the radio waves from the sky. He initially identified two types of signal: radio waves generated by nearby thunderstorms, and radio waves generated by distant thunderstorms. He also found a third type, a form of what he thought was static. The interesting thing about the static was that it seemed to rise and fall once a day, which suggested to Jansky that it consisted of radio waves being generated from the Sun, but then over a period of weeks the rise and fall of the static deviated from a 24-hour cycle. Jansky could rotate his antennae on a set of Ford Model T tyres to follow the mysterious signal, and he soon realised the brightest point was not coming from the direction of the Sun, but from the centre of the Milky Way Galaxy in the direction of the constellation of Sagittarius.
Coinciding with the economic impact of the Great Depression, Jansky’s pioneering work did not immediately lead to an expansion in the new science of radio astronomy, but ultimately exploring the radio sky has become one of the most powerful techniques used in understanding the Universe beyond our solar system
Of the six thousand or so stars we can see from Earth with the naked eye, only one object lies beyond the gravitational pull of our galaxy. The picture below is of Andromeda, which is the nearest spiral galaxy to the Milky Way Galaxy and the most distant object visible to anyone who looks up into the night sky with just the naked eye. It may appear as nothing more than a smudge in the heavens, but recent observations by NASA’s Spitzer Space Telescope suggest that it is home to a trillion suns.
Andromeda is just one of a hundred billion galaxies in the observable Universe, but there is one thing that singles it out, other than its proximity. While most galaxies are rushing away from each other as the Universe expands, Andromeda is in fact moving directly towards us, getting closer at a rate of around half a million kilometres (310,000 miles) every hour. It seems the two galaxies are destined to meet, guided by the force of gravity.
A galactic collision sounds like a rare and catastrophic event – the meeting of a trillion suns – but in fact such collisions and the resultant mergers of galaxies are not unusual occurrences in the history of the Universe; both the galaxies of Andromeda and the Milky Way have absorbed other galaxies into their structures over the billions of years of their existence.
The sequence of images on the next page has been created as a computer simulation of what would happen during a galactic collision between our neighbour Andromeda and our own Milky Way. The Milky Way Galaxy is shown face-on and you can see it moving from the bottom, up to the left of Andromeda, and then finally to the upper right. From this perspective Andromeda appears tilted.
These images are 1 million light years across, and the timescale between each frame of the sequence is 90 million years. After the initial collision, an open spiral pattern is excited in both the Milky Way and Andromeda, and long tidal tails and the formation of a connecting bridge of stars are apparent. Initially the galaxies move apart one from another, but then they fall back together to meet in a second collision.
As more stars are thrown off in complex ripple patterns, they settle into one huge elliptical galaxy. Spiral galaxies such as Andromeda and the Milky Way are the pinnacle of complexity, order and beauty, but elliptical galaxies are sterile worlds where few stars form. If we humans, and indeed Earth itself, are still here in roughly 3 billion years, this collision will be a spectacular event. Just before we collide, the night sky will be filled by our giant neighbour. When the two galaxies clash there will be so much energy pumped into the system that vast amounts of stars will form, lighting up the whole sky
The Andromeda Galaxy is shown here in its full glory through an infrared composite image from NASA’s Spitzer Space Telescope, which shows the galaxy’s older stars (left) and dust (right) separately. Spiral galaxies such as this one tend to form new stars in their dusty, clumpy arms.
WHEN GALAXIES COLLIDE
This supercomputer animated sequence shows the merger of the Milky Way and Andromeda Galaxies. The sequence begins just before the collision and follows the dynamics of the galaxies until they merge. There are about 90 million years between each frame shown in this sequence.
FEELING THE FORCE
Gravity certainly feels like a powerful force. It built our planet, our solar system, and all the billions of star systems in the Universe, diligently assembling clouds of dust and gas into neatly ordered spheres. Matter curves the fabric of the Universe, and in doing so the spheres are bound together and marshalled into orbits, generating the cyclical cosmos we witness from Earth – from our journey through the yearly seasons to the daily ebb and flow of the tides. Gravity reaches far across the space between the star systems, forming galaxies, clusters and superclusters which all beat out orbital rhythms on longer and longer timescales. Gravity is the creator of order and rhythm in our dynamic and turbulent universe.
Galaxy clusters like this one, MS0735.6+7421, are all subject to the power and force of gravity.
B. MCNAMARA (UNIVERSITY OF WATERLOO) / NASA / ESA/ STScI / SCIENCE PHOTO LIBRARY
THE GRAVITY PARADOX
Despite its reach and influence, there is a mystery surrounding nature’s great organisational force; although it is an all-pervasive influence, it is in fact an incredibly weak force – by far the weakest force in the Universe. It is so weak that we overcome it every day in the most mundane of actions. Lift up a teacup and you are resisting the force of gravity exerted on the cup by an entire planet – Earth is trying to stop you, but it is no match for the power of your arm. The reason for this weakness is not known, and the puzzle is brought into stark relief by considering what happens when you lift up the cup. The force that operates your muscles and holds the atoms of your body together is electromagnetism. It is a million million million million million million times stronger than gravity, which is why you will always win in a battle against Earth. Even so, we have evolved to live on the surface of a planet with a particular gravitational field strength, and evolution doesn’t produce animals with muscles and skeletons that are stronger than they need to be. Biology rarely wastes precious resources! To demonstrate this, someone at the BBC thought that it would be amusing to see how a human body – mine – would respond if it were transported to a more massive planet.
