The story of how Physics was born out of Astronomy
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This is the story of how, in the 150 years from 1570 AD to 1720 AD, Tycho Brahe, Kepler, Galileo and Newton changed the ideas that people held about the Universe and the laws of nature.
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Ptolemy
It was the time when everybody including astronomers believed that the Sun and all the planets went around our Earth. The idea that the Earth was the center of the Universe was the basis of this belief. This was called Ptolemy's theory. For, about two thousand years ago, the Greek astronomer Ptolemy who lived during 85 to 165 AD used this theory to calculate the paths of the Sun and the planets around the Sun.
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All the paths did not lie in circles. During that period, scientists had already determined the times and angles in the sky where the planets were seen. That data did not agree with circular orbits. Ptolemy constructed smaller circles (called epicircles) going on the big circle. If the planets are made to move on the epicircles, the data fitted better. If it did not, he made still smaller circle to go on the older small circle. Thus the Sun and the planets were made to go on smaller circles that go on bigger circles. This was called Ptolemy's theory and this theory was believed for 1400 years.
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Copernicus
Copernicus, an astronomer who lived during 1473 to 1543, had the idea that Sun and planets do not go around the Earth, but all the planets and the Earth go around the Sun. This theory is called Copernicus's theory. But, since this was considered to be contrary to the tenets of Christianity, Copernicus was afraid of making the Christian Church angry. So Copernicus did not publish his ideas during his lifetime. Only after his death his book bearing his theory was published.
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Which is correct, Ptolemy's theory or Copernicus's? Is Earth the center of the Universe or do the planets including Earth go around the Sun? This question was raised and debated by many astronomers, but nobody knew the answer.
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Tycho Brahe
Tycho Brahe (1546-1601) was closely related to the royal family and was wealthy. He became interested in Astronomy ever since he saw a solar eclipse when he was young. His interest and enthusiasm became a passion. Using his wealth and his relationship to royalty, he constructed a castle in his own island and spent his whole life in gazing at the sky.
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He gazed at the planets Mars, Mercury, Jupiter, Venus, and Saturn every night and recorded their positions and the times. He prepared tables of all this data. Until then nobody had such precise data about the planets. This was many years before telescope was invented. Tycho Brahe's labour and achievements are truly breath-taking.
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Kepler
Next came Johannes Kepler (1571 to 1630) who was born in Germany.His life was quite opposite to that of Tycho Brahe. He belonged to a poor family. We do not know whether he really believed in astrology, but those in the royal family believed in it. So Kepler could earn a little by preparing horoscopes for the members of the royal family. His mother was branded as a witch and punished. His efforts to save her did not succeed. We can infer the nature of the prevailing environment from this.
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Kepler was the opposite of Tycho in many other respects also. Tycho was not interested in mathematics. Kepler was a good mathematician. Kepler had imagined many ideas on the paths of planets. Tycho had no such interest. His passion was fixed only on the observation of the planetary positions. In this he was superb.
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Kepler found the correct and complete answer to the question as to which is correct, Ptolemy's geocentric theory or Copernicus's heliocentric theory. But the basis of Kepler's answer was Tycho's observations.
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It was Kepler who was the first to realize that it is necessary to know the planetary positions accurately, for arriving at the correct answer. Planetary
positions at different times were known for 2000 years, but their accuracy was not enough. The first astronomer to measure them with sufficient accuracy was Tycho Brahe. The tables of planetary positions became famous as Tycho-Tables. So Kepler wrote to Tycho requesting him to give the tables to help his research. Tycho refused.
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In spite of many attempts, Kepler could not succeed. Finally Kepler went and joined Tycho as his assistant. In that capacity he tried to get the tables. But the old man did not budge.
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Finally, Time came to Kepler's rescue. Tycho Brahe died. The tables came to the hands of Kepler.
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Kepler used Tycho's tables and his knowledge of mathematics and determined the paths of planets. The famous Kepler's laws on planetary motion are the following.
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1. All the planets including Earth go around the Sun, but not in circular orbits. The orbits are elliptical with Sun at one of the foci. (A circle has one center, whereas an ellipse has two centres called foci.)
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2. If we draw a straight line connecting Sun to a planet, that line sweeps equal areas in equal times. In other words, the aerial velocity of the planet
is constant.
