History of newton

I  INTRODUCTION

Newton, Sir Isaac (1642-1727), mathematician and physicist, one of the foremost scientific intellects of all time. Born at Woolsthorpe, near Grantham in Lincolnshire, where he attended school, he entered Cambridge University in 1661; he was elected a Fellow of Trinity College in 1667, and Lucasian Professor of Mathematics in 1669. He remained at the university, lecturing in most years, until 1696. Of these Cambridge years, in which Newton was at the height of his creative power, he singled out 1665-1666 (spent largely in Lincolnshire because of plague in Cambridge) as "the prime of my age for invention". During two to three years of intense mental effort he prepared Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) commonly known as the Principia, although this was not published until 1687.

As a firm opponent of the attempt by King James II to make the universities into Catholic institutions, Newton was elected Member of Parliament for the University of Cambridge to the Convention Parliament of 1689, and sat again in 1701-1702. Meanwhile, in 1696 he had moved to London as Warden of the Royal Mint. He became Master of the Mint in 1699, an office he retained to his death. He was elected a Fellow of the Royal Society of London in 1671, and in 1703 he became President, being annually re-elected for the rest of his life. His major work, Opticks, appeared the next year; he was knighted in Cambridge in 1705.

As Newtonian science became increasingly accepted on the Continent, and especially after a general peace was restored in 1714, following the War of the Spanish Succession, Newton became the most highly esteemed natural philosopher in Europe. His last decades were passed in revising his major works, polishing his studies of ancient history, and defending himself against critics, as well as carrying out his official duties. Newton was modest, diffident, and a man of simple tastes. He was angered by criticism or opposition, and harboured resentment; he was harsh towards enemies but generous to friends. In government, and at the Royal Society, he proved an able administrator. He never married and lived modestly, but was buried with great pomp in Westminster Abbey.

Newton has been regarded for almost 300 years as the founding examplar of modern physical science, his achievements in experimental investigation being as innovative as those in mathematical research. With equal, if not greater, energy and originality he also plunged into chemistry, the early history of Western civilization, and theology; among his special studies was an investigation of the form and dimensions, as described in the Bible, of Solomon's Temple in Jerusalem.

II  OPTICS
In 1664, while still a student, Newton read recent work on optics and light by the English physicists Robert Boyle and Robert Hooke; he also studied both the mathematics and the physics of the French philosopher and scientist René Descartes. He investigated the refraction of light by a glass prism; developing over a few years a series of increasingly elaborate, refined, and exact experiments, Newton discovered measurable, mathematical patterns in the phenomenon of colour. He found white light to be a mixture of infinitely varied coloured rays (manifest in the rainbow and the spectrum), each ray definable by the angle through which it is refracted on entering or leaving a given transparent medium. He correlated this notion with his study of the interference colours of thin films (for example, of oil on water, or soap bubbles), using a simple technique of extreme acuity to measure the thickness of such films. He held that light consisted of streams of minute particles. From his experiments he could infer the magnitudes of the transparent "corpuscles" forming the surfaces of bodies, which, according to their dimensions, so interacted with white light as to reflect, selectively, the different observed colours of those surfaces.

The roots of these unconventional ideas were with Newton by about 1668; when first expressed (tersely and partially) in public in 1672 and 1675, they provoked hostile criticism, mainly because colours were thought to be modified forms of homogeneous white light. Doubts, and Newton's rejoinders, were printed in the learned journals. Notably, the scepticism of Christiaan Huygens and the failure of the French physicist Edmé Mariotte to duplicate Newton's refraction experiments in 1681 set scientists on the Continent against him for a generation. The publication of Opticks, largely written by 1692, was delayed by Newton until the critics were dead. The book was still imperfect: the colours of diffraction defeated Newton. Nevertheless, Opticks established itself, from about 1715, as a model of the interweaving of theory with quantitative experimentation.

III  MATHEMATICS
In mathematics too, early brilliance appeared in Newton's student notes. He may have learnt geometry at school, though he always spoke of himself as self-taught; certainly he advanced through studying the writings of his compatriots William Oughtred and John Wallis, and of Descartes and the Dutch school. Newton made contributions to all branches of mathematics then studied, but is especially famous for his solutions to the contemporary problems in analytical geometry of drawing tangents to curves (differentiation) and defining areas bounded by curves (integration). Not only did Newton discover that these problems were inverse to each other, but he discovered general methods of resolving problems of curvature, embraced in his "method of fluxions" and "inverse method of fluxions", respectively equivalent to Leibniz's later differential and integral calculus. Newton used the term "fluxion" (from Latin meaning "flow") because he imagined a quantity "flowing" from one magnitude to another. Fluxions were expressed algebraically, as Leibniz's differentials were, but Newton made extensive use also (especially in the Principia) of analogous geometrical arguments. Late in life, Newton expressed regret for the algebraic style of recent mathematical progress, preferring the geometrical method of the Classical Greeks, which he regarded as clearer and more rigorous.

Newton's work on pure mathematics was virtually hidden from all but his correspondents until 1704, when he published, with Opticks, a tract on the quadrature of curves (integration) and another on the classification of the cubic curves. His Cambridge lectures, delivered from about 1673 to 1683, were published in 1707.

The Calculus Priority Dispute
Newton had the essence of the methods of fluxions by 1666. The first to become known, privately, to other mathematicians, in 1668, was his method of integration by infinite series. In Paris in 1675 Gottfried Wilhelm Leibniz independently evolved the first ideas of his differential calculus, outlined to Newton in 1677. Newton had already described some of his mathematical discoveries to Leibniz, not including his method of fluxions. In 1684 Leibniz published his first paper on calculus; a small group of mathematicians took up his ideas.