MY FACE ON A MORE MASSIVE PLANET
The centrifuge at the Royal Netherlands Air Force physiology department was one of the first devices built to spin humans around at speed. Its purpose is to subject fighter pilots to the high G-forces they experience in combat, both for research and to teach them not to black out. As we have discussed, acceleration is indistinguishable from gravity, and spinning around is a good way to achieve high accelerations in a small space. In the case of the human centrifuge, the acceleration is directed towards the centre of the spinning arm, and is caused by the force (known as centripetal force) that acts on your body through the seat to keep you flying in a circle.
My first destination was the gas giant Neptune. Just over seventeen times more massive than Earth, you might expect that the force of gravity would be seventeen times stronger at its surface. However, Neptune’s radius is 3.89 times that of Earth at its Equator, so by using Newton’s law of gravitation, you’ll find that the surface gravity on Neptune is only around 14 per cent greater than Earth’s (written as 1.14G). Even with such a small change, I could feel a difference as I lifted up my arms, because they were 14 per cent heavier than normal.
Next up was Jupiter, which is 318 times more massive than Earth. With an equatorial radius 11.2 times greater, the surface gravity would be just over 2.5 times that of our planet. At 2.5G, my arms were 2.5 times heavier than normal, which made them difficult to lift. Apart from this, though, I wasn’t in too much discomfort. This all changed when my director decided to send me to exoplanet OGLE2 TR L9b in the constellation of Carina. Over four times the mass of Jupiter, but with a radius only 50 per cent bigger, OGLE2 TR L9b has a surface gravity four times that of Earth. At 4G, things got quite uncomfortable. I could still speak, but I couldn’t lift my arms. It was also quite difficult to breathe because my ribcage and everything else in my body was four times its normal weight, and my muscles aren’t used to working that hard.
It may look like a diabolical machine designed to assassinate James Bond and test his escapolgy skills, but this centrifuge at Cologne, Germany, is used to prepare astronauts and fighter pilots for very high G-forces.
© Roger Ressmeyer/CORBIS
We then decided to journey beyond OGLE and see how far I could go. As the G-force increased, things got uncomfortable. After a minute or so at 5G, the blood begins to drain from the head, because the heart finds it difficult to pump it up into the brain. This causes faintness and is accompanied by a slight but noticeable narrowing of vision. I had had enough just below 6G, when I was told that my face had been contorted into a funny enough shape to be amusing to the viewers. My job was done. Slowing down was probably more unpleasant than the high-G bit, because the senses are so confused that you feel as if you are tumbling forwards. Gus Grissom described this sensation in the post-flight report of the second manned Mercury mission on Liberty Bell 7, noting that when the main engines shut down after launch, reducing the G-force rapidly, he had to glance at his instruments to reassure himself that his spacecraft was not tumbling.
After my ride I chatted with an F16 pilot who had been subjected to a very fast acceleration and deceleration to 9G. (NATO requires all fighter pilots to be able to deal with this violent ride without passing out.) He told me the centrifuge is far worse than anything you feel in a fighter jet, and having flown in a Lightning and a Hunter, I concur. It’s the sustained nature of the G-force in the centrifuge that makes you feel odd; our bodies have not evolved to cope with the weak force of gravity at strengths much greater than those on Earth.
The body with the highest surface gravitational force in the Solar System is the Sun; with a mass 333,000 times that of our planet, it has a surface gravity over 28 times more powerful. The centrifuge cannot go that fast, because this would be a completely unsurvivable G-load.
To find still stronger gravitational fields we have to travel beyond our solar system and look for objects more exotic than mere stars. Our next stop is on one of the strangest worlds in the Universe – one once thought to be populated by aliens
This mosaic image, taken by NASA’s Hubble Space Telescope, shows the Crab Nebula, an expanding remnant of a star’s supernova explosion. Chinese astronomers recorded this violent event in July 1054, and so too did the people of the Chaco Canyon in New Mexico.
THE LAND OF LITTLE GREEN MEN
In 1967 postgraduate student Jocelyn Bell and her supervisor Anthony Hewish were using a newly completed radio telescope at Cambridge to search for quasars, the most luminous, powerful and energetic objects in the Universe. Quasars, or quasi-stellar radio sources, are now widely believed to be the small, compact regions around supermassive black holes at the centre of very young galaxies. A vast amount of radiation (in excess of the output of an entire galaxy of a trillion suns), is emitted as gas and dust spiral into the black hole.
As Bell and Hewish searched the data for these highly active, ancient galactic centres, they stumbled upon a very strange signal; a pulse that repeated every 1.3373 seconds precisely. It seemed to the Cambridge team to be almost impossible to believe that such a fast regular pulse could come from a natural source, so they named it LGM-1, which stands for Little Green Men.
At Chaco Canyon a small, unremarkable-looking painting has been discovered amongst the rocks which probably depicts the explosion of the star that created the Crab Nebula.
If they had discovered a radio beacon from an alien civilisation, you’d have heard about it. The source was entirely natural, as astronomer Sir Fred Hoyle realised immediately on hearing the announcement. However, they had made a new discovery, for which Hewish and fellow astronomer Martin Ryle (though inexplicably and controversially not Bell) received the Nobel Prize in Physics in 1974. Interestingly, though, Bell and Hewish were certainly not the first humans to see one of these wonders – they were beaten to it by an ancient civilisation that witnessed the birth of one almost a thousand years earlier.