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3. The time period that a planet takes to go around the Sun once is proportional to the 3/2 power of the length of the larger diameter called major axis of the ellipse. Thus Kepler discovered that all the planets go around the Sun in elliptic orbits. Ptolemy's circle and epicircles were thrown away.
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Kepler did not regard his three laws as his important discovery and buried them deep in his book. That distinction he gave to another thing which is described below.
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Everybody knows that cube has 6 faces that are regular. That is, each face is a square of the same size. So cube is called a regular solid. How many regular solids exist?
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Two thousand years ago, Greek geometers had discovered that there are only 5 regular solids. They are called Platonic solids. They are tetrahedron, square, octohedran, dodecahedron and icasohedron. They have 4,6,8,12 and 20 faces respectively.
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Before he discovered the elliptic orbits of the planets, Kepler put the circular orbits of Saturn, Jupiter, Mars, Venus, Earth and Mercury on 6 spheres. Between these 6 spheres there were 5 intervals. He fitted the 5 Platonic solids in these 5 intervals. Everything seemed to fit. So Kepler thought he had discovered the secret of the Universe and regarded this as his greatest discovery. He gave it the pride of place in his book.
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In the history of Science, the Platonic solids that Kepler fitted and his secret of the Universe suffered the same fate as Ptolemy's epicircles. They were thrown away. Kepler's three laws on planetary motion have been accepted as correct and have become a corner stone of Astronomy.
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Galileo
Many might have heard about Galileo (1564-1642) who lived In Italy 400 years ago. He was the first astronomer who looked at the Moon, the planets like Jupiter and Mars and solved their mysteries and puzzles.
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He found that Moon's surface is covered by high mountains and deep craters and it is also like our Earth a sphere made of rock and soil and so it is not divine. He inferred that Venus goes around the Sun since its phases wax and wan like Moon. He discovered many satellites going around Jupiter. He concluded that all these phenomena prove the Copernican theory.
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Galileo announced to the whole world "Copernicus's heliocentric theory is correct and Ptolemy's geocentric theory is wrong. Earth and the other planets go around the Sun."
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Since the truth that Earth is not the center of the Universe, but goes around the Sun was considered to be contrary to the tenets of Christianity, Galileo was punished. He was put in prison.
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It was Copernicus who was the first to realize that heliocentric system is correct. But he was afraid of the Church and did not publish his views. As we said already, his book containing his views came out only after his death.
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But Galileo did not have any fear. Infact he did not hesitate to even ridicule the churchmen. This is one more reason for his punishment.
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In any case, what Galileo did for Science was very great. In those days scholars wrote their books only in Latin language. Since Galileo wanted laymen also to understand his scientific discoveries, he wrote his books in Italian. He was very skilled in explaining difficult scientific matters in easy language.
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Since the time of Aristotle for 2000 years, it was believed that heavier objects fall down to the ground faster than lighter objects. Galileo dropped a heavy and a light object from the leaning tower of Pisa and showed that they fell to the ground at the same time. An idea that was believed for two thousand years was proved to be wrong by Galileo by a simple experiment. Thus Galileo demonstrated the importance of experiments.
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That is not all. Galileo discovered that all bodies moving because of gravitation increase their speeds to the same extent. The heavy Moon and a stone that we drop from a height acquire the same acceleration. Acceleration due to gravitation does not depend on the mass of the object.
It is this which became the seed for the construction of the theory of General Relativity by Einstein 300 years later.
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An important event did not take place - that is the meeting of Kepler and Galileo. Ever since Kepler heard that by looking through some instrument Galileo discovered many things about Moon and the planets he wanted to meet Galileo and see that instrument. Although he wrote many times, Galileo did not even reply.
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Another achievement of Galileo was his demonstration of the importance of mathematics through his explanation of many things in physics through simple mathematics. We already saw how he demonstrated the importance of experiments. So we may take the following as Galileo's laws:
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1. Laws of Nature are written in the language of Mathematics.
2. But those laws can be proved disproved only by experiments or direct observation.
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Only by following these laws that Science, in particular, Physics could progress.
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Newton
Then came Isaac Newton (1642-1726) who attained the pinnacle of achievements and fame. Galileo died in 1642. Newton was born in the same year. The revolution in Physics started by Galileo was successfully completed by Newton.
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Newton's creations are two. One, the laws of motion of all material bodies, second, the law of universal gravitation between all material bodies.