In the 1690s Newton's friends proclaimed the priority of Newton's methods of fluxions. Supporters of Leibniz asserted that he had communicated the differential method to Newton, although Leibniz had claimed no such thing. Newtonians then asserted, rightly, that Leibniz had seen papers of Newton's during a London visit in 1676; in reality, Leibniz had taken no notice of material on fluxions. A violent dispute sprang up, part public, part private, extended by Leibniz to attacks on Newton's theory of gravitation and his ideas about God and creation; it was not ended even by Leibniz's death in 1716. The dispute delayed the reception of Newtonian science on the Continent, and dissuaded British mathematicians from sharing the researches of Continental colleagues for a century.

IV  MECHANICS AND GRAVITATION 
According to the well-known story, it was on seeing an apple fall in his orchard at some time during 1665 or 1666 that Newton conceived that the same force governed the motion of the Moon and the apple. He calculated the force needed to hold the Moon in its orbit, as compared with the force pulling an object to the ground. He also calculated the centripetal force needed to hold a stone in a sling, and the relation between the length of a pendulum and the time of its swing. These early explorations were not soon exploited by Newton, though he studied astronomy and the problems of planetary motion.

Correspondence with Hooke (1679-1680) redirected Newton to the problem of the path of a body subjected to a centrally directed force that varies as the inverse square of the distance; he determined it to be an ellipse, so informing Edmond Halley in August 1684. Halley's interest led Newton to demonstrate the relationship afresh, to compose a brief tract on mechanics, and finally to write thePrincipia.

Book I of the Principia states the foundations of the science of mechanics, developing upon them the mathematics of orbital motion round centres of force. Newton identified gravitation as the fundamental force controlling the motions of the celestial bodies. He never found its cause. To contemporaries who found the idea of attractions across empty space unintelligible, he conceded that they might prove to be caused by the impacts of unseen particles.

Book II inaugurates the theory of fluids: Newton solves problems of fluids in movement and of motion through fluids. From the density of air he calculated the speed of sound waves.

Book III shows the law of gravitation at work in the universe: Newton demonstrates it from the revolutions of the six known planets, including the Earth, and their satellites. However, he could never quite perfect the difficult theory of the Moon's motion. Comets were shown to obey the same law; in later editions, Newton added conjectures on the possibility of their return. He calculated the relative masses of heavenly bodies from their gravitational forces, and the oblateness of Earth and Jupiter, already observed. He explained tidal ebb and flow and the precession of the equinoxes from the forces exerted by the Sun and Moon. All this was done by exact computation.

Newton's work in mechanics was accepted at once in Britain, and universally after half a century. Since then it has been ranked among humanity's greatest achievements in abstract thought. It was extended and perfected by others, notably Pierre Simon de Laplace, without changing its basis and it survived into the late 19th century before it began to show signs of failing. See Quantum Theory; Relativity.

V  ALCHEMY AND CHEMISTRY 
Newton left a mass of manuscripts on the subjects of alchemy and chemistry, then closely related topics. Most of these were extracts from books, bibliographies, dictionaries, and so on, but a few are original. He began intensive experimentation in 1669, continuing till he left Cambridge, seeking to unravel the meaning that he hoped was hidden in alchemical obscurity and mysticism. He sought understanding of the nature and structure of all matter, formed from the "solid, massy, hard, impenetrable, movable particles" that he believed God had created. Most importantly in the "Queries" appended to "Opticks" and in the essay "On the Nature of Acids" (1710), Newton published an incomplete theory of chemical force, concealing his exploration of the alchemists, which became known a century after his death.

VI  HISTORICAL AND CHRONOLOGICAL STUDIES
Newton owned more books on humanistic learning than on mathematics and science; all his life he studied them deeply. His unpublished "classical scholia"—explanatory notes intended for use in a future edition of the Principia—reveal his knowledge of pre-Socratic philosophy; he read the Fathers of the Church even more deeply. Newton sought to reconcile Greek mythology and record with the Bible, considered the prime authority on the early history of mankind. In his work on chronology he undertook to make Jewish and pagan dates compatible, and to fix them absolutely from an astronomical argument about the earliest constellation figures devised by the Greeks. He put the fall of Troy at 904 BC, about 500 years later than other scholars; this was not well received.

VII  RELIGIOUS CONVICTIONS AND PERSONALITY
Newton also wrote on Judaeo-Christian prophecy, whose decipherment was essential, he thought, to the understanding of God. His book on the subject, which was reprinted well into the Victorian Age, represented lifelong study. Its message was that Christianity went astray in the 4th century AD, when the first Council of Nicaea propounded erroneous doctrines of the nature of Christ. The full extent of Newton's unorthodoxy was recognized only in the present century: but although a critic of accepted Trinitarian dogmas and the Council of Nicaea, he possessed a deep religious sense, venerated the Bible and accepted its account of creation. In late editions of his scientific works he expressed a strong sense of God's providential role in nature.

VIII  PUBLICATIONS
Newton published an edition of Geographia generalis by the German geographer Varenius in 1672. His own letters on optics appeared in print from 1672 to 1676. Then he published nothing until thePrincipia (published in Latin in 1687; revised in 1713 and 1726; and translated into English in 1729). This was followed by Opticks in 1704; a revised edition in Latin appeared in 1706. Posthumously published writings include The Chronology of Ancient Kingdoms Amended (1728), The System of the World (1728), the first draft of Book III of the Principia, and Observations upon the Prophecies of Daniel and the Apocalypse of St John (1733).

more info can be found at...

http://www.newton.ac.uk/newton.html

history of Galileo Galilei

history of Galileo Galilei

Galileo Galilei was born in Pisa, Italy on February 15, 1564. He was the oldest of seven children. His father was a musician and wool trader, who wanted his son to study medicine as there was more money in medicine. At age eleven, Galileo was sent off to study in a Jesuit monastery.[Image]Galileo Galilei - Rerouted from Religon to ScienceAfter four years, Galileo had announced to his father that he wanted to be a monk. This was not exactly what father had in mind, so Galileo was hastily withdrawn from the monastery. In 1581, at the age of 17, he entered the University of Pisa to study medicine, as his father wished.Galileo Galilei - Law of the PendulumAt age twenty, Galileo noticed a lamp swinging overhead while he was in a cathedral. Curious to find out how long it took the lamp to swing back and forth, he used his pulse to time large and small swings. Galileo discovered something that no one else had ever realized: the period of each swing was exactly the same. The law of the pendulum, which would eventually be used to regulate clocks, made Galileo Galilei instantly famous.Except for mathematics, Galileo Galilei was bored with university.

