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
NASA
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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.
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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.
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ESA / DLR / FU BERLIN (G.NEUKUM) / SCIENCE PHOTO LIBRARY
THE GEOID
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.
NASA
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!
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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.
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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.
Wonders of the Universe Page 15