Copernicus’s model wasn’t convincing to many astronomers and natural philosophers of the day. It’s revealing to read a criticism from the greatest observational astronomer of the age, Tycho Brahe: ‘… such a fast motion could not belong to the Earth, a body very heavy and dense and opaque, but rather belongs to the sky itself whose form and subtle and constant matter are better suited to a perpetual motion, however fast.’
This depiction of Copernicus’ heliocentric system of the Universe shows the Sun, the orbits of the planets and the firmament of the fixed stars.
Here again we see how difficult it is to accept that we live on a moving planet when we feel so powerfully that we are standing still.
We don’t need to resort to the laboratory to observe a direct physical effect of the Earth’s rotation because we have spacecraft and weather.
Almost 150 years after Copernicus, the Italian priest and astronomer Giovanni Riccioli offered a more scientific objection to Copernicus’s spinning Earth than the rather philosophical statement that it just doesn’t feel right. He carried out a rather beautiful analysis of the motion of projectiles on a spinning planet in Almagestum Novum (New Almagest), published in 1651, when the young Isaac Newton was just 9 years old. Riccioli was concerned with laying out the evidence for and against the motion of the Earth, which he did in 77 carefully constructed arguments. Argument number 18 is an analysis of the motion of a cannonball on a spinning planet. Riccioli argued that a cannon ball fired northwards (in the northern hemisphere) should follow a flight path that is distorted by the spin of the Earth. Here is what he said:
‘If a ball is fired along a Meridian toward the pole (rather than toward the East or West), diurnal motion will cause the ball to be carried off [that is, the trajectory of the ball will be deflected], all things being equal: for on parallels of latitude nearer the poles, the ground moves more slowly, whereas on parallels nearer the equator, the ground moves more rapidly.’
Riccioli could find no experimental evidence to show that cannonballs are deflected as they fly north, so he concluded that the Earth is not spinning. It’s probably more correct to say that he reinforced his own prejudice that the Earth isn’t spinning. But that’s not the point. Riccioli didn’t have access to good enough data to see the effect of Earth’s spin on a flying cannonball, which is deflected in flight because of the Earth’s spin. Riccioli didn’t stop there, though. He also proposed that the same effect should be seen for objects falling vertically to the ground, a point he made poetically in argument number 10 of New Almagest:
This grainy black-and-white image occupies an historic place in the archives of meteorology. Taken by NASA’s TIROS-3 satellite, it is the first time a hurricane was discovered using satellite imagery and is one of the first photographs of a tropical cyclone from space.
‘If an angel were to let fall a metal sphere of great weight hung to a chain, while holding the other end of the chain immobile, that chain by the force of the sphere might be extended to its full length perpendicularly toward the Earth. But following the Copernicans, it ought to curve obliquely toward the east.’
Right again, and with plenty of towers to choose from in northern Italy, Riccioli climbed to the top of the Torre degli Asinelli in Bologna and dropped some weights. He searched for a deflection in vain, which again confirmed his belief that the Earth is not spinning. His problem, again, was not his theoretical prediction (which is spot on), but the quality of his experimental data.
A seventeenth-century illustration of a compound microscope as used by English natural philosopher Robert Hooke (1635–1703).
For those attempting to find Earthly experimental proof for the Copernican view of a Sun-centred Solar System, Riccioli’s experiment was a prime target. Writing in 1679, Newton shared ‘a fansy of my own about discovering the Earth’s diurnal motion’ with his contemporary and rival physicist, Robert Hooke. Hooke decided to attempt the experiment, culminating in a demonstration at the Royal Society on 22 January 1680. With such slight margins – a modern calculation of the deflection for an 8-metre drop is 0.3mm – the experiment failed and the records of the Royal Society give no indication that Hooke ever attempted it again.
To this day, drop-experiments such as the Torre degli Asinelli experiment proposed by Riccioli are reasonably difficult to perform, although certainly not impossible1, but we don’t need to resort to the laboratory to observe a direct physical effect of the Earth’s rotation because we have spacecraft and weather.
The grainy black-and-white image shown opposite occupies an historic place in the archives of meteorology. The TIROS satellites were little spinning drums, just over a metre in diameter, and carried two wide-angled television cameras, a tape recorder for the images and a 2-watt transmitter. On 10 September 1961, TIROS-3 peered down onto the Atlantic Ocean from low Earth orbit and observed the birth of Hurricane Esther hours before its formation was spotted back on Earth.
Half a century later, the quality of space-based weather imagery is extraordinary. High-definition images allow us to keep track of the surface of the Earth and the formation of major weather systems in real time. They are ubiquitous, and because of this we know what storm systems look like. The most obvious feature is that they rotate, and the reason for this is the rotation of the Earth, as Riccioli predicted. The force that acts on weather systems causing them to rotate is the Coriolis Force, named after the French mathematician Gaspard-Gustave de Coriolis, who first published a full mathematical treatment as part of an analysis of the physics of water wheels in 1835.