Galileo's family was informed that their son was in danger of flunking out. A compromise was worked out, where Galileo would be tutored full-time in mathematics by the mathematician of the Tuscan court. Galileo's father was hardly overjoyed about this turn of events, since a mathematician's earning power was roughly around that of a musician, but it seemed that this might yet allow Galileo to successfully complete his college education. However, Galileo soon left the University of Pisa without a degree.Galileo Galilei - MathematicsTo earn a living, Galileo Galilei started tutoring students in mathematics. He did some experimenting with floating objects, developing a balance that could tell him that a piece of, say, gold was 19.3 times heavier than the same volume of water. He also started campaigning for his life's ambition: a position on the mathematics faculty at a major university. Although Galileo was clearly brilliant, he had offended many people in the field, who would choose other candidates for vacancies.Galileo Galilei - Dante's InfernoIronically, it was a lecture on literature that would turn Galileo's fortunes. The Academy of Florence had been arguing over a 100-year-old controversy: What were the location, shape, and dimensions of Dante's Inferno? Galileo Galilei wanted to seriously answer the question from the point of view of a scientist. Extrapolating from Dante's line that "[the giant Nimrod's] face was about as long/And just as wide as St. Peter's cone in Rome," Galileo deduced that Lucifer himself was 2,000 arm-length long. The audience was impressed, and within the year, Galileo had received a three-year appointment to the University of Pisa, the same university that never granted him a degree!The Leaning Tower of PisaAt the time that Galileo arrived at the University, some debate had started up on one of Aristotle's "laws" of nature, that heavier objects fell faster than lighter objects. Aristotle's word had been accepted as gospel truth, and there had been few attempts to actually test Aristotle's conclusions by actually conducting an experiment!According to legend, Galileo decided to try. He needed to be able to drop the objects from a great height.

The perfect building was right at hand--the Tower of Pisa, 54 meters tall. Galileo climbed up to the top of the building carrying a variety of balls of varying size and weight, and dumped them off of the top. They all landed at the base of the building at the same time (legend says that the demonstration was witnessed by a huge crowd of students and professors). Aristotle was wrong.However, Galileo Galilei continued to behave rudely to his colleagues, not a good move for a junior member of the faculty. "Men are like wine flasks," he once said to a group of students. "...look at....bottles with the handsome labels. When you taste them, they are full of air or perfume or rouge. These are bottles fit only to pee into!"Not surprisingly, the University of Pisa chose not to renew Galileo's contract.Necessity is the Mother of InventionGalileo Galilei moved on to the University of Padua. By 1593, he was desperate in need of additional cash. His father had died, so Galileo was the head of his family, and personally responsible for his family. Debts were pressing down on him, most notably, the dowry for one of his sisters, which was paid in installments over decades (a dowry could be thousands of crowns, and Galileo's annual salary was 180 crowns). Debtor's prison was a real threat if Galileo returned to Florence.What Galileo needed was to come up with some sort of device that could make him a tidy profit. A rudimentary thermometer (which, for the first time, allowed temperature variations to be measured) and an ingenious device to raise water from aquifers found no market. He found greater success in 1596 with a military compass that could be used to accurately aim cannonballs. A modified civilian version that could be used for land surveying came out in 1597, and ended up earning a fair amount of money for Galileo. It helped his profit margin that 1) the instruments were sold for three times the cost of manufacture, 2) he also offered classes on how to use the instrument, and 3) the actual toolmaker was paid dirt-poor wages.A good thing. Galileo needed the money to support his siblings, his mistress (a 21 year old with a reputation as a woman of easy habits), and his three children (two daughters and a boy). By 1602, Galileo's name was famous enough to help bring in students to the University, where Galileo was busily experimenting with magnetsIn Venice on a holiday in 1609, Galileo Galilei heard rumors that a Dutch spectacle-maker had invented a device that made distant objects seem near at hand (at first called the spyglass and later renamed the telescope). A patent had been requested, but not yet granted, and the methods were being kept secret, since it was obviously of tremendous military value for Holland.Galileo Galilei - SpyglassGalileo Galilei was determined to attempt to construct his own spyglass. After a frantic 24 hours of experimentation, working only on instinct and bits of rumors, never having actually *seen* the Dutch spyglass, he built a 3-power telescope. After some refinement, he brought a 10-power telescope to Venice and demonstrated it to a highly impressed Senate. His salary was promptly raised, and he was honored with proclamations.Galileo Galilei - The MoonIf he had stopped here, and become a man of wealth and leisure, Galileo Galilei might be a mere footnote in history. Instead, a revolution started when, one fall evening, the scientist trained his telescope on an object in the sky that all people at that time believed must be a perfect, smooth, polished heavenly body--the Moon. To his astonishment, Galileo Galilei viewed a surface that was uneven, rough, and full of cavities and prominences. Many people insisted that Galileo Galilei was wrong. Some of their arguments were very clever, like the mathematician who insisted that even if Galileo was seeing a rough surface on the Moon, that only meant that the entire moon had to be covered in invisible, transparent, smooth crystal.Galileo Galilei - JupiterMonths passed, and his telescopes improved. On January 7, 1610, he turned his 30 power telescope towards Jupiter, and found three small, bright stars near the planet. One was off to the west, the other two were to the east, all three in a straight line. The following evening, Galileo once again took a look at Jupiter, and found that all three of the "stars" were now west of the planet, still in a straight line!Observations over the following weeks lead Galileo to the inescapable conclusion that these small "stars" were actually small satellites that were rotating about Jupiter. If there were satellites that didn't move around the Earth, wasn't it possible that the Earth was not the center of the universe? Couldn't the Copernican idea of the Sun at the center of the solar system be correct?The Starry MessengerGalileo Galilei published his findings--as a small book titled The Starry Messenger. 550 copies were published in March of 1610, to tremendous public acclaim and excitement.Galileo Galilei - SaturnAnd there were more discoveries via the new telescope: the appearance of bumps next to the planet Saturn (Galileo thought they were companion stars; the "stars" were actually the edges of Saturn's rings), spots on the Sun's surface (though others had actually seen the spots before), and seeing Venus change from a full disk to a sliver of light.For Galileo Galilei, saying that the Earth went around the Sun changed everything since he was contradicting the teachings of the Church.

