Mizan Rahman
One
From early childhood, we’ve all heard two famous stories involving fruit trees. One is the tale of Adam and Eve’s ‘forbidden’ fruit, and the other is the story of Isaac Newton and the apple that supposedly fell from a tree. It took me quite some time to realize that the ‘forbidden’ fruit actually symbolizes ‘knowledge’, even though people of that era (and even today) have mostly taken the story literally (and while religious leaders have no doubt about its truth, modern scientists remain skeptical). However, the apple story is far more earthly and thus more believable. But did it really happen as told? Did the hapless apple truly fall right on Newton’s head?
Everyone enjoys clever anecdotes about great individuals. Few of us truly comprehend Einstein’s theory of relativity, but who doesn’t love the thrilling tale of cosmic journeys in an imaginary vehicle? It is, after all, an astonishing story: the elder brother returns from space only to find his younger brother now older than him! What could be a greater wonder? This bit of mystery is enough for us—the name ‘Einstein’ is forever etched in our minds. What’s true or not hardly matters—as long as the story is good.
Archimedes of Syracuse (287–212 BC), recognized as one of the ancient world’s greatest scientists, was a physicist, engineer, astronomer, and, above all, the leading mathematician of his era. But how do ordinary people remember him? By a single word: “Eureka”—meaning, “I have found it.” And they remember his running naked from his home, shouting this word. Just as we might, in a mad fit, dance naked on the streets if we won the lottery, Archimedes hadn’t won any such thing—he just had a ‘big idea’ strike him while bathing in a tub. The story is juicy, no doubt, and that’s enough for most people. Who cares that he laid the groundwork for engineers’ studies of statics and hydrostatics, pioneered the theory of specific gravity, and that this very idea is what sent him, in his excitement, streaking into the street? Few even know he died at the hands of a Roman soldier during the Greco-Roman wars.
Newton’s apple story may not be as entertaining but carries a touch of romanticism. Imagine an apple orchard, a young Newton lying lost in thought on the grass. Suddenly, an apple falls squarely on his forehead. Instantly an extraordinary idea dawns on him—it signals the presence of a profound cosmic force. Almost as if a divine revelation, he is inspired. In fact, Newton himself is said to have thought of the apple tree as the biblical ‘tree of knowledge’ (while this may not be true, Newton was deeply religious, and not immune to tales of the supernatural). In any case, this article’s goal is to explore: how much truth is there in these stories, and how much is pure invention? Did an apple really fall on Newton’s head? Or is it as dubious as the Archimedes legend?
It seems the apple incident did happen at Newton’s country home—there are at least two historical records. The first is by John Conduitt, Newton’s niece’s husband, who later worked closely with Newton when the latter was director of the Royal Mint. According to Conduitt, in 1666, during the great epidemic in Britain, Newton returned from Cambridge to his mother’s home in Lincolnshire—something he frequently did during breaks. One day, as he walked pensively in the garden, a ripe apple suddenly fell right before his eyes. That fall struck him as hugely significant. Why did it fall down? And why directly down, not at an angle or curve? From this, three things became clear to him. One, the apple falls—it does not fly upward—because some attractive force pulls it downward. Two, the fact that it falls straight—not at an angle—proves that the pull is directed toward the center of the Earth; that is, gravity is a *central* force, with deep significance. Three, this force acts not just on apples—this is a universal property, applying to all masses. Every body attracts every other in this way; the effect is unnoticeable for small objects, but for large ones—like the Earth—it’s very prominent.
The second testimony comes from Newton’s close friend (a man of considerable influence but few confidants), William Stukeley (1687–1765), a prominent biographer and historian, who wrote in Newton’s biography that he heard the apple story directly from Newton in 1726—just a year before Newton’s death—while the two were conversing in Kensington Park, London. Stukeley’s description closely matches Conduitt’s account, suggesting that—at least in this case—the science legend is likely not a fabrication.
