Chapter 7 Chapter 6 The Music of Celestial Motion

One of the most magnificent dramas known to man is the individual progress of the planets in our solar system in their orbits.The drama is always played out before our eyes, with the sun playing the leading role and the planets, including our own Earth and its moon, playing supporting roles.Humanity has long observed this play as if it were a scene on a stage.But it is not like a human drama, it has no definite beginning and end, not even any obvious plot.But these exciting events have aroused the curiosity of mankind, and mankind has tried to understand this matter for thousands of years. For thousands of years, human beings have mainly used poetry and religious words to understand the objects in the sky and their behavior.Both the sun and the moon are gods, and the sky is where they set foot.Only three hundred years ago, when Kepler and Newton grasped the laws of planetary motion, human beings had a general understanding of what they were looking at.Then, in our own century, the beholders became active hands-on, building satellites and interstellar rockets.

Many people have seen artificial satellites gliding silently across the night sky, and they have been deeply moved, even shocked, by thinking that human beings have successfully entered areas that have not been allowed to go to since ancient times.At the same time, we are baffled by the bizarre routes that artificial satellites take to travel the world's skies.Once on the celestial stage, an artificial satellite follows with extreme precision the laws of planetary and moon motion.Human beings have been just spectators in nature since ancient times. If you want to perform on stage, you must first master the rules of the script.

The movements of the celestial characters have been almost exactly the same since the creation of the solar system some four billion years ago.During this terribly long period, the actions of the celestial characters are almost always unwatched by an educated spectator.It wasn't until about 10,000 to 15,000 years ago that humankind managed to explain this great drama. The interpretations were later reflected in the ancient cultures of the Chinese, Indians, Mayans, Egyptians, and Babylonians. .These ancient peoples not only tried to understand the motion of the stars, but they also tried to do something even bigger, namely explain how the whole universe came into being.They settled the matter with vivid religious imagination, and thus the most vivid myths of how the gods created the world were handed down from generation to generation.

In the sixth century BC, the great Greek philosopher Pythagoras and his disciples broke through the delusion of mythology, and first tried to understand the scene of heaven with reason.They had brilliant notions that the motion of the lights in the heavens could be understood only by mathematics, numbers and geometry.They believe that numbers are the essence of all things, and businessmen who despise vulgarity only know how to use numbers to calculate goods and make profits. Pythagoras (Pythagoras) taught the world that numbers are the key to understanding nature and the universe.This is still extremely prevalent today; in fact, it is the beginning of our modern scientific thinking.The Pythagorean figures applied mathematics to the heavens, offering an unprecedented scientific explanation of the celestial drama.

They believe that the sun, moon and planets seem to revolve around the earth, and the earth seems to be at the center of everything.They explained the movement of these stars by the existence of eight concentric spheres, each representing the sun, moon, and five planets visible to the naked eye (Mercury, Venus, Mars, Jupiter, and Saturn), the eighth sphere representing The stars that carry all that is fixed.The earth is in the center, and the spheres each carry a star inlaid on the sphere, slowly turning round and round, each according to the predetermined speed. The people of the Pythagorean school set the volume for each sphere, which shows that this school pays great attention to the harmony of numbers.Indeed, one of their most cherished treasures was the mathematical harmony discovered by their teacher.Pythagoras discovered that harmonics are produced because the lengths of several strings express a series of simple numerical intervals; therefore the Pythagoreans believed that the numerical laws of music were their world system an indispensable part of.They postulate that the volume of the planetary bodies increases from one to the next in a manner that increases in volume as the strings of a musical instrument such as a harp increase in length.But they thought that the spheres in the sky were made of the clearest crystal, and when these glass bell-like spheres moved majestically, they rubbed against each other and made a harmonious music, which was so wonderful and sweet that only God Only the ears can hear.This is the famous celestial harmony theory.

The Pythagorean school's explanation of the actions of celestial bodies is too much like a poet's whim to be in line with modern scientific thinking.But it is much more real than the idea that the planets are gods whose actions are capricious.This is the first time that human beings use number theory to describe the movement of stars. Following the path of the Pythagorean school, it took only two hundred and fifty years for someone to correctly solve the riddle of heaven. This riddle was given by the Greek astronomer and Samian Aristarchus in Jesus It was proposed two hundred and eighty years before its birth.The sun, says Aristarches, is in the center, and the planets, including our own earth, revolve in great orbits around this central fire.Thus Aristarches was the first to clearly and correctly describe the great picture of the sky.This is a marvelous intellectual achievement, but the world is too young to appreciate it and accept it.The foresight of this great thinker has been forgotten for almost two thousand years and no one mentions it in late antiquity and the Middle Ages.In the minds of the world, the earth still stands at the center of the universe; the grandeur of nature has always been misunderstood.