While some of the Church's mathematicians wrote that his observations were clearly correct, many members of the Church believed that he must be wrong.In December of 1613, one of the scientist's friends told him how a powerful member of the nobility said that she could not see how his observations could be true, since they would contradict the Bible. The lady quoted a passage in Joshua where God causes the Sun to stand still and lengthen the day. How could this mean anything other than that the Sun went around the Earth?Galileo Galilei - Heresy ChargesGalileo Galilei was a religious man, and he agreed that the Bible could never be wrong. However, he said, the interpreters of the Bible could make mistakes, and it was a mistake to assume that the Bible had to be taken literally.This might have been one of Galileo's major mistakes. At that time, only Church priests were allowed to interpret the Bible, or to define God's intentions. It was absolutely unthinkable for a mere member of the public to do so.And some of the Church clergy started responding, accusing him of heresy. Some credits went to the Inquisition, the Church court that investigated charges of heresy, and formally accused Galileo Galilei. This was a very serious matter. In 1600, a man named Giordano Bruno was convicted of being a heretic for believing that the earth moved about the Sun, and that there were many planets throughout the universe where life--living creations of God--existed. Bruno was burnt to death.However, Galileo was found innocent of all charges, and cautioned not to teach the Copernican system. 16 years later, all that would change.The Final TrialThe following years saw Galileo move on to work on other projects. With his telescope he watched the movements of Jupiter's moons, wrote them up as a list, and then came up with a way to use these measurements as a navigation tool. There was even a contraption that would allow a ship captain to navigate with his hands on the wheel. That is, assuming the captain didn't mind wearing what looked like a horned helmet!As another amusement, Galileo started writing about ocean tides. Instead of writing his arguments as a scientific paper, he found that it was much more interesting to have an imaginary conversation, or dialogue, between three fictional characters. One character, who would support Galileo's side of the argument, was brilliant. Another character would be open to either side of the argument.

The final character, named Simplicio, was dogmatic and foolish, representing all of Galileo's enemies who ignored any evidence that Galileo was right. Soon, he wrote up a similar dialogue called "Dialogue on the Two Great Systems of the World." This book talked about the Copernican system."Dialogue" was an immediate hit with the public, but not, of course, with the Church. The pope suspected that he was the model for Simplicio. He ordered the book banned, and also ordered the scientist to appear before the Inquisition in Rome for the crime of teaching the Copernican theory after being ordered not to do so.Galileo Galilei was 68 years old and sick. Threatened with torture, he publicly confessed that he had been wrong to have said that the Earth moves around the Sun. Legend then has it that after his confession, Galileo quietly whispered "And yet, it moves."Unlike many less famous prisoners, he was allowed to live under house arrest in his house outside of Florence. He was near one of his daughters, a nun. Until his death in 1642, he continued to investigate other areas of science. Amazingly, he even published a book on force and motion although he had been blinded by an eye infection.The Story Continues...The Church eventually lifted the ban on Galileo's Dialogue in 1822--by that time, it was common knowledge that the Earth was not the center of the Universe. Still later, there were statements by the Vatican Council in the early 1960's and in 1979 that implied that Galileo was pardoned, and that he had suffered at the hands of the Church. Finally, in 1992, three years after Galileo Galilei's namesake had been launched on its way to Jupiter, the Vatican formally and publicly cleared Galileo of any wrong doing.

Article: ptolemy

Ptolemy (aka Claudius Ptolemaeus, Ptolomaeus, Klaudios Ptolemaios, Ptolemeus) lived in Alexandria, Egypt and has an important role in the history of astronomy and geography. We know very little of Ptolemy's life, including his birth and death dates. Various sources report different years, however, the first observation made by him which we can date exactly was on 26 March 127 while the last was on 2 February 141. Some experts believe his life spanned the years 87 – 150. During his lifetime, he did much to advance the sciences of astronomy and geography.
We get a few clues about him from his name, Claudius Ptolemy, which is a mixture of the Greek Egyptian 'Ptolemy' and the Roman 'Claudius'. This seems to indicate that he was descended from a Greek family living in Egypt and that he was also a citizen of Rome. This could only have happened as a result of a Roman emperor rewarding one of his ancestors with this favor.

Around 1360, Theodore Meliteniotes claimed that Ptolemy was born in Hermiou (Northern Egypt. Alexandria is slightly farther south.) Due to the fact that Meliteniotes lived more than a thousand years after Ptolemy, and there is no corroboration, there is a lot of skepticism. In fact no evidence exists that he ever lived anywhere other than Alexandria.

