Whose Motion Is It, Really?

You feel none of it. There is no wind from it, no lean, no vibration, and your tea sits level in its cup.

That is worth pausing on, because we are good at detecting motion. A car taking a corner at twenty miles an hour presses you against the door. Yet the same body, riding a planet at a thousand miles an hour, reports nothing at all.

For most of recorded history this was treated as evidence, and the reasoning behind it was physical rather than superstitious. Suppose the Earth spins eastward. Drop a stone from a tall tower. While the stone is in the air the tower is being carried east along with the turning ground — a very long way, if the ground moves as fast as the claim requires. The stone is in the air, attached to nothing. It should be left behind, and land far to the west of the tower.

The same argument covers everything that leaves the ground. Clouds and birds are not fixed to the surface, so they should stream away westward and never catch up. An east wind should blow permanently, at enormous speed, everywhere. An arrow shot straight up should come down a long way from the archer.

None of that happens. The stone lands at the foot of the tower, the arrow returns to the archer, birds fly wherever they please, and the morning air can be completely still. Every check available to a careful person in 1500 pointed the same way, and the conclusion drawn from those checks was that the Earth stands still.

This essay is about how that conclusion was overturned, which took nearly three centuries. The more useful thing it produced along the way was a sharper question. "Is the Earth moving?" turns out to be three questions with three different answers, and most of the confusion in this subject comes from running them together.

The people who held the Earth still were the most careful observers of their age, and the system they built was a working scientific instrument.

By the second century Ptolemy had assembled a machine of circles turning on circles whose purpose went beyond explaining the planets' behaviour in outline: it was to give their positions accurately far into the future — and it did, with a flexibility that let it be adjusted to fit whatever the sky showed.

The motionless Earth was not an extra article of faith attached to that machine. It came out of the physics of the time. In that physics, heavy material moves naturally towards the centre of the universe. The Earth is an enormous quantity of heavy material, so the Earth is simply what has collected at that centre and can fall no further. One idea about matter delivered both the Earth's position and its stillness at once.

That is what any challenger had to beat. A new arrangement of the heavens would have to give a positive reason to prefer it, since the old one already predicted well. And it would have to answer the stone and the tower, because the objections were sound arguments given the physics available.

In 1543 a book appeared that took on the first task and left the second almost untouched. The gap stayed open for the next ninety years.

The book was by Nicolaus Copernicus, a churchman who had spent his working life on astronomy. It proposed that the Sun stands still near the centre, that the Earth turns once a day, and that the Earth and the planets travel around the Sun.

The telescope was still more than sixty years away, so Copernicus had the same sky everyone else had. What he brought to it was an argument about what observation can deliver, and it is the foundation of everything that follows, so it is worth taking slowly.

Start with what you actually see when you see something move. You see its position change relative to something else — a car against a tree, a bird against a rooftop. Every observation of motion is a comparison between two things. There is no separate sensation of motion itself arriving alongside the comparison.

Now suppose you and everything in your view are being carried along together, perfectly in step. Every relative position stays exactly as it was, because everything moved by the same amount. The observation you would use to detect the motion returns nothing, and it returns nothing no matter how fast the shared motion is.

Apply that to the night sky. The stars sweep from east to west once a day. Two arrangements produce that appearance: the heavens turning westward above a stationary Earth, or the Earth turning eastward beneath stationary heavens. In terms of relative positions, which is all the eye reports, the two are indistinguishable. Watching the sky more carefully cannot separate them, and no improvement in eyesight or instruments would help, because the two accounts predict identical appearances.

The choice therefore has to rest on other grounds, and Copernicus offered several. One is a question of proportion: it is a smaller demand to turn one planet than to turn the entire heavens once a day. The others come from putting the Earth among the planets, where a set of facts that Ptolemy had to build in separately start to follow from the arrangement itself.

The clearest case is the strangest behaviour in the sky. Mars normally creeps eastward against the stars from night to night, but every couple of years it slows, halts, travels backwards for some weeks, halts again, and resumes. Ptolemy reproduced this with additional circles fitted for the purpose. In the Sun-centred arrangement it follows from the Earth's own motion: the Earth runs on an inner and faster track, and each time it overtakes Mars, Mars appears to slide backwards for a while — the same appearance a slower car presents when you overtake it on a motorway, though that car never stops going forward. The timing then comes out on its own. The backward stretch has to occur when the Earth passes between Mars and the Sun, and that is exactly when it is observed.

