8.1 Potted biography. 8 Isaac Newton. Rural background. Woolsthorpe Manor. School years. Cambridge University

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8 Isaac Newton 8.1 Potted biography Rural background Woolsthorpe Manor 1642: born in Lincolnshire, East Midlands of England. He was a small & weak baby. Father died before birth.

1 8 Isaac Newton 8.1 Potted biography Rural background Woolsthorpe Manor 1642: born in Lincolnshire, East Midlands of England. He was a small & weak baby. Father died before birth. Mother remarried when he was 2, and moved to live with new husband, leaving N. with his grandparents on the farm until he was 12. Indifferent performance at school until there was an altercation with another student, after which time N. applied himself and came top of the class. Major interest was making models and mechanical toys, but also was always absorbed in reading, and developed a life-long habit of keeping a diary. School years Left school at 16 and was meant to take over running the farm, but showed no aptitude or interest and was a disaster. His mother realized that Newton should go to university--with strong encouragement of his school headmaster, and so arranged for him to finish school. This required boarding with a family in nearby town of Grantham. Husband of this family was a pharmacist and Newton developed a lifelong interest in chemistry, as well as doctoring himself with various chemical remedies. Also fell in love with a Miss Storey, a stepdaughter of his host, and became engaged to marry her ca Cambridge University 1661: went to Trinity College Cambridge as a sizar. At this time Cambridge was rather backward intellectually, and new ideas of Copernicus, Galileo, Kepler, Descartes largely hadn t penetrated: scholarship was focused on Aristotle and on voluminous theological studies. However, Trinity was a hotbed of Cartesian philosophy. The University (and the country) were also just recovering from the Puritanism of the Protectorate & Charles II was proclaimed monarch in Newton would have studied arithmetic, Euclid, and trigonometry, classical & medieval Latin, logic & ethics. But he also studied optics with his tutor, read Kepler s Optics and struggled through Descartes Analytical Geometry graduated with B.A. degree.

2 Back in Woolsthorpe Newton s telescope In 1665 the university was closed due to a resurgence of the Plague. Newton spent much of the next two years back at the family manor, quietly reading and thinking. During these golden years he made three classic discoveries that revolutionized the future of science:! the mathematical method of fluxions, i.e. the calculus,! understanding the composition of light, &! the law of universal gravitation. The chromatic aberration of refracting telescope led to his invention of a reflecting telescope. Cambridge professor In 1667 Newton returned to Cambridge as a Fellow of Trinity. Engagement to Miss Storey ended (or faded away). In 1669 he was appointed (2nd) Lucasian Professor. First lecture course was on optics. His invention of the reflecting telescope brought fellowship in the Royal Society in A year later he published a letter in the Transactions of the Royal Society on his new theory of light and colours. Huygens appears not to have appreciated the significance of this work, nor completely understood it. This was quite a disappointment to Newton. Scientific disputes His publication on light also began a long dispute with Robert Hooke, who claimed priority in Newton s discoveries in optics. (There were more to follow.) A result of these disputes was to strengthen Newton s opposition to publishing his work, believing that others would draw him into further disputes which he considered a waste of time. A major difference in outlook between Newton, Huygens, & Hooke was Newton s insistence on quantitative measurement, rather than qualitative speculation. He did not send any further papers to the Royal Society on optics, and in 1675 offered his resignation as as Fellow, in part because he believed the Society had not supported his ideas. Problems with orthodoxy Newton had always done much theological reading and thinking, and as a result became convinced that the doctrine of the Trinity was not Biblical. This (Arian heresy) was a major problem for him: if this were to become known he would have lost his college fellowship. The law required that the Lucasian Professor become ordained in the Church of England, which would mean affirming the 39 Articles of Religion, including the doctrine of the Trinity, which he refused to do. By 1675 he had given up hope, but at the last minute the King issued a royal dispensation, lifting the requirement that the Lucasian Professor must take holy orders. Thus Charles II saved from oblivion one of the greatest scientists of all time. Life in Cambridge At the request of one of his friends, in 1676 Newton exchanged two letters with Gottfried Leibniz describing some of his mathematical discoveries. These were courteous and open, but later would become part of a long controversy over priority in discovery of the calculus. During this period (from ca. 1669) Newton did much experimentation in chemistry & alchemy (i.e. transmutation of metals and finding an elixir for immortality), having studied all the ancient alchemical treatises. Newton s lifestyle was largely solitary. His concentration was extraordinary: he would become so engaged on a problem he would forget to eat and sleep.