Yet questions remain. That’s the nature of science—nothing is ever finally settled. Seemingly solved questions breed new ones. Even if the apple story is real, did the concept of universal gravitation suddenly occur to Newton, like an oracle’s pronouncement, or did it have historical and scientific precedents? Big scientific ideas rarely fall out of the sky. A genius does not just emerge from sleep proclaiming ‘Eureka’ with an entire theory in hand. The practice of science requires long preparation and continuity of thought, whether the thinking is original or logical. Einstein’s relativity was foreshadowed three centuries prior by Galileo Galilei, who himself proposed a kind of relativity and thus inspired Einstein’s imagination. Also, Newton’s gravity theory was a crucial foundation for Einstein’s revolutionary ideas. And, perhaps most importantly for theoreticians like Newton, the greatest resource is often the experimental findings of applied scientists, not just other theories.
Newton was not content to merely notice the existence of gravitational force; he described its nature fully. Two bodies do indeed attract each other, but the strength of that attraction decreases with distance—something almost intuitive—but that this decrease follows the *inverse square* of the distance is far less obvious. Newton grasped this with apparent ease—but how? Was he the first to discover the inverse square law? There’s a backstory there.
Interest in the motions of heavenly bodies is ancient. We gaze in awe at the night sky, trying to unravel the flickering constellation mysteries; ancient people tried as eagerly to decipher their movements. Today we have powerful instruments to see stars invisible to the naked eye; then, they had only direct observation. They noticed the moon appearing as a crescent, swelling into a full orb over two weeks, then disappearing in the same cyclic rhythm—giving birth to the lunar year, used historically worldwide. Today, secular calendars do not follow the lunar year, but religious observances (in almost every Muslim country and in Israel) rely on lunar calendars—the Jewish and Islamic ones, respectively.
While the Western world now leads in science, until the medieval era their position was the opposite—especially compared to India, China, and the Middle Eastern Muslim states, then leaders in the golden age of Islamic civilization. Aryabhata, renowned Indian mathematician-astronomer, as early as 499 CE, introduced the heliocentric model—stating that Earth orbits the Sun and rotates on its own axis. Around 1000 CE, Arab scholar Abu Rayhan al-Biruni put forward a similar proposal, likely unaware of Aryabhata’s work (remember, not even paper was widely in use then, let alone Google search). Unfortunately, Biruni later abandoned the heliocentric view in favor of the geocentric consensus. Circa 1300, Najm al-Din al-Katibi likewise tried to prove Earth’s orbit around the Sun with diagrams—but later reverted, for reasons unknown.
Were these efforts futile, mere confusion for people? Not at all. Research never fails, even if its conclusions do not always stand. Katibi’s diagrams, it turns out, were extensively drawn upon by Poland’s Nicolaus Copernicus (1473–1543), although never openly credited (the match between their diagrams leads historians to this conclusion). Copernicus’ “On the Revolution of Celestial Spheres” (1543) triggered a scientific revolution in the West, shaking the entrenched beliefs of the Christian Church based on Ptolemaic and Aristotelian geocentrism, and replaced dogma with reason. He died soon after its publication, perhaps sparing him the Church’s wrath. Others later faced misery for defending his views—most famously Galileo. But nothing could stop progress. Stifling the natural flow of reason inevitably leads to stagnation—European civilization is stark proof, as is, similarly, the pre-medieval Islamic world.
