Newton's First and Second laws, in Latin, from the original 1687 Principia Mathematica.

Walter Lewin explains Newton's first law and reference frames. (MIT Course 8.01)^[1]

Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces. They have been expressed in several different ways over nearly three centuries,^[2] and can be summarized as follows:

1. First law: The velocity of a body remains constant unless the body is acted upon by an external force.^[3][4][5]
2. Second law: The acceleration a of a body is parallel and directly proportional to the net force F and inversely proportional to the mass m, i.e., F = ma.
3. Third law: The mutual forces of action and reaction between two bodies are equal, opposite and collinear.

The three laws of motion were first compiled by Sir Isaac Newton in his work Philosophiæ Naturalis Principia Mathematica, first published in 1687.^[6] Newton used them to explain and investigate the motion of many physical objects and systems.^[7] For example, in the third volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion.

Overview[link]

Newton's laws are applied to bodies (objects) which are considered or idealized as a particle,^[8] in the sense that the extent of the body is neglected in the evaluation of its motion, i.e., the object is small compared to the distances involved in the analysis, or the deformation and rotation of the body is of no importance in the analysis. Therefore, a planet can be idealized as a particle for analysis of its orbital motion around a star.

In their original form, Newton's laws of motion are not adequate to characterize the motion of rigid bodies and deformable bodies. Leonard Euler in 1750 introduced a generalization of Newton's laws of motion for rigid bodies called the Euler's laws of motion, later applied as well for deformable bodies assumed as a continuum. If a body is represented as an assemblage of discrete particles, each governed by Newton’s laws of motion, then Euler’s laws can be derived from Newton’s laws. Euler’s laws can, however, be taken as axioms describing the laws of motion for extended bodies, independently of any particle structure.^[9]

Newton's laws hold only with respect to a certain set of frames of reference called Newtonian or inertial reference frames. Some authors interpret the first law as defining what an inertial reference frame is; from this point of view, the second law only holds when the observation is made from an inertial reference frame, and therefore the first law cannot be proved as a special case of the second. Other authors do treat the first law as a corollary of the second.^[10][11] The explicit concept of an inertial frame of reference was not developed until long after Newton's death.

In the given interpretation mass, acceleration, momentum, and (most importantly) force are assumed to be externally defined quantities. This is the most common, but not the only interpretation: one can consider the laws to be a definition of these quantities.

Newtonian mechanics has been superseded by special relativity, but it is still useful as an approximation when the speeds involved are much slower than the speed of light.^[12]

Newton's first law[link]

Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.

Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.^[13]

This law states that if the net force (the vector sum of all forces acting on an object) is zero, then the velocity of the object is constant. Mathematically stated:

Failed to parse (Missing texvc executable; please see math/README to configure.): \sum \mathbf{F} = 0 \Rightarrow \frac{d \mathbf{v} }{dt} = 0.

Consequently:

• An object that is at rest will stay at rest unless an unbalanced force acts upon it.
• An object that is in motion will not change its velocity unless an unbalanced force acts upon it.

Newton placed the first law of motion to establish frames of reference for which the other laws are applicable. The first law of motion postulates the existence of at least one frame of reference called a Newtonian or inertial reference frame, relative to which the motion of a particle not subject to forces is a straight line at a constant speed.^[14][10] Newton's first law is often referred to as the law of inertia. Thus, a condition necessary for the uniform motion of a particle relative to an inertial reference frame is that the total net force acting on it is zero. In this sense, the first law can be restated as:

In every material universe, the motion of a particle in a preferential reference frame Φ is determined by the action of forces whose total vanished for all times when and only when the velocity of the particle is constant in Φ. That is, a particle initially at rest or in uniform motion in the preferential frame Φ continues in that state unless compelled by forces to change it.^[15]

Newton's laws are valid only in an inertial reference frame. Any reference frame that is in uniform motion with respect to an inertial frame is also an inertial frame, i.e. Galilean invariance or the principle of Newtonian relativity.^[16]