Medieval thinking about the heavens was finally brushed aside by the clear-headed thinkers of the Renaissance.The year of prosperity and decline is 1543. In this year, Nicholas.Copernicus published a major work on the rotation of celestial bodies.This book was published after his death, because he did not dare to put forward views contrary to the absolute truth held by the priests and laity of the church during his lifetime.Copernicus, like Aristarches more than 2,000 years earlier, depicted the sun as the center of a planetary system.This idea gained a firm foothold and became the beginning of a great revolution in human thought.The vast tricks performed in the sky have finally been glimpsed.But this is only the beginning of understanding; the finer details remain obscure.

Ancient astronomers took it for granted that the paths of the planets form circles.They believed that only numerically perfect circles and their divine harmony were sufficient orbits for celestial bodies.Even Copernicus believed that the orbits of all planets and satellites are exact mathematical circles.But it was later found that the motions of the planets did not quite follow the circular lines man had imagined; the mathematics of nature was more complicated than man had imagined.German Johannes.Johannes Kepler, born thirty years after Copernicus, was the first to explain satisfactorily the motion of the planets.His understanding is based on his painstakingly collected Tycho.The results of long-term, detailed and precise observations of celestial bodies by Tycho Brahe and others.

Kepler proposed some famous laws. The first law says that the orbits of celestial bodies are all elliptical, not circular.The shape of an ellipse is difficult to describe, and it must be seen to be understood and felt.An ellipse is rather like a circle flattened by pressure from two sides, but it is more graceful than that would suggest.The curvature is the same everywhere on the circle, but the curvature of the ellipse changes gradually little by little.An ellipse also has a center, but its diameter varies in different directions.The longest diameter is called the major axis, and the one perpendicular to the major axis is the shortest diameter, called the minor axis.

Each ellipse has two distinct points, which lie on the major axis and are equidistant from the center.These two points, called foci, express a strange geometrical law of the ellipse.Choose any point on the circumference of the circle, draw two lines, each reaching a focal point; choose another point on the circle, and draw these two lines, each reaching a focus.As soon as it is measured, it is known that the total length of the two lines drawn from these two points on the circumference is equal.This is true of any line drawn from any two points on the circumference of an ellipse; indeed, it is in this way that mathematicians define ellipses.