Returning to our question—who discovered what, and when? For both universal gravitation and especially the inverse square law, the original pioneer was Robert Hooke. When Newton published his unified gravitational theory and other discoveries on July 5, 1687, he did mention Hooke by name, but was not willing to share the title of ‘originator’. Poor Hooke. Was it really Newton alone, after his apple revelation, who formulated the inverse square law, or was there a prior story? Indeed, Robert Hooke (the same ‘Hooke’ as in ‘Hooke’s Law’), not only intuited gravity’s nature, but had even written a paper stating that gravity obeyed the inverse square law, and presented it to the Royal Society on March 21, 1670. Moreover, he sent a copy to Newton by mail in 1769. Does this prove that the true originator of gravity theory was Hooke, not Newton? Newton’s own works, published in 1687 as *Philosophiae Naturalis Principia Mathematica*, recount the full history of the idea, and he acknowledged Hooke’s credit generously, referencing Hooke’s paper and letters—just as any honorable scientist should. Yet Newton would not surrender his claim as principal discoverer. His argument: yes, Hooke (and a few others before him) sensed the force and its inverse-square nature, but none supplied proof that it applied universally. They failed to establish their results with rigorous mathematics and evidence—while Newton insisted on scientific demonstration. It was only after showing that gravity fit the observed orbits (especially Kepler’s planetary motions) that the theory was accepted. Newton used Johannes Kepler’s (1571–1630) empirical findings and showed they aligned beautifully with his calculations. Most importantly, the required branch of mathematics—calculus—was Newton’s own invention.
But what were these “Kepler’s laws”? Kepler didn’t simply imagine the planetary movements in the Solar System. His predecessor, the Danish-born (now Swedish-claimed) astronomer Tycho Brahe (1546–1601), was a telescope enthusiast, relentlessly tracking the night sky. A cantankerous man, Brahe even quarreled with the King of Denmark and moved to Prague, where he gained enough freedom (and a grand observatory) to work. Unable to handle the work alone, in 1600 he brought on a brilliant German, Johannes Kepler, as assistant. The two clashed, mainly over salary, but soon settled in to determine the correct structure of the Solar System. Fatefully, Brahe died just a year later, and Kepler took over. Using Brahe’s trove of telescopic measurements, Kepler formulated two laws:
1. All the planets (including Earth) orbit the Sun in ellipses (Copernicus had thought the orbits were circular—the ancients considered circles perfect, as befits the work of a perfect Creator. Copernicus himself believed this).
2. The line joining a planet to the Sun sweeps out equal areas in equal times.
He declared these principles as derived from meticulous telescopic observation, first announced in 1609. Then came Kepler’s third law:
3. The square of the orbital period (the time for a full revolution around the Sun) is proportional to the cube of the ellipse’s semi-major axis. Thus each planet’s year is geometrically linked to its orbit’s dimensions; the farther the planet, the longer its year.
Kepler took ten years to establish this last law, finally published in 1619.
But did Hooke know of Kepler’s work? If he did, there is no trace of it in Hooke’s seventeenth-century writings. Lacking this—and data—he couldn’t demonstrate his theory with experimental results. Newton could, thanks to calculus—his own creation. Also, Newton had another trump card—his three laws of motion. By combining calculus and these laws, Newton easily demonstrated that, when the inverse square law for gravity is applied, Kepler’s three laws all follow seamlessly—something undergraduates can now derive at home. (I myself did so in my university applied mathematics class.) However, Newton’s original proof used geometry rather than calculus, making it rather complex for modern students.
So, at the Newton’s orchard, when the apple fell, did he know about earlier gravitation theories? At the time, he was 24, the top math and physics student at Cambridge. He might have heard of Ismaíl from France and the works of Arab scientists. But that gravity followed the inverse square law—no one had conclusively said, or proven. Previous scientists had speculated about inverse squares, some, like Kepler, even suggesting the decrease was merely inverse to distance, not the square. But no one had proof.
I am convinced that the insight about gravity Newton gained from the apple was wholly original, not borrowed—a testament to his exceptional acuity and powers of observation and reasoning. People like him are born perhaps once in a thousand years.
As a student, in my own limited way, I once imagined a force in nature whose attraction and repulsion laws weren’t governed by squares, but followed some completely different rule—a naive, youthful fantasy. Now I understand that nature’s laws are so finely tuned that even a slight deviation would render our existence impossible. Newton showed mathematically that if Kepler’s solar system laws are true, the force must obey the inverse square law; conversely, only with the inverse square law do Kepler’s rules hold.