Newton's first law is a restatement of the law of inertia which Galileo had already described and Newton gave credit to Galileo. Aristotle had the view that all objects have a natural place in the universe: that heavy objects like rocks wanted to be at rest on the Earth and that light objects like smoke wanted to be at rest in the sky and the stars wanted to remain in the heavens. He thought that a body was in its natural state when it was at rest, and for the body to move in a straight line at a constant speed an external agent was needed to continually propel it, otherwise it would stop moving. Galileo, however, realized that a force is necessary to change the velocity of a body, i.e., acceleration, but no force is needed to maintain its velocity. This insight leads to Newton's First Law —no force means no acceleration, and hence the body will maintain its velocity.

The law of inertia apparently occurred to several different natural philosophers and scientists independently, including Thomas Hobbes in his Leviathan.^[17] The 17th century philosopher René Descartes also formulated the law, although he did not perform any experiments to confirm it.

Newton's second law[link]

Walter Lewin explains Newton's second law, using gravity as an example. (MIT OCW)^[18]

The second law states that the net force on a particle is equal to the time rate of change of its linear momentum p in an inertial reference frame:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{F} = \frac{\mathrm{d}\mathbf{p}}{\mathrm{d}t} = \frac{\mathrm{d}(m\mathbf v)}{\mathrm{d}t},

where, since the law is valid only for constant-mass systems,^[19][20][21] the mass can be taken outside the differentiation operator by the constant factor rule in differentiation. Thus,

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{F} = m\,\frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t} = m\mathbf{a},

where F is the net force applied, m is the mass of the body, and a is the body's acceleration. Thus, the net force applied to a body produces a proportional acceleration. In other words, if a body is accelerating, then there is a force on it.

Any mass that is gained or lost by the system will cause a change in momentum that is not the result of an external force. A different equation is necessary for variable-mass systems (see below).

Consistent with the first law, the time derivative of the momentum is non-zero when the momentum changes direction, even if there is no change in its magnitude; such is the case with uniform circular motion. The relationship also implies the conservation of momentum: when the net force on the body is zero, the momentum of the body is constant. Any net force is equal to the rate of change of the momentum.

Newton's second law requires modification if the effects of special relativity are to be taken into account, because at high speeds the approximation that momentum is the product of rest mass and velocity is not accurate.

Impulse[link]

An impulse J occurs when a force F acts over an interval of time Δt, and it is given by^[22][23]

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{J} = \int_{\Delta t} \mathbf F \,\mathrm{d}t .

Since force is the time derivative of momentum, it follows that

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{J} = \Delta\mathbf{p} = m\Delta\mathbf{v}.

This relation between impulse and momentum is closer to Newton's wording of the second law.^[24]

Impulse is a concept frequently used in the analysis of collisions and impacts.^[25]

Variable-mass systems[link]

Variable-mass systems, like a rocket burning fuel and ejecting spent gases, are not closed and cannot be directly treated by making mass a function of time in the second law.^[20] The reasoning, given in An Introduction to Mechanics by Kleppner and Kolenkow and other modern texts, is that Newton's second law applies fundamentally to particles.^[21] In classical mechanics, particles by definition have constant mass. In case of a well-defined system of particles, Newton's law can be extended by summing over all the particles in the system:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{F}_{\mathrm{net}} = M\mathbf{a}_\mathrm{cm}

where F_net is the total external force on the system, M is the total mass of the system, and a_cm is the acceleration of the center of mass of the system.

Variable-mass systems like a rocket or a leaking bucket cannot usually be treated as a system of particles, and thus Newton's second law cannot be applied directly. Instead, the general equation of motion for a body whose mass m varies with time by either ejecting or accreting mass is obtained by rearranging the second law and adding a term to account for the momentum carried by mass entering or leaving the system:^[19]

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf F + \mathbf{u} \frac{\mathrm{d} m}{\mathrm{d}t} = m {\mathrm{d} \mathbf v \over \mathrm{d}t}

where u is the relative velocity of the escaping or incoming mass with respect to the center of mass of the body. Under some conventions, the quantity (u dm/dt) on the left-hand side, known as the thrust, is defined as a force (the force exerted on the body by the changing mass, such as rocket exhaust) and is included in the quantity F. Then, by substituting the definition of acceleration, the equation becomes

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf F = m \mathbf a.