After a brief description of the geometrical properties of ellipses, we return to Kepler and his first law.The full text of this law is: The orbit of each planet is an ellipse, with the sun at one of the two foci.This law also applies to the satellites of all planets, which fly around them in elliptical orbits: each planet is always at one of the two foci of the satellite's elliptical orbit. The orbit of the earth around the sun is elliptical, which is only slightly different from a perfect circle. (The same is true for other planets. No wonder the ancients always thought their orbits were circular.) Since the orbit of the earth is an ellipse, the sun is not in the center of the ellipse. As the earth flies around the sun, its distance from the sun gradually changes.When the earth flies to a certain point, it is closest to the sun, and this point is called perihelion.The point where the earth is farthest from the sun is called aphelion. Kepler's first law describes the shape of the orbits of celestial bodies; his second law concerns the speed at which celestial bodies move round and round in their orbits.It proves that astronomers of the past were wrong.Those people thought that the planets and satellites were rotating steadily at a constant speed, but Kepler found that the speed of the planets and satellites was constantly changing.For example, when the earth passes the perihelion of its orbit, it flies the fastest; then it gradually reduces its speed until it passes the aphelion, and the speed is the smallest;The planets orbit the sun like a child's yo-yo, spinning lazily in vertical circles, slowly going up and quickly passing the bottom of their orbit.Kepler's second law describes this ever-changing velocity in mathematical terms. Kepler's law was a triumph of mankind: the theatergoers then understood at least part of the drama that nature played out on the celestial stage—that is: how the planets actually moved.Still, the big question remains: Why on earth do the planets move?The man who found the answer was born in 1643, exactly one hundred years after the death of Copernicus and the publication of his famous work.This man is Isaac from England.Sir Isaac Newton, whose discovery is the fundamental principle of the universe: the law of gravity. According to legend, Newton was sitting under an apple tree when he saw an apple fall.It struck him that the same force that made the apple fall was the same force that kept the planets and moons in their orbits.This anecdote may be entirely fabricated; but the eighteenth-century French wise man Voltaire said that the story, if not true, had to be fabricated.Voltaire, who was a famous admirer of Newton, may have imagined the story.But that didn't matter; Newton conceived the idea of ​​gravity, formulated the law of gravity, and thus became one of the great figures in human history. We do not discuss here how mathematically great Newton's laws are; we only follow his reasoning to the point where we can see why the planets and satellites move as they do.We also want to make it clear to ourselves that we would not understand how to put a satellite into orbit and make it fly around the earth without Newton first proposing the concept. Gravity is the force of attraction between all objects in the universe: the sun, planets, satellites and even apples all have gravity.Newton showed that the magnitude of gravitational force can be calculated, as long as we know the mass (the amount of matter) in each object and the distance between each object. Let's look at how gravity affects the earth and the sun.There is a great attraction between these two bodies, but the earth, because it is in motion, is able to resist this constant pull.If the Earth suddenly stopped moving in its orbit, it would begin to fall toward the sun (that is, be pulled by the sun), and after about two months of falling faster and faster, it would be swallowed by the sun.Conversely, if the sun suddenly disappeared, the earth would immediately stop moving in an elliptical orbit: it would go in a straight line and fly to the depths of the universe.As far as the current situation is concerned, the orbit of the earth is caused by the simultaneous action of the inertia of the earth's motion and the gravitational force.It can be said that the earth is constantly torn by external force and cannot fly straight, so its flight path forms a closed orbit. Newton then used gravity to infer Kepler's laws of planetary motion.The formula Newton came up with included the law of gravitation, the masses of the sun and planets, the distances between the celestial bodies, and the time of rotation.In this way, it can be shown mathematically how the planets and their satellites, which are condensed into spherical shapes by countless tons of matter, fly hundreds of millions of miles in space according to precise routes. A genius who admired Newton said that Newton was the luckiest man; there is only one universe, so only one person can discover the principles that govern it. Now, when rocket engineers shoot artificial satellites into the sky, they follow the laws discovered by Kepler and Newton.Although an artificial satellite is small, its motion around the earth is like the motion of the earth around the sun.The orbit of each artificial satellite is an ellipse. To launch a satellite into an orbit hundreds of miles above the ground, it must reach a speed of 17,000 miles per hour, because the gravity of the earth is extremely strong.The satellite needs to be subjected to a great pushing force to counteract this powerful gravitational force; it takes three or four stages of rockets to be sufficient to generate this pushing force.The trick is to manage each stage of the rocket in order to propel the satellite into orbit at the right altitude, at the right speed, and in the right direction.Newton's equation tells us: these three conditions are the three conditions, which determine the orbit of the satellite, and the satellite must be dominated by these three conditions. The rockets used to launch satellites must be manipulated extremely precisely, because the shape, size, and position of satellite orbits are completely determined by the rocket. When the rocket launches the satellite into orbit, as long as there is a slight change in altitude, speed, and direction, the orbit of the satellite will change accordingly.Some satellite launches were unsuccessful, although every stage of the rocket was functional from start to finish.This is often because the rocket propels the satellite into the orbit in the wrong direction or does not give the satellite the proper speed; the resulting orbit is then inappropriate and will lead the satellite back into the dense atmosphere.As a result, the satellite rubbed against the air, generating great heat, and turned to ashes like a burning star around it. The elliptical orbit of a satellite has two foci, only one of which is at the core of the earth. Therefore, for the earth, the position of the satellite orbit is often not as flat as a circle around the center of a circle, but skewed.The closest point in orbit to Earth is called perigee.The opposite of this is the point in the orbit farthest from the Earth, called the apogee. Now we imagine an example of a satellite moving under certain conditions.Suppose a satellite is rocketed into orbit at an altitude of 300 miles above the earth, in a direction which crosses the vertical at right angles.At an altitude of 300 miles, the resistance of the atmosphere is almost non-existent.The velocity at which the satellite is launched from the rocket into orbit is assumed to be exactly 19,000 miles per hour.This speed exceeds the speed needed to counteract the gravity of the earth.The satellite rose serenely along an arc, constantly decelerating as it was pulled by gravity.Finally, it reaches the highest point in its orbit, the apogee, at an altitude of about 1,400 miles, just opposite the launch point (where the satellite left the rocket).Then, the satellite does not descend along the descending arc of its elliptical orbit, and according to Kepler's second law, it descends faster and faster.It circles the earth, continues to accelerate, and when it reaches the point of launch (perigee of its orbit) 300 miles above the earth, it again travels at the same speed of 19,000 miles per hour as at the beginning.So, it started a second circle. The first satellites launched by the Soviet Union and Great Britain were launched into orbit at an altitude of less than 300 miles.At this altitude, there are not too many molecules in the atmosphere, but enough to cause a slight but noticeable friction.When these satellites orbited the earth again and again, the slight friction had an impact, which gradually consumed the motion of the satellites, making their orbits gradually shrink, and the satellites turned closer and closer to the earth.The life of a satellite is only a few weeks or months, and at the end it burns up as it enters a denser and denser atmosphere. The first Vanguard satellite to be successfully launched was about the size of a juan (a fruit grown in California, like a grapefruit), and its orbit was extremely wide.Its perigee is more than 300 miles above the ground, avoiding the deadly tug of the atmosphere.This small satellite is expected to orbit the Earth for more than a hundred years.This ball, which elevated man to the status of a celestial body, played a part in the drama of nature, outlived those who saw it ascend into heaven. In terms of principles, the founders of celestial mechanics, Kepler and Newton, knew everything about the motion of celestial bodies.But in their time, people did not use electricity, and the steam engine was still more than a hundred years away.Kepler and Newton wrote the laws of nature with a quill and by candlelight.Yet it was with such humble conditions that these two great philosophers laid the foundations of astronomy, and the conquest of space began with the most exciting technological advances of the modern era.