Curiously, nature seems to have a special preference for this ‘inverse square’ relationship. Not just gravity, but magnetism, static electricity, and light—all follow the same rule. Two electric charges attract or repel according to the inverse square law, as do the poles of magnets. Similarly, when a torch is shone in a dark room, the brightness of the light on a surface diminishes with the square of the distance from the source. This happens because the area of a spherical shell at radius r grows as r squared, so the brightness per unit area drops as 1/r^2.
What made Newton’s gravity theory uniquely profound was not simply his mathematical rigor, but the universal applicability. Earlier theorists didn’t specify that gravity applied to any and every object in the universe—including celestial bodies far beyond local environments. Newton did, and this universality is what makes his theory so remarkable.
But was Newton’s theory perfect? For most practical purposes—yes. His laws are still used, even in engineering modern spacecraft. Yet, science, too, evolves. New research and tools, especially in the late nineteenth century, revealed that Newton’s implicit assumption that light traveled at infinite speed was incorrect—dramatized by Michelson-Morley experiments and, later, by Einstein. Do these findings refute Newtonian mechanics? Not at all—for everyday purposes, Newton still reigns and likely will forever. It’s only in subtle cases—like Mercury’s orbit—where Newton’s equations don’t quite fit, but Einstein’s do. Newton’s universe is boundless; Einstein showed its boundaries are set by the speed of light. Einstein’s other radical insight: even massless light bends around stars, as if attracted by mass—profound, yet irrelevant to daily life. For us, Newton’s world suffices.
Two
Another limitation of Newton’s gravity theory is that it explains attraction between only two bodies. For two objects, Newton’s equations and the inverse square law together precisely determine their orbits. But real-world scenarios almost never involve just two bodies—especially in astronomy, where interactions among planets and their moons are the norm.
Take the Moon, our nearest neighbor—it’s Earth’s satellite, though only because its smaller mass makes it orbit Earth rather than the Sun. But the Moon’s situation isn’t simple; it exists in a three-body problem: the Sun, solemn as the supreme lord, sits at center; Earth, held by the Sun’s grip, is next; then the Moon, whose pull is not insignificant. Now, three players interact. If Newton’s theory is valid just for two, does the three-body setup nullify its gravity law? Luckily, no—the basic equations still hold, but the prediction of motion becomes vastly more complex. It no longer yields to a handful of neat equations. For centuries, brilliant minds have tried to solve the ‘three-body problem’—in English, the ‘three-body problem’ is far more challenging than Newton’s ‘two-body problem’. Special solutions for certain restricted cases have been found; but in general, no one—using even Newton’s own calculus—has found a fully general solution to this day.
One might ask: Why bother? We will never leave Earth’s gravity, so why waste money and effort on hypothetical cosmic interactions? There are two main answers, both essential for humanity. First: the insatiable quest to know the boundaries of our knowledge elevates our humanity. Understanding our relationship to the stars helps us grasp our origins and destiny. Second: in terms of modern science—the necessity of space travel. You may say, who needs to travel in space? People go to Florida or Europe, not space! Well, the greatest scientists are ‘mad’ in this way—devoting their lives to research that, ultimately, has made our lives comfortable, drowning us in a flood of electronics. Moreover, it’s no fantasy—since 1969, humanity has voyaged to the Moon. Mars may soon follow. Space travel, therefore, crucially depends on multi-body gravitational theory. On live broadcasts, we’ve all seen astronauts floating weightless; as the craft moves higher, they enter new gravitational arenas, often influenced by multiple large bodies—resulting in a bewildering push and pull. In such multi-body conditions, Newton’s equations don’t easily yield trajectories. Yet mapping out the journey—before launch—is critical; that is the responsibility of mission controllers.
So what’s the solution? If Newtonian mathematics can’t handle it, what alternatives are there?
Because of these needs, mathematicians in the late nineteenth century turned their attention to three-body and multi-body problems, striving to uncover the geometry of their orbits. A deadlock ensued—and then, something extraordinary occurred.