A thousand years ago, between AD 900 and 1150, a great civilisation built a series of vast stone structures, known as the Great Houses, along the floor of the arid Chaco Canyon in New Mexico. These buildings remained the largest manmade structures in North America until the nineteenth century. The largest contains more than 700 rooms, many of which are still intact. It is known that these buildings, bizarrely, were not used as permanent residences, because they contain no traces of fires, cooking implements or animal bones. Instead, they seem to have been largely ceremonial; some archaeologists believe that the architecture of the canyon, including its precisely aligned and complex road system, were designed to symbolise and re-enforce the canyon’s position not only as the centre of local culture, commerce and religion, but also as the centre of the Universe. The roads and buildings in the canyon and surrounding areas certainly appear to be aligned with the compass points and, it has been suggested, with important moments in the yearly cycle of the Sun – such as the summer and winter solstices. It is difficult to know for sure whether all of the claimed alignments were intentional, but it is known that the Chacoan peoples were keen observers of the skies and possessed a very intricate and advanced cosmology, along with stories of the creation of the constellations and the Universe itself.
One particular site, hidden a mile or so from the main ruins, is the reason for our visit. I have known about it and wanted to come here since I was a little boy; I had no idea where Chaco Canyon was, but I knew about the existence of a small, unremarkable-looking painting on the underside of a rocky overhang next to a dry riverbed half a world away. It was Carl Sagan’s Cosmos, the book and television series, that introduced me to the wonders of the Universe. In the chapter ‘The Lives of the Stars’, there is a small black and white photo of the painting, showing three symbols: a handprint, a crescent moon and a bright star. It is known that the painting was made some time around AD 1054, and this was the year of one of the most spectacular astronomical events in recorded history. On 4 July AD 1054, a nearby star exploded. Chinese astronomers recorded the precise date, and the Chacoans would certainly have seen it too because the explosion was visible even in daylight for three weeks, and the fading new star remained visible to the naked eye at night for two years. It would have dominated the skies; a strange and magical sight, perhaps celebrated, perhaps feared; we will never know. We do know precisely where the explosion happened in the sky because its remnant is today one of the most famous and beautiful sights in the heavens: the Crab Nebula.
Every 18.5 years, the ruins of the Great Houses of Chaco Canyon and the beautiful rock faces that line the floor of this arid valley are the perfect place from which to see the Crab Nebula in all its glory.
Apart from the date of the painting, which is not precisely known, the best evidence that this does indeed chronicle the event that the Chinese astronomers recorded is the alignment of the painting. Every 18.5 years, the Moon and Earth will return to the same positions they were in on the nights around 4 July AD 1054. If on one of those rare evenings you go to Chaco Canyon and position yourself beside the painting, the Moon will pass by the position in the sky indicated by the hand print. At that moment, to the left of the Moon, exactly as depicted in the painting, you will see the Crab Nebula.
The explosion of 4 July 1054 was a supernova, the violent death of a massive star. It is expected that, on average, there should be around one supernova in our galaxy every century, and this one was almost uncomfortably close, at only 6,000 light years away. The Crab Nebula is the rapidly expanding remains of a star that was once around ten times the mass of our sun; after only a thousand years, the cloud of glowing gas is 11 light years across and expanding at 1,500 kilometres per second. At the heart of the glowing cloud sits the exposed stellar core, which is all that remains of a once-massive sun. It might not look like much when viewed with an optical telescope, but point a radio telescope at it and you will detect a radio signal, pulsing at a rate of precisely 30.2 times a second. It was an object like this that Jocelyn Bell and her colleagues observed in 1967. The Cambridge team weren’t listening to little green men, they were listening to the extraordinary sound of a rapidly rotating neutron star – called a pulsar.
Neutron stars are truly amongst the strangest worlds in the Universe; they are matter’s last stand against the relentless force of gravity. For most of a star’s life, the inward pull of gravity is balanced by the outward pressure caused by the energy released from the nuclear fusion reactions within its core. When the fuel runs out, the star explodes, leaving the core behind. But what prevents this stellar remnant from collapsing further under its own weight? The answer lies not in the physics of stars, but in the world of sub-atomic particles.
The answer to the question of what stops normal matter collapsing in on itself, surprisingly, was not proven until 1967, when physicists Freeman Dyson and Andrew Lenard showed that the stability of matter is down to a quantum mechanical effect called the Pauli exclusion principle. There are two types of particles in nature, which are distinguished by a property known as spin. The fundamental matter particles, such as electrons and quarks, and composite particles, such as protons and neutrons, have half-integer spin; these are known collectively as fermions. The fundamental force carrying particles such as photons have integer spin; these are known as bosons. Fermions have the important property that no two of them can occupy the same quantum state. Put more simply, but slightly less accurately, this means you can’t pile lots and lots of them into the same place. This is the reason why atoms are stable and chemistry happens. Electrons occupy distinct shells around the atomic nucleus, and as you add more and more electrons, they go into orbits further and further away from the nucleus. It is only the behaviour of the outermost electrons that determine the chemical properties of an element. Without the exclusion principle, all the electrons would crowd into the lowest possible orbit and there would be no complex chemical reactions and therefore no people.
Located around 6,000 light-years from Earth, the Crab Nebula is the remnant of a star that exploded as a supernova in AD 1054. This image, taken by NASA’s Hubble Space Telescope, shows the centre of the nebula in unprecedented detail.
The Crab Nebula is the rapidly expanding remains of a star that was once around ten times the mass of our sun; after only a thousand years, the cloud of glowing gas is 11 light years across and expanding at 1,500 kilometres per second.