Publication of the Principia In 1684 Edmund Halley visited Newton and asked what the shape of a planetary orbit would be if the force between it and the Sun varied as the inverse square of the

3 Publication of the Principia In 1684 Edmund Halley visited Newton and asked what the shape of a planetary orbit would be if the force between it and the Sun varied as the inverse square of the distance between them. Newton replied that it would be an ellipse, and that he had worked it out years before. He later produced a proof for Halley, in the course of which he began developing a book-length discussion on the subject of motion of bodies in orbit. This was written out during 1685 & 1686 into his magnum opus. In 1687 Newton published the Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). Parliamentary service In 1687 James II became King. He was a devout Roman Catholic and eventually declared his intent to overthrow the English Church. As an example the monarch sent a letter to Cambridge commanding that a Benedictine monk should be given an M.A. degree without requiring him to sign the 39 Articles of Religion of the Anglican Church. Newton encouraged the University to resist, and in the end the King backed down. In 1688 the University chose Newton to represent them in the House of Commons for two years. He seems to have especially enjoyed this period in London and participation in the halls of government. Newton: portrait of 1689 (aged 46) Newton s breakdown In 1689 Newton s mother died. In 1692 a young Swiss mathematician, Fatio de Duillier who was an admirer and had proposed to edit a new edition of the Principia, abruptly ended his friendship. In this period Newton also became obsessed with obtaining a government position, and felt let down by his friends when a position was not forthcoming. In 1692 he suffered a major mental breakdown. By 1693 he seems to have recovered, but had no interest in creative scientific work, despite the fact that the Principia was out of print and others were following up his ideas. Life in London In 1694 one of Newton s former Trinity students, Charles Montague (later Lord Halifax), became Chancellor of the Exchequer. One of his decisions was the recoinage of English currency. In 1696 Newton was appointed Warden of the Mint, and the recoinage project was executed with great success. He moved to London and set up house with his niece, Catharine Barton. In 1699 Newton was appointed Master of the Mint, and held this position until his death. There is no doubt he carried out his duties as a civil servant with distinction. The Great Man In 1699 the dispute between Leibniz and Newton became a major international conflict. Yet another major quarrel erupted between Newton & John Flamsteed, the Astronomer Royal. In 1703 Newton was elected President of the Royal Society, and continued so until he died. In 1704 Newton published his Opticks (in English), & the Latin translation in It was wildly popular. In 1705 he was knighted. By this time Newton had become one of the most celebrated persons of his time. In 1727 Newton died and was buried in a spectacular tomb at Westminster Abbey.

Newton, 1726 Newton s tomb, Westminster Abbey 8.2 The Principia Newton s title page changes for the 2nd edition of the Principia Principia summary Book I! Laws of motion Book II!

Accounts of oblate shapes of the Earth & other planets! Masses of celestial objects in terms of mass of the Earth.

years of analysis of decades of observations). He also showed how his laws of motion and gravitation could explain new phenomena:! the tides The Principia!

The Principia, cont d In short, Newton s laws of motion and the law of universal gravitation not only described precisely the motions of planets orbiting the Sun, they enabled people calculate things

4 Newton, 1726 Newton s tomb, Westminster Abbey 8.2 The Principia Newton s title page changes for the 2nd edition of the Principia Principia summary Book I! Laws of motion Book II! Hydrostatics and hydrodynamics, in which Newton demolishes Descartes vortex model for the planets. Book III! Law of universal gravitation! Tides! Accounts of oblate shapes of the Earth & other planets! Masses of celestial objects in terms of mass of the Earth. Using his laws of motion and gravitation, Newton showed that he could deduce mathematically all three of Kepler s laws of planetary motion (which Kepler had of course worked out painstakingly by years of analysis of decades of observations). He also showed how his laws of motion and gravitation could explain new phenomena:! the tides The Principia! the oblate shapes of Earth and other planets.! He calculated the mass of a planet in terms of the Earth s mass.! And he showed that the Great Comet of 1680 was in a Keplerian orbit about the Sun. The Principia, cont d In short, Newton s laws of motion and the law of universal gravitation not only described precisely the motions of planets orbiting the Sun, they enabled people calculate things they had not previously thought were possible. Comparison of predictions of Newton s theory with observations confirmed the validity of Newton s ideas. Newton could predict from his theory all the observational work of centuries. This was a spectacular achievement, something no one had ever done before. And so it is not surprising that Newton was regarded as one of the great intellectual giants of all time.