Other facts fall out the same way. Mercury and Venus are never seen far from the Sun, which is forced if their orbits lie inside the Earth's. And once the Earth is one planet among several, the observations fix the size of every orbit relative to the Earth's, with the more distant planets working out slower in an unbroken order. In Ptolemy's astronomy each planet carried its own independent machinery and could be rescaled without disturbing the others. In the new arrangement the parts are locked together.

There are limits on all this, and they matter more than the usual telling admits.

The first is that the tidy diagram of circles around the Sun is not the system Copernicus actually published. That simple picture does not fit the observational record. To match the data as well as Ptolemy did, he had to move the centre of the Earth's orbit away from the Sun, then use that displaced centre rather than the Sun itself as the reference for the other orbits, so that the planetary paths are centred on neither. He kept small epicycles. He added a circle turning once in about 3,400 years, and another running over 53,000 years, to handle slow changes in the Earth's orbit. The gain was in coherence, not in simplicity of machinery.

The second is that the new system predicted no better than the old one. On accuracy the two were level, and for decades astronomers used the new tables without accepting the claim behind them. Meanwhile the original objection stood exactly where it had been. If the Earth is doing all of this, why does a dropped stone land at the foot of the tower?

Copernicus gave that objection a few pages and moved on; the developed answer came ninety years later, and it is the subject of the next section.

The developed answer was published in 1632, in a book Galileo wrote as a conversation between three men: one defending the older astronomy, one arguing for the moving Earth, and a third presented as neutral, whose part is to say which way his mind is drawn. The form let each case be stated at full strength.

The argument was not new in 1632. Several of its points had been anticipated in the fourteenth century by Buridan and Oresme, and Oresme in particular had considered a rotating Earth seriously; Copernicus then made the relativity of observed motion central to his case, with the image of two ships in harbour, one pulling away, and a man aboard unable to tell which is moving without a look at the land. What 1632 supplied was the fully developed demonstration.

Shut yourself in a cabin below the deck of a large ship, with no view outside. The sea is calm and the ship is moving steadily, without rocking, turning, speeding up or slowing down. Now run experiments. Jump straight up and you land where you took off. Throw something to someone across the cabin and it takes the same effort in every direction. Water dripping from a container falls straight into a vessel underneath it. Insects fly about the cabin equally easily in all directions.

Every result matches what you get with the ship tied up at the dock. The reason is that everything in the cabin shares the ship's motion, the air included, and keeps sharing it. Since each object's motion relative to every other object in the room is unchanged, and relative motion is what experiments inside the room can measure, the ship's speed makes no difference to any of them.

The same reasoning handles the mast. Drop a stone from the masthead of a moving ship and it lands at the foot of the mast rather than in the water behind. The stone had been travelling forward with the ship for the whole voyage, and releasing it does not remove that forward motion. On the way down it keeps moving forward while gravity adds a downward motion, and the two proceed without interfering. Someone on deck, sharing the forward motion, sees only the part they do not share, which is the fall.

Now the tower. On a rotating Earth, a stone held at a tower's top is not somehow exempt from the rotation, waiting to be left behind. It has been carried eastward by the tower, the ground and the air for its entire existence. Released, it keeps that eastward motion while it falls and comes down at the foot of the tower — to the eye, exactly where a stationary Earth would put it. The large westward lag the old argument demanded does not appear, on either account.

That is the part usually lost. To the precision of an unaided observer, both accounts give the same landing point, so where the stone appears to land carries no information about which of them is right. The strongest argument for a motionless Earth had been resting on an observation that could not discriminate between the two at the scale anyone was looking.

One qualification, which the essay will collect later. A rotating Earth does predict a difference — a very small one, in the opposite direction from the one the ancients expected. The top of a tower travels a slightly larger daily circle than its base, so a stone released there carries a little more eastward speed than the ground it falls to, and should land a fraction ahead of the foot rather than behind it. That difference is real, it was eventually measured, and it is one of the three ways rotation was caught. It plays no part here because it is far below anything the tower argument was built on, and because the ancient prediction was for a large lag the other way.