If you try to press atoms together you force their electron clouds together until at some point you are asking all the electrons to occupy the same place (it is more correct to say the same quantum state). This is forbidden, and leads to an effective force that prevents you squashing the atoms together any further. This force is called electron degeneracy pressure, and it is very powerful. In Chapter 4, we will discuss white dwarf stars, the fading embers of suns left to slowly cool after nuclear fusion in their cores ceased. How did they continue to defy the crushing force of gravity? The answer is by electron degeneracy pressure, the dogged reluctance of electrons to being forced too closely together.
But what happens if you keep building more massive white dwarfs, increasing the gravitational force still further? The great Indian astrophysicist Subrahmanyan Chandrasekhar found the answer in one of the landmark calculations of the early years of quantum theory. In 1930, Chandrasekhar showed that electron degeneracy pressure can prevent the collapse of white dwarfs with masses up to 1.38 times the mass of our sun. For masses greater than this, the electrons won’t give in to gravity and move closer together, because they can’t. Instead, they give up and disappear.
This composite image of the Crab Nebula has X-ray (blue), and optical (red) images superimposed on it. It is an ever-expanding cloud of gas, and is perhaps the most famous and conspicuous of its kind.
They don’t, of course, vanish into thin air, because they carry properties such as electric charge which cannot be created or destroyed. Instead, the intense force of gravity makes it favourable for them to merge with the protons in the nuclei of the atoms to form neutrons. This is possible through the action of the weak nuclear force in the reverse of the process that turns protons into neutrons in the heart of our sun, allowing hydrogen to fuse into helium. For dying stars with masses above the Chandrasekhar limit, this is the only option, and the entire core turns into a dense ball of neutrons.
Most of the matter that makes up the world around us is empty space. A typical nucleus of a neutron star, which contains virtually all the mass, is around a hundred thousand times smaller in diameter than its atom; the rest is made up of the fizzing clouds of electrons, kept well away from each other by the exclusion principle. If the nucleus were the size of a pea, the atom would be a vast sphere around a hundred metres across, and this is all empty space. With the electrons gone, matter collapses to the density of the nucleus itself; all the space is squashed out of it by gravity, leaving an impossibly dense nuclear ball. A typical neutron star is around 1.4 times as massive as the Sun, just around the Chandrasekhar limit, crushed into a perfect sphere 20 kilometres (12 miles) across. Neutron star matter is so dense that just one sugar cube of it would weigh more than Mount Everest here on Earth.
This computer simulation of a pulsar shows the beams of radiation emitting from a spinning neutron star. First observed in 1967, the actual mechanism is still the subject of intense theoretical and experimental study.
The anatomy of neutron stars is still being intensely researched, but they are certainly far more complex than just a ball of neutrons. The surface gravity is of the order of 100,000,000,000G, which is little more than I experienced in the centrifuge. The surface is probably made up of a thin crust of iron and some lighter elements, but the density of neutrons increases as you burrow inwards, for the reasons explained above. Deep in the core, temperatures may be so great that more exotic forms of matter may exist; perhaps quark-gluon plasma, the exotic form of pre-nuclear matter that existed in the Universe a few millionths of a second after the Big Bang.
The unimaginable density and exotic structure aren’t the only fantastical feature of neutron stars; many of these worlds, including LGM1 and the neutron star at the heart of the Crab Nebula, have intense magnetic fields and spin very fast. The magnetic field lines, which resemble those of a bar magnet, get dragged around with the stars’ rotation, and if the magnetic axis is tilted with respect to the spin axis, this results in two high-energy beams of radiation sweeping around like lighthouse beams. The details of this mechanism are the subject of intense theoretical and experimental study. These are the pulses Bell and Hewitt observed in 1967; the stars are known as pulsars. The fastest known pulsars – millisecond pulsars – rotate over a thousand times every second. Imagine the violence of such a thing; a star the size of a city, a single atomic nucleus, spinning on its axis a thousand times every second.
In January 2004, astronomers using the Lovell Telescope at the Jodrell Bank Centre for Astrophysics, near Manchester, and the Parkes Radio Telescope, in Australia, announced the discovery of a double pulsar system, surely one of the most incredible of all the wonders of the Universe. The system is made up of two pulsars; one with a rotational period of 23 thousandths of a second, the other with a period of 2.8 seconds, orbiting around each other every 2.4 hours. The diameter of the orbit is so small that the whole system would comfortably fit inside our sun. Pulsars are incredibly accurate clocks, allowing astronomers to use the system to test Einstein’s theory of gravity in the most extreme conditions known. Imagine the intense warping and bending of space and time close to these two massive, spinning neutron stars. Remarkably, in perhaps the most powerful and beautiful test of any physical theory I know, the predictions of Einstein’s Theory of General Relativity, our best current theory of gravity, in the double pulsar system have been confirmed to an accuracy of better than 0.05 per cent. How majestic, how powerful, how wonderful is the human intellect that a man living at the turn of the twentieth century could devise a theory of gravity, inspired by thinking carefully about falling rocks and elevators, that is able to account so precisely for the motion of the most alien objects in the Universe in the most extreme known conditions. That is why I love physics
The Lovell Telescope at Jodrell Bank Centre for Astrophysics aided the exciting discovery of a double pulsar system, announced in January 2004.
MARTIN BOND / SCIENCE PHOTO LIBRARY
WHAT IS GRAVITY?
Mercury’s unpredictable orbit has caused real problems for scientists researching Newton’s theory of gravity within the Solar System.