Three
In 1887, on his sixtieth birthday, Oscar III, king of then-united Sweden and Norway, announced a one-time prize. The king was deeply interested in science, particularly mathematics—rare among monarchs now, but not then. Among his closest friends was Mitchag-Leffler (1846–1927), one of Sweden and all Europe’s leading mathematicians. His name is unusual—Mitchag was his father’s, Leffler his mother’s maiden name; he eventually fused both, becoming Mitchag-Leffler. A highly respected name in mathematics; to Swedes, a national hero.
Mitchag-Leffler knew full well that the hardest unsolved problems were the three-and multi-body problem; he persuaded the king to make this the challenge for the royal prize, and the decision was broadcast throughout the mathematics world.
Geniuses love tough problems—the three-body problem was then the most celebrated puzzle. So, mathematicians around the world rose to the challenge, motivated by the prize and the glory.
Among the contenders was France’s young star, Henri Poincaré (1854–1912), an authority on mechanics, well-versed in the foundational works of Newton, Euler, Lagrange, Hamilton, and Jacobi. Poincaré had thought about the three-body problem before, but with the prize, his focus intensified. After intense research, he believed he had solved it entirely and submitted his paper to Mitchag-Leffler. Mitchag-Leffler, having utmost respect for Poincaré, reviewed it carefully but found no faults. He decided to award Poincaré the prize, a decision greeted with excitement in the scientific world. After a ceremonial presentation at the palace, Mitchag-Leffler sent the winning paper to a leading mathematics journal he had founded, selecting the young Edvard Fredholm to proofread it—Fredholm noticed a logical flaw in the proof, and wrote to Poincaré (though without any impolite implications). By then, the journal was already published—nobody else had noticed the gap.
Upon reading Fredholm’s letter, Poincaré re-examined his work—and was mortified to discover a deep error, not only in proof but in the very premise. The result, though apparently reasonable, was actually false. Poincaré was mortified; the journal was already published! In haste, he wrote to Mitchag-Leffler to withdraw the paper and offered to cover the cost of reprinting a corrected version himself. Mitchag-Leffler agreed.
The subsequent story is epochal. Poincaré concluded that the traditional mathematical approaches could not solve the three (or multi)-body problem. A wholly new perspective was needed. Abandoning calculus and algebra, he turned to geometry—and there, achieved a breakthrough. Through relentless effort, Poincaré brought a remarkable gift to mathematics. His geometric method, applied to the subtle behaviors that had eluded Newtonian mechanics in the multi-body case, led not only to a solution but also to the birth of a new branch of geometry: topology (for which Bengali still lacks an exact term). In this geometry, a square and a circle (so long as their interiors are equally ‘empty’) are fundamentally the same—each can be continuously transformed into a point, making them topologically identical. This is worlds apart from classic Euclidean geometry.
Poincaré’s most striking insight was that, in nature—even as the number of interacting bodies rises beyond two—no matter how complex the attract/repulse, each moving object eventually returns to its initial state, at least temporarily, so long as the process continues without interruption. It’s somewhat like the hands of a clock. I emphasize ‘eventually’ because this return is not readily observed—it may take ages. Not all motions are periodic, but those that are give us stability—like Earth revolving around the Sun. In his own words: “The reason the periodic solutions are so precious to us is that they are the only opening by which we can enter this inaccessible fortress.” Mathematicians, too, can be poetic, it seems.
We might laugh and call all these things “crazy mathematicians’ fantasies,” but they have real implications. Poincaré’s prediction is proven before our very eyes: the familiar Sun-Earth-Moon trio enacts the three-body problem in reality. They tug at each other, but the Sun’s massive size dampens its own perturbation, which shows up mostly as subtle shifts in Earth’s and the Moon’s orbits—imperceptible to us, but detected by astronomers. Yet, after much time, they all return to their original positions—a manifestation of Poincaré’s ‘long wait’ for recurrence. Thus, cosmic stability is preserved.