History[link]

Newton's original Latin reads:

Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.

This was translated quite closely in Motte's 1729 translation as:

Law II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd.

According to modern ideas of how Newton was using his terminology,^[26] this is understood, in modern terms, as an equivalent of:

The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed.

Motte's 1729 translation of Newton's Latin continued with Newton's commentary on the second law of motion, reading:

If a force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.

The sense or senses in which Newton used his terminology, and how he understood the second law and intended it to be understood, have been extensively discussed by historians of science, along with the relations between Newton's formulation and modern formulations.^[27]

Newton's third law[link]

Newton's third law. The skaters' forces on each other are equal in magnitude, but act in opposite directions.

A description of Newton's third law and contact forces^[28]

A more direct translation than the one just given above is:

LAW III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. — Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone: for the distended rope, by the same endeavour to relax or unbend itself, will draw the horse as much towards the stone, as it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other. If a body impinges upon another, and by its force changes the motion of the other, that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, toward the contrary part. The changes made by these actions are equal, not in the velocities but in the motions of the bodies; that is to say, if the bodies are not hindered by any other impediments. For, as the motions are equally changed, the changes of the velocities made toward contrary parts are reciprocally proportional to the bodies. This law takes place also in attractions, as will be proved in the next scholium.^[29]

In the above, as usual, motion is Newton's name for momentum, hence his careful distinction between motion and velocity.

The Third Law means that all forces are interactions between different bodies,^[30][31] and thus that there is no such thing as a unidirectional force or a force that acts on only one body. Whenever a first body exerts a force F on a second body, the second body exerts a force −F on the first body. F and −F are equal in magnitude and opposite in direction. This law is sometimes referred to as the action-reaction law, with F called the "action" and −F the "reaction". The action and the reaction are simultaneous.

As shown in the diagram opposite, the skaters' forces on each other are equal in magnitude, but act in opposite directions. Although the forces are equal, the accelerations are not: the less massive skater will have a greater acceleration due to Newton's second law. The two forces in Newton's third law are of the same type (e.g., if the road exerts a forward frictional force on an accelerating car's tires, then it is also a frictional force that Newton's third law predicts for the tires pushing backward on the road).

Put very simply: a force acts between a pair of objects, and not on a single object. So each and every force has two ends. Each of the two ends is the same except for being opposite in direction. The ends of a force are mirror images of each other, one might say.

From a mathematical point of view, Newton's third law is a one-dimensional vector equation, which can be stated as follows. Given two objects A and B, each exerting a force on the other,

Failed to parse (Missing texvc executable; please see math/README to configure.): \sum \mathbf{F}_{a,b} = - \sum \mathbf{F}_{b,a}

where

F_a,b are the forces from B acting on A, and

F_b,a are the forces from A acting on B.

Newton used the third law to derive the law of conservation of momentum;^[32] however from a deeper perspective, conservation of momentum is the more fundamental idea (derived via Noether's theorem from Galilean invariance), and holds in cases where Newton's third law appears to fail, for instance when force fields as well as particles carry momentum, and in quantum mechanics.

Importance and range of validity[link]

Newton's laws were verified by experiment and observation for over 200 years, and they are excellent approximations at the scales and speeds of everyday life. Newton's laws of motion, together with his law of universal gravitation and the mathematical techniques of calculus, provided for the first time a unified quantitative explanation for a wide range of physical phenomena.