The video describes different views of ptolemy in understanding planetoru model and the phases of venus

keplers laws

Kepler's Three Laws

In the early 1600s, Johannes Kepler proposed three laws of planetary motion. Kepler was able to summarize the carefully collected data of his mentor - Tycho Brahe - with three statements that described the motion of planets in a sun-centered solar system. Kepler's efforts to explain the underlying reasons for such motions are no longer accepted; nonetheless, the actual laws themselves are still considered an accurate description of the motion of any planet and any satellite.
Kepler's three laws of planetary motion can be described as follows:

• The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses)
• An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas)
• The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (The Law of Harmonies)

Kepler's first law - sometimes referred to as the law of ellipses - explains that planets are orbiting the sun in a path described as an ellipse. An ellipse can easily be constructed using a pencil, two tacks, a string, a sheet of paper and a piece of cardboard. Tack the sheet of paper to the cardboard using the two tacks. Then tie the string into a loop and wrap the loop around the two tacks. Take your pencil and pull the string until the pencil and two tacks make a triangle (see diagram at the right). Then begin to trace out a path with the pencil, keeping the string wrapped tightly around the tacks. The resulting shape will be an ellipse. An ellipse is a special curve in which the sum of the distances from every point on the curve to two other points is a constant. The two other points (represented here by the tack locations) are known as thefoci of the ellipse. The closer together that these points are, the more closely that the ellipse resembles the shape of a circle. In fact, a circle is the special case of an ellipse in which the two foci are at the same location. Kepler's first law is rather simple - all planets orbit the sun in a path that resembles an ellipse, with the sun being located at one of the foci of that ellipse.
Kepler's second law - sometimes referred to as the law of equal areas - describes the speed at which any given planet will move while orbiting the sun. The speed at which any planet moves through space is constantly changing. A planet moves fastest when it is closest to the sun and slowest when it is furthest from the sun. Yet, if an imaginary line were drawn from the center of the planet to the center of the sun, that line would sweep out the same area in equal periods of time. For instance, if an imaginary line were drawn from the earth to the sun, then the area swept out by the line in every 31-day month would be the same. This is depicted in the diagram below. As can be observed in the diagram, the areas formed when the earth is closest to the sun can be approximated as a wide but short triangle; whereas the areas formed when the earth is farthest from the sun can be approximated as a narrow but long triangle. These areas are the same size. Since thebase of these triangles are shortest when the earth is farthest from the sun, the earth would have to be moving more slowly in order for this imaginary area to be the same size as when the earth is closest to the sun.

Kepler's third law - sometimes referred to as the law of harmonies- compares the orbital period and radius of orbit of a planet to those of other planets. Unlike Kepler's first and second laws that describe the motion characteristics of a single planet, the third law makes a comparison between the motion characteristics of different planets. The comparison being made is that the ratio of the squares of the periods to the cubes of their average distances from the sun is the same for every one of the planets. As an illustration, consider the orbital period and average distance from sun (orbital radius) for Earth and mars as given in the table below.

Planet	Period (s)	Average Dist. (m)	T2/R3 (s2/m3)
Earth	3.156 x 107 s	1.4957 x 1011	2.977 x 10-19
Mars	5.93 x 107 s	2.278 x 1011	2.975 x 10-19

Observe that theT²/R³ratio is the same for Earth as it is for mars. In fact, if the sameT²/R³ratio is computed for the other planets, it can be found that thisratio is nearly the same value for all the planets (see table below). Amazingly, every planet has the sameT²/R³ratio.

Planet	Period (yr)	Ave. Dist. (au)	T2/R3 (yr2/au3)
Mercury	0.241	0.39	0.98
Venus	.615	0.72	1.01
Earth	1.00	1.00	1.00
Mars	1.88	1.52	1.01
Jupiter	11.8	5.20	0.99
Saturn	29.5	9.54	1.00
Uranus	84.0	19.18	1.00
Neptune	165	30.06	1.00
Pluto	248	39.44	1.00

(NOTE: The average distance value is given in astronomical units where 1 a.u. is equal to the distance from the earth to the sun - 1.4957 x 10¹¹ m. The orbital period is given in units of earth-years where 1 earth year is the time required for the earth to orbit the sun - 3.156 x 10⁷ seconds. )

Kepler's third law provides an accurate description of the period and distance for a planet's orbits about the sun. Additionally, the same law that describes the T²/R³ratio for the planets' orbits about the sun also accurately describes theT²/R³ratio for any satellite (whether a moon or a man-made satellite) about any planet. There is something much deeper to be found in thisT²/R³ratio - something that must relate to basic fundamental principles of motion, these principles will be investigated as we draw a connection between the circular motion principles discussed in Lesson 1 and the motion of a satellite.

history of ptolemy

One of the most influential Greek astronomers and geographers of his time, Ptolemy propounded the geocentric theory in a form that prevailed for 1400 years. However, of all the ancient Greek mathematicians, it is fair to say that his work has generated more discussion and argument than any other. We shall discuss the arguments below for, depending on which are correct, they portray Ptolemy in very different lights. The arguments of some historians show that Ptolemy was a mathematician of the very top rank, arguments of others show that he was no more than a superb expositor, but far worse, some even claim that he committed a crime against his fellow scientists by betraying the ethics and integrity of his profession.

We know very little of Ptolemy's life. He made astronomical observations from Alexandria in Egypt during the years AD 127-41. In fact the first observation which we can date exactly was made by Ptolemy on 26 March 127 while the last was made on 2 February 141. It was claimed by Theodore Meliteniotes in around 1360 that Ptolemy was born in Hermiou (which is in Upper Egypt rather than Lower Egypt where Alexandria is situated) but since this claim first appears more than one thousand years after Ptolemy lived, it must be treated as relatively unlikely to be true. In fact there is no evidence that Ptolemy was ever anywhere other than Alexandria.