There is a further problem with the old argument. It described the falling stone as travelling "straight down" and treated that as a plain observation. Straight down relative to what? Relative to the tower and the ground — which is precisely the thing whose stillness was supposed to be under test. Watched from off the Earth, the same stone traces a long curve. Describing the fall as straight already assumes the answer.

Some details of the history are worth keeping, because they are more interesting than the version usually told. Galileo never dropped a stone from the mast of a moving ship. In the book, asked directly whether he has performed the experiment, his spokesman says he has not, and that he does not need to, because the result follows necessarily from the reasoning. He was right, and Gassendi later carried out such experiments from moving ships and carriages, but what stands on Galileo's page is an argument. And the book states its own result more carefully than its readers usually do. At the close of the discussion the Aristotelian character sums up that the arguments for a stationary Earth have been shown to prove nothing, while no proof has been given that the Earth moves — and Galileo's spokesman agrees with him. An objection can be demolished without the opposite being established, and that is where the argument stood in 1632. Establishing it would require some measurement on which the two accounts actually differ, and the rest of this essay follows that search.

The cabin result is permanent, and stating it precisely matters more here than anywhere else in the essay, because almost every popular version overstates it.

Both Galileo and, later, Newton were careful to specify the case. The ship is specified as either standing still or running forward along a straight course, neither turning nor swaying about. What holds for a ship like that is this: no experiment performed inside the cabin can distinguish it from a cabin at rest. Uniform motion in a straight line, shared by the whole system, produces no internal effect for an internal experiment to find.

Some vocabulary makes the rest of the essay easier. A reference body is just the thing you choose to measure positions against — the cabin, the platform, the ground, the Sun. Any object will do, and the choice is yours. Among all those possible choices, a particular family behaves especially simply: those moving uniformly in a straight line, without rotation. These are the ones the cabin result is about, and they are the ones later physics singles out.

Now the fence, and it has two rails.

The motion has to be shared. The cabin works because it carries its own air along with everything else. Out on the open deck, in the wind, the situation is different, and Galileo says so.

The motion has to be uniform, in a straight line, without rotation. This rules out more than it appears to. Rotation is not uniform straight-line motion: a point on a spinning globe is continually changing direction. And travelling around the Sun is not uniform straight-line motion either, for the same reason — an orbit is a curve, and moving along a curve means the direction of travel keeps changing.

So the cabin argument, applied within its stated conditions, settles one of our three questions and leaves two open. The Earth's rotation and the Earth's orbit are both outside its scope. Whether either of them can be detected, and how, has to be worked out separately.

Of the two, rotation is much the easier, and it is where the next section begins.

Rotation is different because it involves continuous change of direction, and change of motion has consequences that uniform motion does not.

Take a merry-go-round turning at a constant rate. Standing on it, you have to lean inward and hold on, and you can feel the effort. Nothing of the sort is needed on a smoothly moving train. In the standard Newtonian account, what is happening is that some force — the handrail, friction, the tension in a cord — is pulling you towards the centre of the circle, because travelling in a circle requires a centre-directed force at every instant. The outward pull you feel is the sensation of your body being turned by that force, described from the turning platform you are standing on. The centre-directed force is what does the physical work; the outward description belongs to the rotating viewpoint.

The Earth turns far more gently than a merry-go-round: once a day rather than once a second. The consequences are correspondingly small, but a planet is large, and small effects on something that large become measurable. Three of them settled the question, and they are not all the same kind of test, so it is worth saying what each one needs.

The planet is the wrong shape. In the Newtonian account, the material of a spinning planet requires a centre-directed force to keep it turning with the rest, and the available force falls slightly short near the equator, where the daily circle is largest. The result is that a spinning planet should not be a sphere: it should be wider across the equator than from pole to pole. Newton predicted this and pointed to Jupiter, which is visibly flattened through a telescope.