Illustration from Riccioli’s 1651 New Almagest showing the effect a rotating Earth should have on projectiles. Riccioli’s explanation for expecting a curved path is as follows: The more southerly cannon is moving faster relative to the more northerly target (E). Because the ground is moving more slowly at the target (E), it will follow a curved path and land to the right of the target at (G) instead. No such effect should be seen if the cannon is fired in the direction of the Earth’s spin at an easterly target (C). This is because in this case the cannon and the target are both travelling at the same speed relative to each other and so the cannonball will fly as if the Earth is completely still. This last part of Riccioli’s argument is incorrect, but he was on the right track.
The Coriolis Force is known as a ‘fictitious force’, although its effects on weather systems are very real. It’s called a fictitious force because it’s not a fundamental force of Nature. It’s not gravity, it’s not electromagnetism, and it’s not the strong or weak nuclear force. Rather, its origin lies in the fact that the Earth’s surface is NOT an inertial reference frame. Why is the Earth not an inertial frame? Because if we stand on the surface of the Earth we are constantly changing direction as we spin around in a circle once every day. We are certainly not moving in a straight line and we are therefore not in an inertial reference frame.
How might this lead to a force ‘magically’ appearing? Imagine that you’re sitting on a train moving at constant speed and you decide to put a cricket ball on the table in front of you. It will stay exactly where you put it. This is as it should be, because the train is an inertial reference frame and there is no experiment we can do to tell whether or not we are moving. We must all have had the experience of sitting peacefully in a train carriage, rolling gently through a station at constant speed and getting the slightly dizzying feeling that the station is drifting by. This isn’t an error of perception; you are absolutely entitled to claim that you aren’t moving and the platform is. If the train accelerates quickly out of the station, however, the ball will roll towards you. How should you interpret what is happening?
Newton’s second law of motion states that F = ma. From your perspective on the train, you’ll see the ball accelerate towards you on the table, and you will describe the acceleration as being due to a force acting on the ball. This force is a fictitious force. It appears because you are no longer in an inertial frame of reference because the train is accelerating. This
might appear to be a subtle point, but it provides a way of determining experimentally whether or not you are in an inertial frame. If things in your world deviate from their state of rest or uniform motion in a straight line and the cause isn’t one of the fundamental forces of nature, then you can deduce that you are not in an inertial frame, and here is where the abstract becomes concrete. This fictitious force is very real from the point of view of the person sitting in the accelerating frame. If you were resting your face on the table when the train started accelerating, the cricket ball would hit you in the head, and there is nothing fictitious about a broken nose. The Coriolis Force that drives the great storm systems on the surface of our planet is another very powerful example of a fictitious force.
The origin of the Coriolis Force is not as simple as the accelerating train, or for that matter as simple as Riccioli’s description in his cannonball experiment; this is why it isn’t called the Riccioli Force. Here is the explanation.
Trajectory of a ball rolled on a rotating disc.
The Earth is a three-dimensional spherical object, which complicates things, so let’s consider what happens to an object that moves around on a flat spinning disc. The arguments will be the same and easier to visualise. Imagine the rotating disc from two different perspectives. One will be that of an observer watching everything from afar – dare we say it, in an inertial frame of reference. (There is a drinking game here somewhere.) The other will be that of an observer sitting at the edge of the rotating disc, whizzing around with it. This is our situation as we sit on the surface of our spinning planet.
Now imagine that the rotating observer decides to throw a ball directly towards the centre of the disc. From their perspective, the ball sets off happily in the direction in which it is thrown but immediately starts to curve away in the direction of rotation. What is happening? It’s easiest to see from the perspective of the observer watching from afar (see above).
From the distant perspective, the ball is flying around in a circle with the disc, before it is thrown inwards. When it’s thrown, it hangs on to the initial speed it had in the direction of rotation. This is the law of inertia again. Nobody pushed on the ball in the direction of the spin of the disc, which is known as the tangential direction, so it simply keeps on going. As it rolls inwards, however, it finds itself travelling too fast in the tangential direction for the inner parts of the disc. This is because the points closer to the centre have less far to travel to circle once around, so they must be travelling more slowly than the points further out. As a result, the ball gets ahead of the disc and curves away in the direction of rotation. From the distant observer’s perspective, there is no force acting on the ball. The curved path is explained purely in terms of the rotation of the disc.
From the rotating observer’s perspective, however, there appears to be a force acting on the ball in accord with Newton’s first law, because it doesn’t travel in a straight line relative to them. This is the Coriolis Force. It acts at right angles to the direction of motion of the ball, deflecting it onto a curved path. On the surface of the Earth, the Coriolis Force always pushes objects moving in the northern hemisphere to the right, and objects in the southern hemisphere to the left, if we view the Earth as being orientated with the North Pole at the top. At the Equator, the Coriolis Force pushes neither to the right nor the left, although it does try to lift an object gently off the surface! Such is the complexity of a rotating three-dimensional sphere rather than a disc, but the principle is the same.