His name, Claudius Ptolemy, is of course a mixture of the Greek Egyptian 'Ptolemy' and the Roman 'Claudius'. This would indicate that he was descended from a Greek family living in Egypt and that he was a citizen of Rome, which would be as a result of a Roman emperor giving that 'reward' to one of Ptolemy's ancestors.

We do know that Ptolemy used observations made by 'Theon the mathematician', and this was almost certainly Theon of Smyrna who almost certainly was his teacher. Certainly this would make sense since Theon was both an observer and a mathematician who had written on astronomical topics such as conjunctions, eclipses, occultations and transits. Most of Ptolemy's early works are dedicated to Syrus who may have also been one of his teachers in Alexandria, but nothing is known of Syrus.

If these facts about Ptolemy's teachers are correct then certainly in Theon he did not have a great scholar, for Theon seems not to have understood in any depth the astronomical work he describes. On the other hand Alexandria had a tradition for scholarship which would mean that even if Ptolemy did not have access to the best teachers, he would have access to the libraries where he would have found the valuable reference material of which he made good use.

Ptolemy's major works have survived and we shall discuss them in this article. The most important, however, is the Almagest which is a treatise in thirteen books. We should say straight away that, although the work is now almost always known as the Almagest that was not its original name. Its original Greek title translates as The Mathematical Compilation but this title was soon replaced by another Greek title which means The Greatest Compilation. This was translated into Arabic as "al-majisti" and from this the title Almagest was given to the work when it was translated from Arabic to Latin.

The Almagest is the earliest of Ptolemy's works and gives in detail the mathematical theory of the motions of the Sun, Moon, and planets. Ptolemy made his most original contribution by presenting details for the motions of each of the planets. The Almagest was not superseded until a century after Copernicus presented his heliocentric theory in the De revolutionibus of 1543. Grasshoff writes in

Ptolemy's "Almagest" shares with Euclid's "Elements" the glory of being the scientific text longest in use. From its conception in the second century up to the late Renaissance, this work determined astronomy as a science. During this time the "Almagest" was not only a work on astronomy; the subject was defined as what is described in the "Almagest".

Ptolemy describes himself very clearly what he is attempting to do in writing the work

We shall try to note down everything which we think we have discovered up to the present time; we shall do this as concisely as possible and in a manner which can be followed by those who have already made some progress in the field. For the sake of completeness in our treatment we shall set out everything useful for the theory of the heavens in the proper order, but to avoid undue length we shall merely recount what has been adequately established by the ancients. However, those topics which have not been dealt with by our predecessors at all, or not as usefully as they might have been, will be discussed at length to the best of our ability.

Ptolemy first of all justifies his description of the universe based on the earth-centred system described by Aristotle. It is a view of the world based on a fixed earth around which the sphere of the fixed stars rotates every day, this carrying with it the spheres of the sun, moon, and planets. Ptolemy used geometric models to predict the positions of the sun, moon, and planets, using combinations of circular motion known as epicycles. Having set up this model, Ptolemy then goes on to describe the mathematics which he needs in the rest of the work. In particular he introduces trigonometrical methods based on the chord function Crd (which is related to the sine function by sin a = (Crd 2a)/120).

Ptolemy devised new geometrical proofs and theorems. He obtained, using chords of a circle and an inscribed 360-gon, the approximation

π = 3 ¹⁷/₁₂₀ = 3.14166

and, using √3 = chord 60°,

√3 = 1.73205.

He used formulae for the Crd function which are analogous to our formulae for sin(a + b), sin(a - b) and sin a/2 to create a table of the Crd function at intervals of ¹/₂ a degree.

This occupies the first two of the 13 books of the Almagest and then, quoting again from the introduction, we give Ptolemy's own description of how he intended to develop the rest of the mathematical astronomy in the work (see for example

[After introducing the mathematical concepts] we have to go through the motions of the sun and of the moon, and the phenomena accompanying these motions; for it would be impossible to examine the theory of the stars thoroughly without first having a grasp of these matters. Our final task in this way of approach is the theory of the stars. Here too it would be appropriate to deal first with the sphere of the so-called 'fixed stars', and follow that by treating the five 'planets', as they are called.

In examining the theory of the sun, Ptolemy compares his own observations of equinoxes with those of Hipparchus and the earlier observations Meton in 432 BC. He confirmed the length of the tropical year as ¹/₃₀₀ of a day less than 365 ¹/₄ days, the precise value obtained by Hipparchus. Since, as Ptolemy himself knew, the accuracy of the rest of his data depended heavily on this value, the fact that the true value is ¹/₁₂₈ of a day less than 365 ¹/₄days did produce errors in the rest of the work. We shall discuss below in more detail the accusations which have been made against Ptolemy, but this illustrates clearly the grounds for these accusations since Ptolemy had to have an error of 28 hours in his observation of the equinox to produce this error, and even given the accuracy that could be expected with ancient instruments and methods, it is essentially unbelievable that he could have made an error of this magnitude. A good discussion of this strange error is contained in the excellent article

Based on his observations of solstices and equinoxes, Ptolemy found the lengths of the seasons and, based on these, he proposed a simple model for the sun which was a circular motion of uniform angular velocity, but the earth was not at the centre of the circle but at a distance called the eccentricity from this centre. This theory of the sun forms the subject of Book 3 of the Almagest.