5 The First Law: Inertia Newton s Laws of Motion Newton s First Law of Motion (Inertia): Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it. As we have seen, both Descartes and Galileo were working toward an idea of inertia. Descartes argued that matter, once in motion, continued to move in a straight line until it collided with another bit of matter, although this assumption is based on purely metaphysical reasoning. Galileo s ideas on inertia were derived from his experiments with balls rolling on inclined planes, and on projectile motion. Newton s Law of Inertia Newton s First Law effectively says that the natural motion of an object at rest is to remain at rest, or, if it is moving, to move in a straight line at constant speed. In other words, if there are no forces on an object, it will either remain at rest or move with constant speed in a straight line: it takes an external force to change either the speed or direction of motion. Note that Newton is adopting the idea of natural motion that goes back to Aristotle, but with a rather different formulation. Note also that the same natural motion applies to objects on Earth and in the heavens. Astronomical application If we accept Newton s First Law, what would we expect the trajectory of the Moon or a planet would be, if there were no forces on it? A straight line! Since the Moon and planets orbit about the Sun, a consequence of the First Law is that there must be a force which pulls them toward the Sun, as Kepler argued. The Second Law Newton s Second Law of Motion: The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. Note that Newton defines the quantity of motion as the velocity and quantity of matter conjointly, so that quantity of motion is not velocity but what we would call momentum = mass x velocity. We see that, whatever force is, it can be measured quantitatively by its effect on the momentum of an object. Note also that quantity of motion has a direction, and the change in quantity of motion is in the same direction as the direction of the force. This can be written: Force is proportional to change in quantity of motion in a given time. Newton s Second Law Repeating: Force! change in quantity of motion per unit time. If mass is constant, then this becomes: Force! (mass) x (change in velocity per unit time), and since acceleration = (change in velocity)/time, Newton s Second Law becomes F! (mass) x (acceleration). With appropriate choice of units this is the famous F = ma. This shows that the mass of an object is its resistance to being accelerated, i.e. a 5 lb force in a slingshot will accelerate a BB to high speed, but will hardly move a bowling ball.

The idea of gravitation 8.2.2. The path to gravitation During the two years back at Woolsthorpe Newton was puzzling just what force could pull planets into orbit round the Sun.

He realized that the same force that pulled the apple to earth should extend much further could be the force that pulled the circling Moon toward the Earth.

stated by several independent sources. Drawing from 1820 of Woolsthorpe Manor and the (only) apple tree in the Manor garden.

6 The idea of gravitation The path to gravitation During the two years back at Woolsthorpe Newton was puzzling just what force could pull planets into orbit round the Sun. The story goes that he was in the garden at Woolsthorpe and he saw an apple fall from the apple tree. He realized that the same force that pulled the apple to earth should extend much further could be the force that pulled the circling Moon toward the Earth. Although this story is sometimes said to be apocryphal, it was written down by John Conduitt, who married Newton s niece Catharine Barton, and who was his assistant at the Mint for many years, and is stated by several independent sources. Drawing from 1820 of Woolsthorpe Manor and the (only) apple tree in the Manor garden. A photograph from 1998 taken with the same view as the 1820 drawing shown previously. The present tree is rooted off the fallen trunk of the original tree. Discovery of Gravitation Newton had worked out that centrifugal force is proportional to v 2 /r. He used Kepler s third law of planetary motion to find an expression for v in terms of r: (period) 2 = (radius of orbit) 3. The period = 2!r/v & therefore (2!r/v) 2 = r 3, so v 2 = 4! 2 /r. Substituting this into the expression for the force required to keep a planet (or the Moon) in its orbit: Force of gravity: mv 2 /r m/r 2. Gravity & the planets Gravity is the force between a planet and the Sun that continually accelerates the planet both in speed (Kepler s second law) and in direction (Kepler s first law). This is how Newton convinced himself that the force required to keep a planet in orbit is proportional to 1/r 2.