When Newton first published his Law of Universal Gravitation in 1687 he transformed our understanding of the Universe. As we have seen, his simple mathematical formula is able to describe with unerring precision the motion of moons around planets, planets around the Sun, solar systems around galaxies, and galaxies around galaxies. Newton’s law is, however, only a model of gravity; it has nothing at all to say about how gravity actually is, and it certainly has nothing to say about a central mystery: why do all objects fall at the same rate in gravitational fields? This question can be posed in a different way by looking again at Newton’s famous equation:
This states that the gravitational force between two objects is proportional to the product of their masses – let’s say that m1 is the mass of Earth and m2 is the mass of a stone falling towards Earth. Now look at another of Newton’s equations: F = ma, which can be written with a bit of mathematical rearrangement as a = F/m. This is Newton’s Second Law of Motion, which describes how the stone accelerates if a force is applied to it. It says that the acceleration (a) of the stone is equal to the force you apply to it (F) divided by its mass (m). The reason why things fall at the same rate in a gravitational field, irrespective of their mass, is that the mass of the stone in these two equations (labelled m2 in the first equation and m in the second), are equal to each other. This means that when you work out the acceleration, the mass of the stone cancels out and you get an answer which only depends on the mass of Earth – the famous 9.81 m/s2. We said this earlier in the chapter in words: if you double the mass of something falling towards Earth, the gravitational force on it doubles, but so does the force needed to accelerate it. But there is a very important assumption here that has no justification at all, other than the fact that it works: why should these two masses be the same? Why should the so-called inertial mass – which appears in F = ma and tells you how difficult it is to accelerate something – have anything to do with the gravitational mass, which tells you how gravity acts on something? This is a very important question, and Newton had no answer to it.
Newton, then, provided a beautiful model for calculating how things move around under the action of the force of gravity, without actually saying what gravity is. He knew this, of course, and he famously said that gravity is the work of God. If a theory is able to account for every piece of observational evidence, however, it is very difficult to work out how replace it with a better one. This didn’t stop Albert Einstein, who thought very deeply about the equivalence of gravitational and inertial mass and the related equivalence between acceleration and the force of gravity. At the turn of the twentieth century, following his great success with the Special Theory of Relativity in 1905 (which included his famous equation E=mc2), Einstein began to search for a new theory of gravitation that might offer a deeper explanation for these profoundly interesting assumptions.
Although not specifically motivated by it, Einstein would certainly have known that there were problems with Newton’s theory, beyond the philosophical. The most unsettling of these was the distinctly problematic behaviour of a ball of rock that was located over 77 million kilometres (48 million miles) from Earth.
The planet Mercury has been a source of fascination for thousands of years. It is the nearest planet to the Sun and is tortured by the most extreme temperature variations in the Solar System. Due to its proximity to our star, Mercury is a difficult planet to observe from Earth, but occasionally the planets align such that Mercury passes directly across the face of the Sun as seen from Earth. These transits of Mercury are one of the great astronomical spectacles, occurring only 13 or 14 times every century. Mercury has the most eccentric orbit of any planet in the Solar System. At its closest, Mercury passes just 46 million kilometres (28 million miles) from the Sun; at its most distant it is over 69 million kilometres (42 million miles) away. This highly elliptical orbit means that the speed of the movement of this planet varies a lot during its orbit, which means in turn that very high-precision measurements were necessary to map its orbit and make predictions of its future transits. Throughout the seventeenth and eighteenth centuries, scientists would gather across the globe to watch the rare transits of Mercury. These scientists used Newton’s Law of Gravity to predict exactly when and where they could view the spectacle, but it became a source of scientific fascination and no little embarrassment when, time after time, Mercury didn’t appear on cue. The planet regularly crossed the Sun’s disc later than expected, sometimes by as much as several hours.
Mercury’s unusual orbit was a real problem, but because of the observational uncertainties it wasn’t until 1859 that the French astronomer Urbain Le Verrier proved that the details of Mercury’s orbit could not be completely explained by Newtonian gravity. To solve the problem, many astronomers reasoned there must be another planet orbiting between the Sun and Mercury. This planet had to be invisible to our telescopes, but it must also exert a gravitational force large enough to disturb Mercury’s orbit. Encouraged by the recent discovery of the planet Neptune, based on a similar anomaly in the orbit of Uranus, they named the ghost planet Vulcan
For decades astronomers searched and searched for Vulcan, but they never found it. The reason for this is that Vulcan doesn’t exist. The errors in the predictions in fact signalled something far more profound: Newton’s Theory of Universal Gravitation is not correct.
This image shows an artist’s impression of the hypothetical planet Vulcan, which was once believed to orbit in an asteroid belt closer to the Sun than Mercury. Vulcan was supposedly first sighted by amateur astronomer Lescarbault on 26 March 1859, but further observations were inconclusive and Vulcan was later proved to be a ghost planet.
SCIENCE PHOTO LIBRARY
EINSTEIN’S THEORY OF GENERAL RELATIVITY
German-born physicist Albert Einstein (left) created the famous Theory of General Relativity. British astrophysicist Sir Arthur Eddington (right), later put this theory to the test and confirmed its accuracy.
ROYAL ASTRONOMICAL SOCIETY / SCIENCE PHOTO LIBRARY
Einstein would have loved the Vomit Comet. The fact that the effects of gravity can be completely removed by falling freely in a gravitational field was, for him, the thought experiment that led to his theory of General Relativity. How wonderful it would have been for him to experience it as I did! The reason I say this is that, as I floated next to my little plastic Albert in the Vomit Comet, I understood very deeply why Einstein was so interested in freefall. The point is this; inside the plane, falling towards Earth, it is absolutely impossible to tell that you are moving. It is impossible to tell that you are near a planet. It is impossible to tell that, according to someone stood on the ground, you are accelerating at 9.81 m/s2 towards the ground. You are simply floating, along with everything else in the plane. I let some little drops of water out of a bottle and they floated in front of my face; the cameraman and director floated next to the water droplets, little plastic Albert and me. There was self-evidently no force acting on anything at all, otherwise things would have moved around.