These three laws hold to a good approximation for macroscopic objects under everyday conditions. However, Newton's laws (combined with universal gravitation and classical electrodynamics) are inappropriate for use in certain circumstances, most notably at very small scales, very high speeds (in special relativity, the Lorentz factor must be included in the expression for momentum along with rest mass and velocity) or very strong gravitational fields. Therefore, the laws cannot be used to explain phenomena such as conduction of electricity in a semiconductor, optical properties of substances, errors in non-relativistically corrected GPS systems and superconductivity. Explanation of these phenomena requires more sophisticated physical theories, including general relativity and quantum field theory.

In quantum mechanics concepts such as force, momentum, and position are defined by linear operators that operate on the quantum state; at speeds that are much lower than the speed of light, Newton's laws are just as exact for these operators as they are for classical objects. At speeds comparable to the speed of light, the second law holds in the original form F = dp/dt, which says that the force is the derivative of the momentum of the object with respect to time, but some of the newer versions of the second law (such as the constant mass approximation above) do not hold at relativistic velocities.

Relationship to the conservation laws[link]

In modern physics, the laws of conservation of momentum, energy, and angular momentum are of more general validity than Newton's laws, since they apply to both light and matter, and to both classical and non-classical physics.

This can be stated simply, "Momentum, energy and angular momentum cannot be created or destroyed."

Because force is the time derivative of momentum, the concept of force is redundant and subordinate to the conservation of momentum, and is not used in fundamental theories (e.g., quantum mechanics, quantum electrodynamics, general relativity, etc.). The standard model explains in detail how the three fundamental forces known as gauge forces originate out of exchange by virtual particles. Other forces such as gravity and fermionic degeneracy pressure also arise from the momentum conservation. Indeed, the conservation of 4-momentum in inertial motion via curved space-time results in what we call gravitational force in general relativity theory. Application of space derivative (which is a momentum operator in quantum mechanics) to overlapping wave functions of pair of fermions (particles with half-integer spin) results in shifts of maxima of compound wavefunction away from each other, which is observable as "repulsion" of fermions.

Newton stated the third law within a world-view that assumed instantaneous action at a distance between material particles. However, he was prepared for philosophical criticism of this action at a distance, and it was in this context that he stated the famous phrase "I feign no hypotheses". In modern physics, action at a distance has been completely eliminated, except for subtle effects involving quantum entanglement. However in modern engineering in all practical applications involving the motion of vehicles and satellites, the concept of action at a distance is used extensively.

Conservation of energy was discovered nearly two centuries after Newton's lifetime, the long delay occurring because of the difficulty in understanding the role of microscopic and invisible forms of energy such as heat and infra-red light.

See also[link]

	Book: Isaac Newton
Wikipedia books are collections of articles that can be downloaded or ordered in print.

• Euler's laws
• Galilean invariance
• Hamiltonian mechanics
• Lagrangian mechanics
• List of scientific laws named after people
• Mercury, orbit of
• Modified Newtonian dynamics
• Newton's law of universal gravitation
• Principle of least action
• Reaction (physics)

References and notes[link]

Further reading and works referred to[link]

• Crowell, Benjamin, (2011), Light and Matter, (2011, Light and Matter), especially at Section 4.2, Newton's First Law, Section 4.3, Newton's Second Law, and Section 5.1, Newton's Third Law.
• Feynman, R. P.; Leighton, R. B.; Sands, M. (2005). The Feynman Lectures on Physics. Vol. 1 (2nd ed.). Pearson/Addison-Wesley. ISBN 0-8053-9049-9. 
• Fowles, G. R.; Cassiday, G. L. (1999). Analytical Mechanics (6th ed.). Saunders College Publishing. ISBN 0-03-022317-2. 
• Likins, Peter W. (1973). Elements of Engineering Mechanics. McGraw-Hill Book Company. ISBN 0-07-037852-5. 
• Marion, Jerry; Thornton, Stephen (1995). Classical Dynamics of Particles and Systems. Harcourt College Publishers. ISBN 0-03-097302-3. 
• Newton, Isaac, "Mathematical Principles of Natural Philosophy", 1729 English translation based on 3rd Latin edition (1726), volume 1, containing Book 1, especially at the section Axioms or Laws of Motion starting page 19.
• Newton, Isaac, "Mathematical Principles of Natural Philosophy", 1729 English translation based on 3rd Latin edition (1726), volume 2, containing Books 2 & 3.
• Thomson, W (Lord Kelvin), and Tait, P G, (1867), Treatise on natural philosophy, volume 1, especially at Section 242, Newton's laws of motion.
• NMJ Woodhouse (2003). Special relativity. London/Berlin: Springer. p. 6. ISBN 1-85233-426-6. http://books.google.com/?id=ggPXQAeeRLgC&printsec=frontcover&dq=isbn=1852334266#PPA6,M1. 