In Books 4 and 5 Ptolemy gives his theory of the moon. Here he follows Hipparchus who had studied three different periods which one could associate with the motion of the moon. There is the time taken for the moon to return to the same longitude, the time taken for it to return to the same velocity (the anomaly) and the time taken for it to return to the same latitude. Ptolemy also discusses, as Hipparchus had done, the synodic month, that is the time between successive oppositions of the sun and moon. In Book 4 Ptolemy gives Hipparchus's epicycle model for the motion of the moon but he notes, as in fact Hipparchus had done himself, that there are small discrepancies between the model and the observed parameters. Although noting the discrepancies, Hipparchus seems not to have worked out a better model, but Ptolemy does this in Book 5 where the model he gives improves markedly on the one proposed by Hipparchus. An interesting discussion of Ptolemy's theory of the moon is given in

Having given a theory for the motion of the sun and of the moon, Ptolemy was in a position to apply these to obtain a theory of eclipses which he does in Book 6. The next two books deal with the fixed stars and in Book 7 Ptolemy uses his own observations together with those of Hipparchus to justify his belief that the fixed stars always maintain the same positions relative to each other. He wrote

If one were to match the above alignments against the diagrams forming the constellations on Hipparchus's celestial globe, he would find that the positions of the relevant stars on the globe resulting from the observations made at the time of Hipparchus, according to what he recorded, are very nearly the same as at present.

In these two book Ptolemy also discusses precession, the discovery of which he attributes to Hipparchus, but his figure is somewhat in error mainly because of the error in the length of the tropical year which he used. Much of Books 7 and 8 are taken up with Ptolemy's star catalogue containing over one thousand stars.

The final five books of the Almagest discuss planetary theory. This must be Ptolemy's greatest achievement in terms of an original contribution, since there does not appear to have been any satisfactory theoretical model to explain the rather complicated motions of the five planets before the Almagest. Ptolemy combined the epicycle and eccentric methods to give his model for the motions of the planets. The path of a planet P therefore consisted of circular motion on an epicycle, the centre C of the epicycle moving round a circle whose centre was offset from the earth. Ptolemy's really clever innovation here was to make the motion of C uniform not about the centre of the circle around which it moves, but around a point called the equant which is symmetrically placed on the opposite side of the centre from the earth.

The planetary theory which Ptolemy developed here is a masterpiece. He created a sophisticated mathematical model to fit observational data which before Ptolemy's time was scarce, and the model he produced, although complicated, represents the motions of the planets fairly well.

Toomer sums up the Almagest in as follows:-

As a didactic work the "Almagest" is a masterpiece of clarity and method, superior to any ancient scientific textbook and with few peers from any period. But it is much more than that. Far from being a mere 'systemisation' of earlier Greek astronomy, as it is sometimes described, it is in many respects an original work.

We will return to discuss some of the accusations made against Ptolemy after commenting briefly on his other works. He published the tables which are scattered throughout the Almagest separately under the title Handy Tables. These were not merely lifted from the Almagest however but Ptolemy made numerous improvements in their presentation, ease of use and he even made improvements in the basic parameters to give greater accuracy. We only know details of the Handy Tables through the commentary by Theon of Alexandria but in the author shows that care is required since Theon was not fully aware of Ptolemy's procedures.

Ptolemy also did what many writers of deep scientific works have done, and still do, in writing a popular account of his results under the title Planetary Hypothesis. This work, in two books, again follows the familiar route of reducing the mathematical skills needed by a reader. Ptolemy does this rather cleverly by replacing the abstract geometrical theories by mechanical ones. Ptolemy also wrote a work on astrology. It may seem strange to the modern reader that someone who wrote such excellent scientific books should write on astrology. However, Ptolemy sees it rather differently for he claims that the Almagest allows one to find the positions of the heavenly bodies, while his astrology book he sees as a companion work describing the effects of the heavenly bodies on people's lives.

In a book entitled Analemma he discussed methods of finding the angles need to construct a sundial which involves the projection of points on the celestial sphere. In Planisphaerium he is concerned with stereographic projection of the celestial sphere onto a plane. This is discussed in  where it is stated:-

In the stereographic projection treated by Ptolemy in the "Planisphaerium" the celestial sphere is mapped onto the plane of the equator by projection from the south pole. Ptolemy does not prove the important property that circles on the sphere become circles on the plane.

Ptolemy's major work Geography, in eight books, attempts to map the known world giving coordinates of the major places in terms of latitude and longitude. It is not surprising that the maps given by Ptolemy were quite inaccurate in many places for he could not be expected to do more than use the available data and this was of very poor quality for anything outside the Roman Empire, and even parts of the Roman Empire are severely distorted. In  Ptolemy is described as:-

... a man working [on map-construction] without the support of a developed theory but within a mathematical tradition and guided by his sense of what is appropriate to the problem.

Another work on Optics is in five books and in it Ptolemy studies colour, reflection, refraction, and mirrors of various shapes. Toomer comments in

The establishment of theory by experiment, frequently by constructing special apparatus, is the most striking feature of Ptolemy's "Optics". Whether the subject matter is largely derived or original, "The Optics" is an impressive example of the development of a mathematical science with due regard to physical data, and is worthy of the author of the "Almagests

An English translation, attempting to remove the inaccuracies introduced in the poor Arabic translation which is our only source of the Optics is given in

The first to make accusations against Ptolemy was Tycho Brahe. He discovered that there was a systematic error of one degree in the longitudes of the stars in the star catalogue, and he claimed that, despite Ptolemy saying that it represented his own observations, it was merely a conversion of a catalogue due to Hipparchus corrected for precession to Ptolemy's date. There is of course definite problems comparing two star catalogues, one of which we have a copy of while the other is lost.