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Newton's laws of motion:
1.Any body which is at rest will continue to be at rest or, if it is moving it will continue to move in a straight line with the same speed unless an external force acts on it.
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2.If a force acts on it, its velocity will increase. The rate of increase of the velocity or the acceleration will be given by the formula:
mass of the body x acceleration = Force
Acceleration will be in the direction of the force.
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3.For every action there is an equal but opposite reaction.
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Newton's law of gravitation:
Every material body attracts another body by the force of gravitation. Its magnitude is given by the formula:
Force = G x M x m / r x r.
Here the masses of the two bodies are M and m. r is the distance between the two bodies.
G is a universal constant.
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In order to calculate speed and acceleration precisely, Newton created Calculus. This is a great creation. Later, Mathematics, Physics and Engineering progressed only through calculus.
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Through the creation of calculus, Newton became a great mathematician also (apart from being a great physicist). Another great mathematician Leibnitz from Germany also discovered calculus. Who discovered it first, Newton or Leibnitz? This debate is still going on.
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We said Galileo emphasized the importance of mathematics. Newton's calculus confirmed Galileo's statement very forcefully.
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From his laws of motion and law of gravitation, Newton derived Kepler's three laws of planetary motion. Thus it became clear that the elliptic orbits of the planets and the other two laws of Kepler are due to the gravitational force of the Sun.
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To go further, we need some mathematics. This will also show that there is no Physics without Mathematics. Those who know mathematics will understand this easily.
If others go over it even superficially, they will get some idea.
We rewrite Newton's second law of motion as
ma = F (1).
Here m is the mass, a is the acceleration and F is the force.
We rewrite the law of gravitation also:
F = G Mm/rr (2).
Here F is the gravitational force, M and m are the masses of the two bodies. r is the
distance between them.
Equations (1) and (2) can be combined into the form:
ma = GMm/rr (3).
If we divide both sides of this equation by m, we get
a = GM/rr (4).
In the equation (4), the mass m does not occur. Eq (4) gives the acceleration suffered by any body due to the gravitational force of another body of mass M. It does not depend on the mass m of the body. This is what Galileo discovered by his experiment. Thus Newton's law of motion and law of gravitation together contain the truth discovered by Galileo. We already mentioned how this discovery of Galileo got enshrined in Einstein's
General Theory of Relativity.
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Either by throwing a stone upwards and measuring the speed with which it falls on the ground or by by measuring the speed with which an apple falls to the ground from the tree or by measuring the time taken by a cylinder when it rolls down an inclined plane or by measuring the period of oscillation of a pendulum, we can determine the acceleration due to Earth's gravity. It is 980 centimetre per second per second.
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We can illustrate the important discovery of Newton that gravitational force decreases if the distance increases and that this decrease is inversely proportional to the distance multiplied by itself, by an example.
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The acceleration due to Earth's gravity is given in Eq (4). As we mentioned above, this acceleration on the surface of the Earth is 980 cm per sec per sec. The surface of the Earth is at a distance of 6000 kilometre from its center. The distance of Moon is about 60 times this distance. So the acceleration of the Moon must be smaller than that of the falling apple by a factor 1/(60 x 60) = 1/3600.
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Moon does not go in a straight line. The path is curved because of the acceleration due to Earth's gravity. From the period of Moon going around the Earth and its distance from the Earth, this acceleration can be calculated. Thus the above ratio 1/3600 can be verified.
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This is the simplest example for verifying Newton's inverse square (1/rr) law of force. It is said that Newton got the idea of gravitation when an apple fell over his head, while seated under the tree. That is why we have given the comparison of the falling apple with the circular motion of the Moon.
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Through his laws Newton proved that the apple falling down from the tree, Moon going around Earth, Earth and all other planets going around the Sun, in fact all material bodies, whether they are terrestrial, or celestial, obey the same Laws of Nature. He also proved that all these motions can be explained through mathematics and human brain is capable of understanding all of it. This is what became the basis for the growth of Physics and in fact all of Science.
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Tycho and Kepler had one leg on the era of astrology and other such superstition and another leg on the opening era of modern Science. It was Galileo who cleared all the cobwebs of superstition and fully opened the gates of Science. Newton strengthened the path, progressed rapidly and gave a treasure house of fantastic discoveries to the world.