Testing it on the Earth is a surveying problem. Travel due north and the pole star climbs; the distance you must cover to raise it by one degree measures how sharply the ground is curving beneath you. On a true sphere that distance is the same everywhere, and on a flattened planet it is longer near the poles.

This became one of the great scientific disputes of the century, because the first measurements came out the other way. French surveys indicated a planet stretched at the poles rather than flattened, and in 1734 Johann Bernoulli published a proof from the rival Cartesian physics that stretched was what it should be. Newton's whole system was at stake. The objection to the French result was that all of it had been taken within France, over too small a range of latitude to be decisive, so in 1736 two expeditions went out to measure a degree at the extremes — one to Lapland, one to what is now Ecuador. Maupertuis led the Lapland party and returned in 1737. Comparing his Lapland degree with the Paris degree, he found the northern one longer, which is what a flattened planet gives. Nobody from the South American party was back until the mid-1740s, and their measurements, together with a re-surveyed Paris degree, confirmed it.

The equatorial radius exceeds the polar radius by about thirteen miles. Newton had predicted seventeen, so the agreement was directional rather than exact. And the historical weight of the result sat elsewhere: by the 1730s the Earth's rotation was not seriously disputed, so the flattened shape counted for more as a victory of Newtonian over Cartesian physics than as news about the spin. It is the first direct physical evidence of the rotation all the same. Note what kind of evidence it is, though. It requires no sight of the sky, but it cannot be obtained in a single room — it takes expeditions to opposite ends of the planet.

Falling bodies land slightly to the east. Here the tower returns with the opposite verdict. The top of a tower stands further from the Earth's axis than its base, so in each daily turn the top travels a slightly larger circle in the same time, which means it is moving slightly faster eastward than the ground below. A stone released at the top keeps the speed it had, by the same reasoning as the ship's mast. The ground it is falling towards is moving slightly slower. The stone should therefore land not quite at the foot, but a little to the east.

The predicted amount is small enough to have hidden inside experimental error for a century. Balls were dropped down the Asinelli tower at Bologna, and down the tower of St Michael's at Hamburg; in 1831 Ferdinand Reich sent a hundred and six balls down a mineshaft at Freiburg. The most careful attempt came in 1902, when Edwin Hall dropped nine hundred and forty-eight balls inside the Jefferson physics building at Harvard and measured a mean eastward deflection of 0.15 centimetres against a prediction of 0.18.

That record needs a qualification. The eastward drift was found repeatedly, at roughly the predicted size, which is what makes it convincing. But most of these experiments also produced a small southward drift that no theory called for and which has never been explained; Hall's southward figure was 0.005 centimetres, within his own margin of error, and a French experiment of about the same period indicated a northward drift instead. The eastward result is trustworthy because it survived repetition at the predicted magnitude, not because any single run was clean. This test needs one site and no sky.

A pendulum shows the floor turning. Léon Foucault built instruments for a living, and he noticed that a steel rod set vibrating on a lathe kept vibrating in the same plane while the lathe turned it. If that is how a swinging object behaves, he reasoned, a pendulum should hold its plane of swing while the Earth turns beneath it, and anyone standing on the Earth and turning with it would see the swing slowly rotate the other way.

The argument is cleanest at the North Pole. There the pivot sits on the Earth's axis and does not travel anywhere, so the pendulum swings in a plane that stays fixed relative to the stars while the planet rotates underneath. An observer standing at the pole, turning with the ground, sees the line of swing sweep right around the compass in a day. The swing plane has persisted; what has turned is the observer's floor.

In 1851 Foucault built it. After a first demonstration for the Académie des Sciences on an eleven-metre pendulum, he hung a sixty-seven-metre wire with a twenty-eight-kilogram bob in the Panthéon in Paris and let the public watch. A long wire and a heavy bob were both necessary, since the swing has to keep going for hours. The line of swing crept clockwise around the hall and came full circle in about thirty-two hours.

The rate is the part that carries the most information. At the pole the turn takes one day. At the equator the plane does not turn at all, however long you wait. In between, the period lengthens as you move away from the pole, working out at about thirty-two hours for the latitude of Paris. Foucault pendulums went up across Europe and America and the measured periods matched the latitudes. A replica of the Panthéon wire still hangs there. This test needs one room, one wire and no sky at all, which is why it remains the most direct demonstration of the rotation available.