And yet, from the point of view of someone on the ground, we were flying in a parabolic arc, moving forwards through the air at hundreds of miles an hour and accelerating violently towards the ground. The force of gravity is very much present in this description. Einstein’s theory takes the view that the two ways of looking at the Vomit Comet – from inside and outside – should be treated as equivalent. No one inside the plane or out has the right to claim that they are right and the other is wrong! If, inside the plane, there is no experiment you can do to prove that you are accelerating towards the ground, you are well within your rights to claim that you are not. Acceleration has cancelled out gravity. Of course, you could look out of the windows, but even then you could claim that Earth is accelerating up towards you and that you are simply floating. From this perspective, everyone on Earth feels a gravitational force pulling them onto the ground because they are being accelerated upwards at a rate of 9.81 m/s2. Acceleration is therefore equivalent to gravity; this is known as the equivalence principle, and it was very important to Einstein.
So what, then, is gravity? The explanation in Einstein’s theory is beautifully simple: gravity is the curvature of spacetime.
In technical language, Einstein would have defined the Vomit Comet, during its time in freefall, as an inertial frame of reference – which is to say that it can be legitimately considered to be at rest, with no forces acting on it.
The assertion that sitting in a falling aircraft should be considered as being absolutely equivalent to floating around in space, far beyond the gravitational pull of any planet or moon, can be used to explain why all objects fall at the same rate.
Why? Simply because there are two equally valid ways of looking at what is happening. From the point of view inside the plane, nothing at all is happening; everything is simply floating, untouched by any forces of any kind. If no forces are acting, then everything naturally stays where it is put. Shift outside the plane, however, and things appear different; everything is falling towards Earth, accelerating under the action of the force of gravity. But, very importantly, the reality of the situation cannot change depending on which point of view we adopt – everything has to behave in the same way in reality, irrespective of how you look at it. If plastic Albert and the globules of water float in front of my face when viewed from my vantage point inside the plane, then plastic Albert and the globules of water had better float in front of my face when viewed from a vantage point outside the plane. In other words, we had all better be accelerating towards the ground at exactly the same rate! Notice that we’ve made no assumptions about the equivalence between gravitational and inertial masses here; we’ve just said that a freely falling box in Earth’s gravitational field is indistinguishable from a freely falling box in space, or indeed any freely falling box anywhere in the Universe, around any planet, any star, or any moon.
So what, then, is gravity? The explanation in Einstein’s theory is beautifully simple: gravity is the curvature of spacetime. What is spacetime? Spacetime is the fabric of the Universe itself.
A good way to picture spacetime, and what it means to curve it, is to think about a simpler surface; the surface of Earth. Our planet has a two-dimensional surface, which is to say that you only need two numbers to identify any point on it: latitude and longitude. Earth’s surface is curved into a sphere, but you don’t need to know that to move around on it and navigate from place to place. The reason we can picture the curvature is that we are happy to think in three dimensions, so we can actually see that Earth’s surface is curved. But imagine that we were two-dimensional beings, confined to move on the surface of Earth with absolutely no concept of a third dimension. We would know nothing about up and down, only about latitude and longitude. It would be very difficult indeed for us to picture in our mind’s eye the curvature of our planet’s surface.
Now let’s extend our analogy to see how the curvature of something can give rise to a force. Imagine that a pair of two-dimensional friends are standing on the Equator and decide to take a journey due north. They decide to walk parallel to each other, with the intention of never bumping into each other. If they both keep walking, they will walk up parallel lines of longitude, and they will find that as they get closer and closer to the North Pole they will get closer and closer together. Eventually, when they reach the North Pole, they will bump into each other! As three-dimensional beings, we can see what happened; Earth’s surface is curved, so all the lines of longitude meet at the poles. However, from the perspective of our two-dimensional friends, even though they kept assiduously to their parallel lines they still were mysteriously drawn together. They may well conclude from this that a force was acting between them, attracting them towards one another. In Einstein’s theory, that force is gravity.
The complicated bit about Einstein’s Theory of General Relativity is that the surface we need to think about, spacetime, is not two-dimensional but four-dimensional. It is a mixture of the familiar three dimensions of space, plus an additional dimension of time mixed in. It will take us too far from our story to explore spacetime in detail, but it was found to be necessary by Einstein and others at the turn of the twentieth century to explain, in particular, the behaviour of light and the form of Maxwell’s equations that we met in Chapter 1. Suffice to say that the surface of our universe, on which we all live our lives, is four-dimensional. What Einstein showed is that the presence of matter and energy – in the form of stars, planets and moons– curves the surface of spacetime, distorting it into hills and valleys. His equations describe exactly what shape spacetime should be around any particular object, such as the Sun, for example, and they also describe how things move over the curved surface. And here is the key point: just like our two-dimensional friends, things move in straight lines; but just like our two-dimensional friends, this isn’t what it looks like if you don’t know that spacetime is curved. When you’re moving across the curved surface, it appears that a force is acting on you, distorting your path. One of the first things Einstein did with his new, geometric theory of gravity was to calculate what Mercury’s straight-line path through the curved spacetime around the Sun would look like to us, trapped on the surface of spacetime. To his delight, he found that Mercury would orbit the Sun, and in precisely the way that had been observed over the centuries of transit observations. Where Newton failed, Einstein succeeded.