7 Newton s theory of gravity Newton realized that to make a planet take an elliptical (or circular) orbit required an attractive force between the planet and the Sun. He formulated this idea in his law of universal gravitation: the attractive force between any two bodies is proportional to the product of their masses (kg) divided by the square of the distance between them: M 1m 1 F = G m 1m 2 r 2 r m 2 Newton s gravitational force In Newton s gravitational force equation: F = Gm 1m 2/r 2 G is the proportionality constant. In MKS units (mass in kg, distance r in meters, force in Newtons) G = 6.67x This proportionality constant, and experimental measurements to confirm Newton s theory, were made by Henry Cavendish in 1797 & (This enabled Cavendish to then calculate the mass of the Earth.) Problems with Newtonian Gravity How is the gravitational force transmitted between the Sun and the planet? Most people in this period could only imagine forces being applied by contact (e.g. Descartes and Huygens). Newton himself was reluctant to accept the idea that gravity was an innate property of matter and could be transmitted without the mediation of some intervening medium: "...that one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that, I believe no man, who has in philosophic matters a competent faculty of thinking, could ever fall into it." Applications of Newton s theories Overview We should not let these comments on loose ends in Newtonian gravity distract from the fact that Newton used his dynamics and theory of gravitation to solve problems or provide quantitative explanations no one else had every been able to do before. In Book III, The System of the World, Newton applies this theories to a variety of astronomical situations, and is able to make quantitative predictions which were revolutionary. He checks them against measurements when possible to see how well his theory does. For the many people who could not understand the Principia itself, confirmation of these quantitative predictions was simply astounding. Orbits Newton adopted the helio-centric model for the solar system. He was able to show purely from calculation Kepler s three laws of planetary motion--which, remember, Kepler had discovered empirically from decades of precise observations made by Tycho. This marks the absolute demise of the old geo-centric picture of the heavens. It is also a striking confirmation of the validity of Newton s theories of dynamics and gravitation. We have now, for the first time, a theory of dynamics which provides quantitative predictions of phenomena.

8 Comets More generally, Newton showed that the orbits of objects moving under the influence of gravity may be ellipses, parabolas, or hyperbolas (these are all conic sections). Newton showed that the Great Comet of 1680 was in an elliptical orbit, and that two apparitions of a comet were in fact the same comet. That all this worked proved that comets are solid, compact, fixed, and durable rather than vapors emitted by the Earth, the Sun, or the planets. Tides Newton s calculations showed that gravitational force from the Moon is the major cause of the tides. (The Sun contributes about 25% of the effect of the Moon.) He calculated the expected heights of tides. He also showed that one gets the strong spring tides when the Sun and Moon are lined up and the weaker neap tides when the Sun and Moon are perpendicular. Centrifugal bulges of planets Newton argued that, since planets are rotating about an axis, self-gravity in a direction perpendicular to the spin axis is somewhat offset by centrifugal force, compared to the direction along the spin axis. This makes the planets into oblate spheroids (pumpkins) with the equatorial diameter larger than the polar diameter. He compared his theoretical predictions with measurements of the slightly slower movement of pendulum clocks at the Earth s equator compared to the polar regions, and found the difference implied that the equatorial diameter is 27 km (the modern value is about 40 km). Masses of planets To calculate the masses of planets Newton could use his form of Kepler s third law: P 2 = 4! 2 R 3 /GM, but he did not know the value for G. So he used the periods, P, and orbit radii, R, for the satellites of a planet and the Earth to get the product GM for each, and thereby the ratio of the planet s mass to that of the Earth. Example: Jupiter s moon Callisto. Period ~ 16 days and R ~ 4.9 x Moon s orbit radius. These give M Jup/M Earth ~ 330. Modern value is 318. In summary What Newton showed in Book III is that there are universal principles or laws that apply to a wide range of physical phenomena. These laws can be expressed in mathematical form, and can make quantitative predictions of the outcomes of experiments. This set the paradigm for physical science which remains with us to today. This also gave people the realization that there are likely other universal laws or principles which can similarly be found by creative thinking of a similar sort to Newton s use of reason for his discoveries. Ode to Newton Here is the last stanza of Halley s Ode to Newton which prefixed the Principia: Then ye who now on heavenly nectar fare, Come celebrate with me in song the name Of Newton, to the Muses dear; for he Unlocked the hidden treasuries of Truth: So richly through his mind had Phoebus cast The radiance of his own divinity. Nearer the gods no mortal may approach. Nothing else can say so clearly the profound effect Newton s achievements had on intellectual life in the 17th C.

The History and Philosophy of Astronomy

Astronomy 350L (Spring 2005) The History and Philosophy of Astronomy (Lecture 13: Newton I) Instructor: Volker Bromm TA: Amanda Bauer The University of Texas at Austin Isaac Newton: Founding Father of