That settles the first of the three questions. The Earth's rotation is real and is detectable by local apparatus. The orbit is a different matter, and none of these three experiments touches it.

The Earth's yearly motion around the Sun is not uniform straight-line motion, so the cabin argument does not cover it. But it is also not detectable by the pendulum-and-falling-stone methods that caught the rotation. The reason it is not is the one place in this essay where the answer depends on which physical framework you are working in, and the next section is about that. For the moment the practical consequence is what matters: none of the terrestrial tests that were tried or proposed — the tower, the cabin, the pendulum, the falling stone, the survey of the planet's shape — reaches the orbit, for reasons the next section gives. It was established from outside instead, from the Earth's changing relation to distant bodies and to the light arriving from them.

The delay that followed is therefore a consequence of where the evidence had to come from rather than of slow institutions, and the obvious external test was parallax. Hold your thumb up at arm's length, close one eye, and note what the thumb covers on the far wall; switch eyes and the thumb jumps sideways. It jumps because your two eyes look from two different places, and a nearer object jumps further. There is no theory in this, only geometry.

Now scale it up. If the Earth travels around the Sun, then the Earth in June and the Earth in December are two viewpoints separated by the full width of the orbit. A nearby star seen from both should shift against the more distant stars behind it, tracing a small closed figure over the year. A stationary Earth produces no such shift at all. Find the shift and the orbit is established.

Nobody could find it. Tycho Brahe, the most accurate observer of the age before telescopes, searched and found nothing, and his failure established an upper bound: any stellar parallax had to be smaller than about one arcminute, one sixtieth of a degree.

That bound is where Tycho's real objection begins, and it is much stronger than the version usually reported. He had also measured the apparent diameters of stars, and found third-magnitude stars coming out at roughly one arcminute across. Put the two measurements together. If a star is far enough away that its parallax stays below Tycho's limit, and it still presents a disc about an arcminute wide, then that star must be enormous — on his figure for the Sun's distance, something like 1,150 times the diameter of the Earth, and the brighter stars larger still. Against that, he measured the Sun itself at about five Earth diameters.

So the choice, as the evidence then stood, was this: either the Earth does not orbit the Sun, or the stars are vastly more distant and therefore vastly larger than anything in the known universe, with an unexplained empty gulf between Saturn and the nearest of them. Tycho found the second option absurd and took the first. This was the strongest scientific objection made against Copernicus, and it was not a failure of nerve. It was an inference from two measurements he had actually made.

Note that this objection has two parts, and only one of them is about instrument precision. A better telescope could lower the parallax bound. It could not, by itself, explain away the measured stellar discs.

The failures of the intervening century made things no better. In 1699 John Flamsteed announced a parallax for the pole star that would have placed it about fourteen thousand times the Earth-Sun distance away. Others examined his measurements and found the pattern did not fit. Out of that came a standard that outlasted the result: a parallax claim could not rest on a handful of observations showing some apparent shift, but required a continuous run of at least a year, tracing the specific closed figure that an orbiting Earth demands. Only the shape and the timing distinguish parallax from the many other things that can move a star across a telescope's field.

There was also a reason beyond astronomy to want an answer. If gravity is universal, stars as close as Flamsteed's figure implied might disturb the planets. No such disturbance was seen, which left either the stars much further off than claimed, or gravity not universal after all.

That is what Samuel Molyneux and James Bradley attempted from December 1725, using a twenty-four-foot telescope fixed vertically and trained on one star, Gamma Draconis, each time it passed directly overhead. Bradley judged the instrument good to about one second of arc — one 3,600th of a degree, where Tycho's bound had been sixty times coarser.

The star moved, by twenty seconds of arc, an effect far larger than the parallax they were hunting. But the timing was wrong.

Parallax has a fixed timetable, because the shift comes from the Earth's position. The star has to reach its extremes when the Earth is at the two ends of its orbit, which for Gamma Draconis meant furthest north in June and furthest south in December.

What Bradley recorded was different. The star drifted south until March, reaching twenty seconds of arc south of its December place; returned to the December position by June; and went on to twenty seconds north by September. A clean annual cycle at a good size, with every extreme falling three months away from where parallax requires it.