Einstein had found a completely geometrical way of describing the force of gravity, and it is quite wonderfully elegant. Not only does it predict the orbit of Mercury, but it also provides a very appealing explanation for the equivalence principle. Why do all objects fall at the same rate in a gravitational field, irrespective of their mass or composition? Because the path they take has nothing to do with them at all – they are simply following straight-line paths through the curved spacetime.
Perhaps the most startling demonstration of this is the bending of light by gravity. Light has no mass, and so in Newton’s theory it shouldn’t be affected by gravity at all. However, according to Einstein’s theory, it doesn’t matter that it has no mass, it will still be following a straight line through the curved spacetime, so it will appear to follow exactly the same path as everything else. Let’s do a thought experiment to see how strange this is. Stand on the ground (on a very, very big planet – I’ll explain why I said this in a moment!) with a rock in one hand and a laser beam in the other. Point the laser beam horizontally, drop the rock and fire the laser. Which one hits the ground first? The answer is that they both hit the ground at the same time, because they both move through the same curved space. Light falls at the same rate in a gravitational field as everything else. Now, there is a caveat here. Why did I say a very very big planet? Because light travels at almost 300,000 kilometres per second, so if the rock takes a second to hit the ground, so will the light. But it will have flown 300,000 kilometres in the horizontal direction by the time it reaches the ground, and on Earth that would mean the surface of the planet had long since curved away! However, the principle still holds.
In the language of General Relativity, we might say that the presence of Earth bends spacetime near it such that time passes more slowly than it does far away.
As an interesting aside, what would happen if you fired the laser beam directly at the ground? Light must always travel at the same speed, it can’t speed up, so it will travel towards the ground at exactly 299,792,458 metres per second. But shouldn’t it accelerate at 9.81 m/s2 as it drops? No, it can’t, because it always travels at exactly 299,792,458 metres per second. So what happens? Well, the energy of the light can change, although the speed cannot, so the light gets shifted towards the blue end of the spectrum as it flies towards the ground and gains energy from its fall. That is to say that its wavelength gets shorter and its frequency increases. This is very interesting because the second is defined as the length of time it takes a fixed number of wavelengths of a particular colour of light to pass by an observer. Let’s say that you use the frequency of the laser beam held in your hand to synchronize a clock, then you fire the laser at the ground; when the light hits the ground, its frequency will have increased. This means that the peaks and troughs of the laser light beam are arriving more frequently than they did when they set off. So, from the point of view of someone on the ground, the clock above the ground will be running slightly fast. Is this true? Yes, it is. The effect is known as gravitational time dilation; gravity slows down time, so clocks close to the ground run slower than those in orbit. In the language of General Relativity, we might say that the presence of Earth bends spacetime near it such that time passes more slowly than it does far away. This is a very real effect and is one that has to be taken into account in the GPS satellite navigation system, which relies on precise timekeeping to measure distances. The GPS satellites orbit at an altitude of 20,000 kilometres (12,500 miles), which means that their clocks run faster than they do on the ground by 45 microseconds per day, because they are in a weaker gravitational field. The fact that they are moving relative to the ground also affects the rate of their clocks, and when everything is taken into account the timeshift reduces to 38 microseconds per day. This would be equivalent to a distance error of over 10 kilometres (6 miles) per day, which would make the system useless. So, every time we get into our cars and use satellite navigation, we are using Einstein’s theory of gravity in order to correctly ascertain our position on the surface of Earth.
As light has no mass, Newton’s theory states that it is not affected by gravity, although observation does infact show that it is.
To summarise, then, had Einstein experienced the Vomit Comet, he would have described it, during its time in freefall, as following a straight-line path through spacetime. As long as it continues on this path, the plane and its passengers will not feel the force of gravity at all; it is only when something stops the plane following its straight-line path through spacetime that a force is felt. If the plane didn’t stop itself falling, this obstacle would be the ground!
It is worth making a final brief aside here, which also serves to underline what we’ve just learnt. The experimental fact that triggered all this discussion is that the gravitational and inertial masses of objects are the same. Einstein provides a natural explanation for this: gravity is simply a result of the fact that there is such a thing as spacetime, and that it is curved, and that things move in straight lines through this curved spacetime. It is also possible to take a different view; there could be some deep reason why the gravitational and inertial masses of things are equal – a reason that we have yet to discover. The fact that they are equal allows us to build a geometric theory of gravity. In that case, Einstein’s theory might more properly be considered to be a model, in the same way that Newton’s theory is a model. At the moment we have no way of deciding between these two possibilities, but it’s worth being aware that they are both valid ways of looking at the situation.
Einstein’s Theory of General Relativity is rightly considered to be one of the great intellectual achievements of all time. It is conceptually elegant and probably the theory that physicists most often attach the word ‘beautiful’ to. Ultimately, though, it doesn’t matter how beautiful a theory is, the only thing that matters is that its predictions are in accord with our observations of the natural world. The orbit of Mercury is one such observation; the slowing down of time in gravitational fields is another; but to really test Einstein’s theory to the limit, we have to journey far out into space and visit the most exotic and massive objects in the known Universe – places where the force of gravity becomes exceptionally strong
This coloured X-ray image shows the area around the supermassive black hole, known as Sagittarius A*, which sits at the centre of the Milky Way Galaxy.