We can now see why storm systems rotate the way they do on the surface of the Earth. Large bodies of air do not move in straight lines because of the action of the Coriolis Force. A cyclone is a region of low pressure. The higher-pressure air around it will fall inwards to try to equalise the pressure. In the northern hemisphere, the moving air will experience a Coriolis Force to the right as viewed from above, and therefore will rotate in an anti-clockwise direction around the low-pressure area. In the southern hemisphere, a cyclone will rotate in a clockwise direction because the inward-falling air is deflected to the left. This is why the hurricanes that form every year in the Atlantic which threaten the Caribbean Islands and the southeastern states of America always rotate anti-clockwise, whereas the tropical cyclones (the name for a hurricane that forms in the southern hemisphere) that batter the Pacific Islands are always rotating in the opposite direction.
High-definition images of major weather systems allow us to keep track of their formation in real time and be able to anticipate, to some degree, their impact on the Earth’s surface. This NASA photograph, taken from the Space Shuttle Atlantis in November 1994, shows Hurricane ‘Florence’ imaged from 165 nautical miles above the Earth.
For anti-cyclones, the opposite is true. The air flows outwards from a high-pressure central region, and the deflection to the right by the Coriolis Force in the northern hemisphere induces a clockwise rotation.
We can clearly see a direct physical effect of the Earth’s rotation through certain weather events, in particular cyclones, which rotate anti-clockwise in the northern hemisphere and clockwise in the southern hemisphere.
As well as creating the distinctive spirals of storm systems as seen from space, the Coriolis Force also increases the strength of the storms. The stronger the deflection of the air current around a high-pressure system, the faster it will rotate. This is one reason why the most powerful storms in the Solar System occur on faster-spinning planets. Jupiter is not only the most massive planet, it is also the fastest rotating, spinning once on its axis approximately every 9.8 hours. The most recognisable storm system in the Solar System is the Great Red Spot, a spiralling storm that has raged on the gas giant for at least two hundred years, but probably far longer. Famously large enough to swallow the Earth whole, it is 20,000 kilometres long, 12,000 kilometres wide and boasts wind speeds of up to 700km/hr. The Coriolis Force generated by the size and rotation speed of Jupiter is a significant contributing factor to the power and size of the Great Red Spot and the many other storm systems that rage through Jupiter’s swirling clouds. The Great Red Spot is an anti-cyclonic (high-pressure) storm in Jupiter’s southern hemisphere and, just as here on Earth, it therefore rotates in an anti-clockwise direction. The laws of Nature are universal.
The most recognisable storm system in the Solar System is the Great Red Spot, a spiralling storm that has raged on the gas giant for at least two hundred years, but probably far longer. Famously large enough to swallow the Earth whole, it is 20,000 kilometres long, 12,000 kilometres wide and boasts wind speeds of up to 700km/hr.
The reason for the rotating storms on Earth and across the Solar System is interesting in itself, but there is a deeper reason why we’ve spent time studying the Coriolis Force. It appears in our description of the physics when we try to explain a real-world natural phenomenon from different perspectives – that is to say from different frames of reference. Hold that thought, because we’ll come back to it.
Recall that we began this chapter musing about the nature of space and time, and hinting at the rather wonderful suggestion that events in our past may have an existence beyond our memories. This chapter is a wandering adventure in a sense; our explanations of natural phenomena will serve to illustrate something we need to know on the road to relativity. Let us explain one more everyday physical phenomenon that requires us to jump between different frames of reference to understand: a classic problem in physics – the ocean tides.
Life on an orbiting, spinning planet
The tides
The ebb and flow of the tides creates a dramatic, recurring and rapid transformation of Earth’s coastline. With a little patience and a comfortable deckchair you can watch the landscape change before your eyes. Geological in timescale it isn’t. The Bay of Fundy on Canada’s east coast holds the record for the greatest tidal range: 56 feet, as measured by the Canadian Hydrographic Service at Burntcoat Head. I am delighted to leave this measurement in feet as a celebration of cultural diversit
y.
The origin of the tides is an ancient puzzle. The connection between the tides and the lunar cycle has been known for well over 2000 years, but the recognition of patterns and the prediction of high, low and spring tides does not require an understanding of the underlying mechanism. If all you want to do is sail, you don’t need to know why; you just need to know when. With the emergence of a heliocentric model of the Solar System in the sixteenth century, the understanding of the origin of the tides received a great deal of attention from the astronomers of the day because it presented an Earth-bound phenomenon that appeared to be connected to the motion of Earth, Moon and Sun. Johannes Kepler asserted that the tides were created by a force of attraction exerted by the Moon on the Earth’s oceans, but was unable to provide a mechanism to explain the force. Galileo disagreed, and in an increasingly fractious dialogue proposed the counter-argument that the tides are a result of the Earth’s rotation and revolution around the Sun: ‘Among all the great men who have philosophised about this remarkable effect, I am more astonished at Kepler than at any other. Despite his open and acute mind, and though he has at his fingertips the motions attributed to the Earth, he nevertheless lent his ear and his assent to the Moon’s dominion over the waters, to occult properties, and to such puerilities.’
Forces of Nature Page 10