Their first thought was that the Earth's axis might be wobbling annually. A second star ruled that out, moving in a way no wobble could produce. Bradley then rebuilt the programme around a shorter twelve-foot instrument with a wider field, so that many stars could be followed rather than one, and pushed the precision to about half a second of arc. Every star showed the same annual figure, always three months out of step with parallax, its shape depending on the star's position in the sky.

The three-month offset is the whole clue, and it is worth working through. A quantity that runs a quarter of a cycle ahead of the Earth's position is not tracking the Earth's position. In a circular orbit there is one thing that always runs a quarter-cycle ahead of position, and that is the direction the Earth is travelling: when the Earth is at the top of its orbit it is moving sideways, and position and heading stay a quarter-turn apart all the way round. Bradley's stars were reporting the Earth's velocity rather than its location.

The explanation needs one everyday picture. Rain is falling vertically. Standing still, you hold the umbrella straight up. Walking, you tilt it forward, because relative to you the rain now arrives partly from ahead. The faster you walk, the more you tilt, and the tilt angle depends on just two things — your speed and the rain's speed.

Starlight is the rain and the telescope is the umbrella. Light travels at a finite speed, so a telescope carried along by a moving Earth has to be aimed a fraction into the Earth's direction of travel for the starlight to run cleanly down the tube. As the Earth's heading swings around the full circle over a year, the required aim swings with it, tracing the small annual figure Bradley was measuring, three months out of step with parallax exactly as observed.

Several things followed. The first is that the tilt exists, on many stars, at a repeatable size and schedule, and a stationary Earth produces no tilt at all. Almost two hundred years after 1543, this was the first direct observational evidence that the Earth moves in an orbit. It was accepted quickly, because the reasoning was tight and the observations were better than anyone else's. The one body of data against it was Hooke's older work, which fitted parallax and conflicted with Bradley's far more precise measurements of the very same star. Independent support arrived from Bologna, where Eustachio Manfredi found the same annual movement in Sirius and Arcturus — measuring east and west where Bradley had measured north and south, so the two sets of observations complement rather than duplicate each other. Manfredi was working in Italy, where the Copernican account was still forbidden, and he never accepted Bradley's explanation of what he had found. The word he used for the effect, aberration, is the one Bradley adopted and the one still in use.

The second is that the tilt's size is fixed by the ratio of two speeds, the Earth's and light's, so the measured angle yields the second speed once the first is known. Bradley's maximum tilt of twenty seconds of arc puts light at more than ten thousand times the Earth's orbital speed, which works out at roughly eight minutes for sunlight to cross from the Sun to us. That was a little faster than the figure Rømer had arrived at by a completely different route half a century earlier. A measurement undertaken to settle whether the Earth moves had produced, as a by-product, a value for the speed of light.

One footnote for completeness, since the essay has been careful to keep the Earth's two motions apart. The rotation produces an aberration effect of its own, on a daily rather than an annual cycle. It is far too small to have mattered here: the Earth's orbital speed exceeds its equatorial rotation speed by a factor of more than seventy.

What Bradley had not found was parallax. The tilt is the same for near and distant stars alike, so it establishes that the Earth moves without saying how far away anything is. Once he understood the effect, he could subtract its predicted amount from his own observations and inspect what remained. What remained showed no parallax on any star, at half a second of arc. The stars were beyond the reach of the finest instrument then in existence.

Another century of instrument-building followed, along with a strategic problem: which star to point at? Nobody knew which stars were nearest. The one usable clue was that a few stars visibly creep across the sky over decades, and a star that creeps is likely to be close — for the same reason that nearby objects sweep past a moving train's window while the horizon barely shifts.

After a hundred years of nothing, three results arrived within about a year.

Friedrich Bessel published at the end of 1838, having chosen 61 Cygni, one of the fast-moving stars, and measured an annual shift of 0.3136 seconds of arc. Thomas Henderson followed from the Cape of Good Hope in January 1839 with about one second of arc for Alpha Centauri, having chosen without knowing it the nearest star to the Sun. Wilhelm Struve published Vega later in 1839 at 0.261 seconds. Struve had in fact printed a preliminary value in 1837, more than a year ahead of Bessel, but it rested on too few observations and differed so much from his own later figure that most astronomers, Struve included, gave Bessel priority. The discarded early value turned out to be the more accurate one.