NASA / SCIENCE PHOTO LIBRARY
INTO THE DARKNESS
The success of Einstein’s Theory of General Relativity is one of the greatest of human achievements, and in my view it will be remembered as such for as long as there is anything worth calling a civilisation. But there is a final twist to the story of gravitation, because Einstein’s remarkable theory predicts its own demise.
The collapse of a neutron star is prevented by neutron degeneracy pressure. Neutrons are fermions, as are electrons, but because they are more massive than electrons, they can be packed much more tightly together before the Pauli exclusion principle steps in once more and forbids further contraction. Another stable staging post against gravity should be provided by quark degeneracy pressure, because quarks too are fermions, but ultimately, if the star is too massive gravity will overwhelm even these fantastically dense objects. It is believed that the limit above which no known law of physics can intervene to stop gravity is around three times the mass of the Sun. This is known as the Tolman-Oppenheimer-Volkoff limit. For the remnants of stars with masses beyond this limit, gravity will win.
In 1915, only one month after Einstein published the Theory of General Relativity, the physicist Karl Schwarzschild found a solution to Einstein’s equations which is now known as the Schwarzschild metric. The Schwarzschild metric describes the structure of spacetime around a perfectly spherical object. There are two interesting features of Schwarzschild’s spacetime: one occurs at a particular distance from the object, known as the Schwarzschild radius, but for distances less than the Schwarzschild radius, space and time are distorted in such a way that the entire future of anything that falls in will point inwards. This sounds weird, but remember that space and time are mixed up together in Einstein’s theory. In more technical language, we say that the future light cones inside the Schwarzschild radius all point towards the centre. This means that, as inexorably as we here on Earth march into the future, if you were to cross the line defined by the Schwarzschild radius, you would inexorably march inwards towards the object that is bending spacetime. There would be no escape, not even for light itself, in the same way that you cannot escape your future. This surface, defined by the Schwarzschild radius surrounding the object, is known as the event horizon. But what has happened to the object itself? This is the second interesting feature of the Schwarzschild metric. Let’s first think about the Sun. If you asked what the Schwarszchild radius for a star with the mass of the Sun is, it would be 3 kilometres (1 mile). This is inside the Sun! So there is no problem here, because you can’t get that close to the Sun without actually being inside it, at which point all the mass outside you doesn’t count any more.
But what about an object like a collapsing neutron star, getting smaller and smaller and denser and denser? What if you could have an object that was dense enough to have the mass of the Sun and yet be physically smaller than the Schwarszchild radius? It seems that there are such objects in the Universe; the stars for which even neutron degeneracy pressure will not suffice to resist the force of gravity. These objects are called black holes. At the very centre of the black hole, at r=0, the Schwarzschild metric has another surprise in store; the spacetime curvature becomes infinite. In other words, the gravitational field becomes infinite. This is known as a singularity. In physical theories, the existence of singularities signals the edge of the applicability of the theory; in simple language, there must be more to it! This has led many physicists to search for a new theory of gravity. Quantum theories of gravity such as string theory may be able to avoid the appearance of singularities, by effectively setting a minimum distance scale below which spacetime does not behave in the manner described by Einstein’s equations.
Black holes are fascinating objects; we don’t understand them, and yet we know they exist. They are of immense importance…the physics that lies inside the event horizon is undoubtedly fundamental.
As yet, we do not know whether any of these current theories are correct, or even if they are on the road to being correct, but what we do know is that black holes exist. At the centre of our galaxy, and possibly every galaxy in the Universe, there is believed to be a supermassive black hole. Astronomers believe this because of precise measurements of the orbit of a star known as S2. This star orbits around the intense source of radio waves known as Sagittarius A* that sits at the galactic centre. S2’s orbital period is just over 15 years, which makes it the fastest-known orbiting object, reaching speeds of up to 2 per cent of the speed of light. If the precise orbital path of an object is known, the mass of the thing it is orbiting can be calculated, and the mass of Sagittarius A* is enormous – 4.1 million times the mass of our Sun. Since the star S2 has a closest approach to the object of only 17 light hours, it is known that Saggitarus A* must be smaller than this, otherwise S2 would literally bump into it. The only known way of cramming 4.1 million times the mass of the Sun into a space less than 17 light hours across is as a black hole, which is why astronomers are so confident that a giant black hole sits at the centre of the Milky Way. These observations have recently been confirmed and refined by studying a further 27 stars, known as the S-stars, all with orbits taking them very close to Sagittarius A*.
This artist’s impression helps us to visualise the mysterious objects in space that are black holes.
Black holes are fascinating objects; we don’t understand them, and yet we know they exist. They are of immense importance, because despite the fact that we will never encounter one directly, the physics that lies inside the event horizon is undoubtedly fundamental. These are objects that will require a new theory of gravity, indeed a new theory of space and time, to describe. One of the holy grails of observational astronomy is to find a pulsar orbiting around a black hole. Such a system surely exists somewhere, and to be able to observe the behaviour of one of these massive cosmic clocks in the intensely curved spacetime close to a black hole would surely test Einstein’s Theory of General Relativity to its limit. It may even, if we are lucky, reveal flaws that point us towards a new theory
THE ANATOMY OF A BLACK HOLE
For all their mystery, we do know that black holes exist. The idea of a body so massive that even light could not escape its grip was first suggested in the eighteenth century, and today we now know that there is not only a black hole at the centre of our galaxy, but also possibly in the centre of every galaxy. We may never directly see one, but the secrets they contain may one day help us answer some of the most fundamental questions in the Universe.
Nathalie Lees © HarperCollins