After comments by Laplace and Lalande, the next to attack Ptolemy vigorously was Delambre. He suggested that perhaps the errors came from Hipparchus and that Ptolemy might have done nothing more serious than to have failed to correct Hipparchus's data for the time between the equinoxes and solstices. However Delambre then goes on to say

One could explain everything in a less favourable but all the simpler manner by denying Ptolemy the observation of the stars and equinoxes, and by claiming that he assimilated everything from Hipparchus, using the minimal value of the latter for the precession motion.

However, Ptolemy was not without his supporters by any means and further analysis led to a belief that the accusations made against Ptolemy by Delambre were false. Boll writing in 1894 says

To all appearances, one will have to credit Ptolemy with giving an essentially richer picture of the Greek firmament after his eminent predecessors.

Vogt showed clearly in his important paper that by considering Hipparchus's Commentary on Aratus and Eudoxus and making the reasonable assumption that the data given there agreed with Hipparchus's star catalogue, then Ptolemy's star catalogue cannot have been produced from the positions of the stars as given by Hipparchus, except for a small number of stars where Ptolemy does appear to have taken the data from Hipparchus. Vogt writes:-

This allows us to consider the fixed star catalogue as of his own making, just as Ptolemy himself vigorously states.

The most recent accusations of forgery made against Ptolemy came from Newton in  He begins this book by stating clearly his views:-

This is the story of a scientific crime. ... I mean a crime committed by a scientist against fellow scientists and scholars, a betrayal of the ethics and integrity of his profession that has forever deprived mankind of fundamental information about an important area of astronomy and history.

Towards the end Newton, having claimed to prove every observation claimed by Ptolemy in the Almagest was fabricated, writes 

[Ptolemy] developed certain astronomical theories and discovered that they were not consistent with observation. Instead of abandoning the theories, he deliberately fabricated observations from the theories so that he could claim that the observations prove the validity of his theories. In every scientific or scholarly setting known, this practice is called fraud, and it is a crime against science and scholarship.

Although the evidence produced by Brahe, Delambre, Newton and others certainly do show that Ptolemy's errors are not random, this last quote from believe, a crime against Ptolemy (to use Newton's own words). The book is written to study validity of these accusations and it is a work which I strongly believe gives the correct interpretation. Grasshoff writes:-

... one has to assume that a substantial proportion of the Ptolemaic star catalogue is grounded on those Hipparchan observations which Hipparchus already used for the compilation of the second part of his "Commentary on Aratus". Although it cannot be ruled out that coordinates resulting from genuine Ptolemaic observations are included in the catalogue, they could not amount to more than half the catalogue.

... the assimilation of Hipparchan observations can no longer be discussed under the aspect of plagiarism. Ptolemy, whose intention was to develop a comprehensive theory of celestial phenomena, had no access to the methods of data evaluation using arithmetical means with which modern astronomers can derive from a set of varying measurement results, the one representative value needed to test a hypothesis. For methodological reason, then, Ptolemy was forced to choose from a set of measurements the one value corresponding best to what he had to consider as the most reliable data. When an intuitive selection among the data was no longer possible ... Ptolemy had to consider those values as 'observed' which could be confirmed by theoretical predictions.

As a final comment we quote the epigram which is accepted by many scholars to have been written by Ptolemy himself, and it appears in Book 1 of the Almagest, following the list of contents

Well do I know that I am mortal, a creature of one day.
But if my mind follows the winding paths of the stars
Then my feet no longer rest on earth, but standing by
Zeus himself I take my fill of ambrosia, the divine dish.

celestial arrangements in space

Its the toughest thing why everyday sun rises in the east and what made earth and other planets and other celestial objects to be placed and mobiled at same place in the same orbit everyday.here the matter comes into existance, that it is clear that whatever may be the quantity of conservation of matter, the force remains same between the two or more more objects for a constant distance. that is it mean that the force depends upon the rotation of the two bodies or if there is a momentum relative to each other. since for a constant distance there may be a different force exists if there is a change in the quantity of matter.so with respect to the relative motion of the body, the force between the objects depend.so, cosmology of universe can be compelled with this force and conservation of matter.
        Due to the explosion of the liquisol matter,the stars and other self luminous and non luminous bodies have been created. due to this there developed a differential temperatures in different points in space. due to this differentiation  and nature of the planets or celestial objects placed at certain temperatures. Due to this inequalities in space, a different type of gases evolved between the layers of the atmosphere.
       Noticably its noticed that after the above versal point, there took place one more collision in sun which exploded certain type of luminous objects called stars, which are more bigger in radius than earth which got settled very far distance to the very induvidual planets. this explosion is because of the above mentioned versal and the process is to say that these gasess and other attractive forces between these celestial objects there developed some clouds in the solar system with some initial temperatures as 4000 degres C.certainly,the temperature increased to one lac degree C.,again an explosion took place where this stars come out of explosion.
so let us discuss this in more brief which needs histories and philosophies to move further
   

basic cosmology

coming to the point of galaxies, these are formed because of thethe exploitation itself, where the first outshred material in the expamsion of universe or formation of universeare these galaxies.these galaxies have more eminent and prominrnt role for the further discussion for the study of universe.these galaxies also plays a vital role to describe the cosmology of universe.
in this universe matter converting to energy and energy converting into matter takes place completely and continuously.,this is what we call in our general life as "Law of conservation of Energy"It's not to say that these takes place only on the law of conservation of Energy, but there are many principles reason for exploision of homogenius and heterogenius particle to form these galaxies with different conservative law.On the basis of above principle there developed a gravitational field in every planet induvidually and a constant force developed between earth, sun and other celestial objects in the system and space.the classicla defination off galaxies says that "Galaxies are large systems of stars and interstellar matter, typically containing several million to some trillion stars, of masses between several million and several trillion times that of our Sun, of an extension of a few thousands to several 100,000s light years, typically separated by millions of light years distance"
we will discuss further the classification of galaxies in detail in the further forum