Converted into distance, those numbers put 61 Cygni about 660,000 times further away than the Sun, Alpha Centauri about 200,000 times, and Vega nearly 800,000.

Several questions closed at once. The stars' positions swing in step with the Earth's position, which a stationary Earth cannot produce, so the orbit was now directly observed. The Copernicans' unverifiable reply — that the stars are too far off for the shift to show — turned out to be correct and acquired a number: the whole width of the Earth's orbit is very nearly a point at those distances. And the same distances explain why stellar gravity does not disturb the solar system.

Tycho's second objection, the one about stellar size, was settled separately and by a longer route, which is why it took so long. Galileo's telescope had struck the first blow: it magnified the Moon and terrestrial objects as expected but did not magnify the stars in the same way, which showed that the discs the eye saw were not the stars' true size. Riccioli, the most formidable of the later opponents of the moving Earth, accepted the smaller telescopic values and rebuilt the objection on them, so it did not go away. What killed it was an observation by Horrocks and Crabtree at a lunar occultation of the Pleiades: on Riccioli's figures a star should have taken about eleven seconds to fade behind the Moon's edge, and instead the stars vanished in an instant, so their true diameters had to be far below anything measured. Halley later confirmed the same from occultations. William Herschel then found the pattern: the measured size of a star depended on its brightness and on the instrument, and increasing a telescope's aperture made the disc smaller. In 1828 John Herschel noticed faint rings around stars at high magnification and connected them to the wave theory of light. In 1835 George Airy worked out the formation of a star's telescopic image on that theory and showed that diffraction accounts for what was being seen. The most important factor in a star's apparent size is the aperture of the telescope; the next is the star's brightness; and the star's actual diameter does not come into it. The discs Tycho measured were made by his instrument.

So Tycho's reasoning had been sound throughout. He had two real measurements and drew the correct inference from them. What he could not have known was that one of the two measurements was an artefact of the optics.

From the book to the direct evidence of the orbit: 1725 for aberration, 1838 for parallax. Two hundred and ninety-five years from publication to the parallax measurement, and the two dates answer different questions — the first shows the Earth is moving, the second shows where it is and how far away the stars are.

One question has been deferred twice, and it has to be faced: if the Earth's orbit is a curve, and travelling along a curve means constantly changing direction, why do the instruments that caught the rotation — the pendulum, the falling stone, the accelerometer — register nothing of the orbit?

The honest answer is that this depends on which framework you are working in, and the two standard frameworks answer it differently. Both are correct within themselves, and neither is a correction of the other. Keeping them apart is the difference between understanding this and being confused by it.

A device makes the question concrete. Take a weight in a tube, held in the middle by a spring at each end. Put it in a car and accelerate: the weight slides back, stretching the front spring and compressing the rear one, until the springs are pulling hard enough to accelerate the weight along with the car. The springs' stretch measures the acceleration, so long as the springs are the only things pushing the weight along the tube. This is an accelerometer, and used within that condition it reports changes of motion from inside a sealed box with no outside reference — exactly the kind of instrument that catches rotation.

Now hold it upright at the top of a tower. The weight sinks down the tube, stretching the upper spring and compressing the lower. Then drop the whole thing. During the fall the springs return to neutral, because the casing and the weight fall together and no spring force is needed to keep them in step. The falling accelerometer reads zero.

At this point the two frameworks part company, and what they disagree about is how to describe what you have just watched rather than what happened. In the Newtonian account, gravity is a real force. The falling instrument is accelerating downwards under it, and the zero reading is a use of the device outside the condition just stated, rather than a fault in it — gravity is now acting on the weight too, so the springs no longer have to do the job whose size they report. On this account the orbiting Earth is accelerating, continuously, under the Sun's gravitational pull. It is not moving uniformly in a straight line, and the cabin argument does not apply to it. But this acceleration is caused by a body outside the Earth and is shared by the entire planet and everything on it, so it produces no relative motion inside for a local experiment to find. That is why the pendulum and the falling stone register the spin and not the orbit: the spin is an acceleration that differs from place to place on the Earth and around a circle, and the orbital acceleration is one the whole planet undergoes together.