Poincaré’s revolutionary research also hinted at another curious facet of nature, known as ‘chaos.’ Although the popular meaning is “disorder,” its scientific sense is more profound—today, it is the foundation of an entire field of applied mathematics. Wherever many bodies interact, chaos arises—a bit like infamous traffic jams in Dhaka. There may not be a perfect Bengali equivalent, and the scientific sense differs greatly from the everyday one.
To summarize: Poincaré’s work led to a new way of thinking—his direct result was the geometric approach to analyzing body motion. Newton taught us to solve every problem through calculus, integrating force and acceleration; Poincaré used geometry—not classic Euclidean diagrams, but ‘phase space’ diagrams, where each point represents both a location and a velocity, not simply a place in three-dimensional space. These diagrams encode the entire history and behavior of a moving object: is it stable or chaotic? In many-body systems, this is essential.
Four
In ancient times, there was little distinction between philosophy, math, and science—the two sides of one coin. Plato and Aristotle (especially Aristotle) were not only philosophers but great scientists and mathematicians; few know Aristotle fathered biology. Even in the Middle Ages, this held: Omar Khayyam’s Rubaiyat contains deep philosophical insight, yet he was a master mathematician and astronomer. Leonardo da Vinci defies summary—no one in a thousand years equaled his polymathic talent. His anatomical studies, aircraft sketches, sculpture, architecture, and mathematical pursuits are legendary, as were his uncanny prophecies about human behavior.
You may wonder what any of this has to do with gravity—everything, thus my digression. In Newton’s era, it was assumed that nature could not ‘err’—there were no childlike mistakes in the Creator’s grand scheme. “Not even a leaf stirs without the will of God,” says the scriptures. Newtonian causality fits perfectly: given the present position, velocity, and forces, the future state is precisely predictable. For daily life, that’s how we plan—when a flight departs London, we know exactly when it will land in Dhaka. That’s because (barring mishaps) the mechanical laws followed by airplanes are as Newton described.
But nature isn’t always so docile. As shown earlier in Poincaré’s struggles with the three-body problem, even Newton’s rules can’t always predict the outcome—just as three people in a household argument can be unpredictable. Tiny instabilities, at times, escalate into total unpredictability (chaos)—a fundamental feature of nature.
In fact, even single-body motion can be unpredictable, depending on the environment. Think of a child on a swing—rarely will they go out of control. Imagine now a perfectly smooth, round bowl. Roll a ball inside at a specific angle. If the angle neatly divides 360°, the ball will eventually return to its starting point, tracing a regular route. If not, it never returns, but always follows a straight path. If the bowl is not round but elliptical, the path curves but remains predictable.
So long as the system is simple, causality holds—Newton’s framework applies. But as soon as the shape of the container gets more complex, the path of the ball grows unpredictable—producing the kind of tangled, cloud-like patterns characteristic of chaos. Words may fail to convey this fully—interested readers might consult Ivar Ekeland’s *The Best of All Worlds* (1) or James Gleick’s book *Chaos* (2). It’s a fascinating topic, blending mathematics, physics, and philosophy into a mysterious world.
Five
Let’s return to the earlier question: what, then, are nature’s laws for assemblies of many bodies? I have said above how nineteenth-century geniuses repeatedly failed at this problem. Even Poincaré (regarded by many as the greatest mathematician of his century or of all time) endured deep embarrassment at discovering, post-publication, that his solution to the three-body problem was mistaken—a blow only softened by a sharp-eyed young mathematician, Fredholm, catching the error in time.
Still, Poincaré’s corrected work not only survived but became an immortal document of his genius. He demonstrated convincingly that, despite Newtonian mechanics remaining valid, calculus alone could not decipher the detailed orbits of celestial bodies—here, Euclidean geometry breaks down, and a new, ‘strange’ mathematics (topology) takes over. On this subject, see Ian Stewart’s acclaimed book (3), from which I have drawn heavily in this essay.
Initially, Poincaré nearly gave up drawing the three-body paths—fixing the Sun in place, the Earth-Moon duo still produce tangled, intersecting orbits, making the tracking nearly impossible. What he may not have realized, then, was that this very complexity presages chaos. Occasionally, a closed (periodic) orbit forms, lending the system its stability—our only hope for existence. Hence, the periodic solution was Poincaré’s prime aim in pioneering non-Euclidean geometry.
