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.
* * *
© NASA/Corbis
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.
NASA
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.
Caltech
* * *
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-scient
ific 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 approx
imately 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.
Wonders of the Universe Page 14