In the general-relativistic account, the zero reading is taken at face value. There is no force of gravity. An object in free fall has no force acting on it at all and is moving as freely as anything can; what is unusual is standing still on the ground, which requires the floor to push you constantly upward. On this account the orbiting Earth is in free fall around the Sun and is not accelerating in the relevant sense — it is following the straightest available path. There is nothing for a local accelerometer to register because there is nothing there.

The two accounts disagree about whether the orbiting Earth accelerates, and both are right, because they are using different definitions of what it means for a force to act. What they agree on is the observable: the instrument reads zero. An accelerometer riding with the Earth registers nothing of the orbit, and the pendulum and falling stone that caught the spin are, for this purpose, accelerometers of the same kind.

There is a caveat that keeps this honest. The equivalence holds strictly for a uniform gravitational field, and the Earth's is not quite uniform. Falling bodies do not drop along exactly parallel lines but converge very slightly towards the planet's centre, and they fall a little faster nearer the surface. Those residual differences are real and measurable in principle. What a sufficiently sensitive experiment detects in them is the non-uniformity of the field itself, which is not the same thing as detecting the Earth's orbital motion, and the essay does not claim it as such.

The argument in this essay has run through seven proposed tests. They are not the same kind of test, and treating them as though they were is the commonest way of getting this subject wrong. What separates them is the minimum external reference each one needs.

The tower, as the ancients posed it. Access: local apparatus, one site, no sky. Detects: nothing. The predicted westward lag does not occur, and its absence is equally consistent with a rotating and a stationary Earth, so the test returns nothing — which is its whole contribution, since this was the argument that was supposed to be decisive. Leaves open: everything the essay goes on to settle, including whether any smaller effect acts on the stone.

The ship's cabin. Access: sealed enclosure, nothing outside consulted. Detects: nothing. Also a null result, and also the point. It establishes that uniform straight-line motion of the whole system is undetectable from within, and it establishes nothing about rotation or orbit.

The pendulum. Access: local apparatus, one room, no sky. Detects: rotation, with the rate fixed by latitude. Leaves untouched: the orbit, and any uniform motion of the whole system.

The deflection of falling bodies. Access: local apparatus, one site, no sky. Detects: rotation, by a few millimetres. Leaves untouched: the same two. Carries an unexplained southward component.

The planet's figure. Access: planet-scale survey — no celestial reference, but expeditions to opposite ends of the Earth. Detects: rotation. Leaves open: the orbit, and any uniform motion of the whole system. It belongs with the pendulum in what it shows and not in what it costs, and this is the row most often filed wrongly.

Aberration. Access: celestial reference required. Detects: that the Earth is moving, via its direction of travel. Leaves untouched: distances, and the Earth's position at any moment. Not a local detection.

Parallax. Access: celestial reference required. Detects: the Earth's changing position, and stellar distances with it. Leaves open: rotation, on which it is silent, and any uniform motion of the whole system, on which nothing in this list bears. Not a local detection either.

Two rows return nothing, and those two were the tests everyone expected to be decisive. Three rows detect rotation without any sight of the sky. The last two, which are the only ones that reach the orbit, both need the sky — and that, rather than any failure of nerve or institution, is why the second tier took until the eighteenth and nineteenth centuries.

The reference body of the ship's cabin acquired a precise name and a precise role in the twentieth century. The family of viewpoints picked out in that section — moving uniformly, in a straight line, without rotation — are what physics now calls inertial frames, and the cabin result became the founding principle of special relativity: physics works identically in all of them, so no experiment performed inside any one can mark it out as the one truly at rest.

Some care is needed with that statement. It is a claim about that restricted family, not about all possible viewpoints, and extending it beyond them was the work of a further decade and a different theory. And it did not arrive as a discovery that motion is relative; that much had been in print since 1543 and demonstrated since 1632. What arrived was the precise scope of the claim, and the reason it holds.