So long as we are content to live quietly on Earth, we needn’t worry. But humanity’s urge to know the unknown is endless—hence airplanes, balloons, and finally interplanetary travel. The moon landing, first with unmanned, then manned missions, realized this dream. But how did NASA engineers decide on the craft’s path to the Moon? The naïve guess—just aim straight at the Moon—fails for two reasons: one, there *is* no “straight at the Moon” (both Earth and Moon are simultaneously moving in their orbits); two, distances vary, since both paths are elliptical. A route must be found that minimizes fuel cost, maximizes safety, and allows for a safe return, ideally with minimal ‘weightless’ time for the astronauts. These are not trivial issues—mission control’s experts consider them minutely before any manned flight.
The chief problem with aiming straight is massive fuel consumption, making the mission uneconomical. After escaping Earth’s gravity, fuel usage drops—but initial acceleration is most expensive. The solution is what’s called the Hohmann transfer orbit: first, move in an arc around Earth, then spiral slowly toward the Moon following a thin ellipse—minimizing fuel use. Once sufficiently distant, the spacecraft enjoys near-weightless freedom, not quite under either Earth’s or Moon’s gravity. Then, it circles the Moon once, again to save fuel, before entering lunar orbit. Every Apollo mission (1960–1970) followed this method.
But to modern astronauts, the Moon is almost routine. Both science and engineering have progressed so far that NASA has even sent robotic craft to Mars. But Mars is harder: its average distance is 225 million km, with a year of 687 days (compared to Earth’s 365), and light takes six minutes for a round trip. The two-body calculations no longer suffice; one must deal with many obstacles, and even Euclidean geometry is inadequate—Poincaré’s ideas are more useful. Still, for our purposes, these technicalities are less relevant—I suggest readers turn to the specialist books I’ve referenced (4, 5) for more detail.
I’ll close by sharing a few notes for potential future space tourists. In deep space, you must assume your weight will drop to zero—while mass remains, weight vanishes. But how long this lasts depends on the craft’s speed, its distance to other planets and moons, and the strengths of other gravitational pulls. Often, the craft will encounter (even collide with) nearby planets, moons, asteroids, and comets. In such conditions, fuel efficiency is crucial; run out of fuel at 100,000 miles altitude and you’ll go straight to your Maker—no chance to see your family again.
Engineers know how to plan for minimal fuel use—the same logic behind building train tunnels through mountains (instead of tracks over them) or subways beneath congested city streets; it saves energy and time. Similarly, in space travel, the term ‘underground rail’ (subway) is sometimes used to describe mathematical pathways—though, of course, there’s no literal ‘underground’ in space, and in this case, these paths exist only in mathematical imagination, often in spaces with more than three dimensions (usually five to seven—the ‘dimension’ here means the English “dimension”). The idea is that ‘space subways’ are routes that require much less fuel, and allow for smooth switching from one planetary orbit to another—like changing trains at a major station on a subway network, using minimal time and cost. That is the appeal of an interplanetary ‘space subway’—easy, efficient, and cheap.
For now, this is all fantasy. But today’s fiction may be reality ten or fifteen years from now—past wild dreams have come true thanks to today’s technology. Who knows what wonders the future will bring!
References:
(1) The Best of All Possible Worlds, by Ivar Ekeland, University of Chicago Press, 2006; Paperback edition, 2007.
(2) Chaos, by James Gleick, Penguin Books paperback edition, 1988.
(3) In Pursuit of the Unknown, by Ian Stewart, Basic Books, 2012.
(4) The Hitchhiker’s Guide to the Galaxy, by Douglas Adams, Published by Del Ray, 2005.
(5) Across the Universe, by Beth Revis, Published by Razorbill, 2011.
(6) Internet.
Ottawa,
August 22, 2012
Muktishon 41
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