External links[link]

• MIT Physics video lecture on Newton's three laws
• Light and Matter – an on-line textbook
• Motion Mountain – an on-line textbook
• Simulation on Newton's first law of motion
• "Newton's Second Law" by Enrique Zeleny, Wolfram Demonstrations Project.
• Newton's 3rd Law demonstrated in a vacuum

In physics, a number of noted theories of the motion of objects have developed. Among the best-known are:

• Classical mechanics
  • Newton's laws of motion
  • Euler's laws
  • Cauchy's equations of motion
  • Kepler's laws of planetary motion
  • General relativity
  • Special relativity
• Quantum mechanics

This disambiguation page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.

Sir Isaac Newton
Godfrey Kneller's 1689 portrait of Isaac Newton (age 46)
Born	(1642-12-25)25 December 1642 [NS: 4 January 1643][1] Woolsthorpe-by-Colsterworth Lincolnshire, England
Died	20 March 1727(1727-03-20) (aged 84) [NS: 31 March 1727][1] Kensington, Middlesex, England
Residence	England
Nationality	English
Fields	Physics, mathematics, astronomy, natural philosophy, alchemy, Christian theology
Institutions	University of Cambridge Royal Society Royal Mint
Alma mater	Trinity College, Cambridge
Academic advisors	Isaac Barrow[2] Benjamin Pulleyn[3][4]
Notable students	Roger Cotes William Whiston
Known for	Newtonian mechanics Universal gravitation Infinitesimal calculus Optics Binomial series Newton's method Philosophiæ Naturalis Principia Mathematica
Influences	Henry More[5] Polish Brethren[6]
Influenced	Nicolas Fatio de Duillier John Keill
Signature
Notes His mother was Hannah Ayscough. His half-niece was Catherine Barton.

Sir Isaac Newton PRS MP (25 December 1642 – 20 March 1727 [NS: 4 January 1643 – 31 March 1727])^[1] was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."^[7] His monograph Philosophiæ Naturalis Principia Mathematica, published in 1687, lays the foundations for most of classical mechanics. In this work, Newton described universal gravitation and the three laws of motion, which dominated the scientific view of the physical universe for the next three centuries. Newton showed that the motions of objects on Earth and of celestial bodies are governed by the same set of natural laws, by demonstrating the consistency between Kepler's laws of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the Scientific Revolution.

The Principia is generally considered to be one of the most important scientific books ever written, due, independently, to the specific physical laws the work successfully described, and for the style of the work, which assisted in setting standards for scientific publication down to the present time. Newton built the first practical reflecting telescope^[8] and developed a theory of colour based on the observation that a prism decomposes white light into the many colours that form the visible spectrum. He also formulated an empirical law of cooling and studied the speed of sound. In mathematics, Newton shares the credit with Gottfried Leibniz for the development of differential and integral calculus. He also demonstrated the generalised binomial theorem, developed Newton's method for approximating the roots of a function, and contributed to the study of power series. Newton's work on infinite series was inspired by Simon Stevin's decimals.^[9] Newton, although an unorthodox Christian, was deeply religious, and wrote more on Biblical hermeneutics and occult studies than on science and mathematics. Newton secretly rejected Trinitarianism, and feared being accused of refusing holy orders.^[10]

Life[link]

Early life[link]

Isaac Newton was born on what is retroactively considered 4 January 1643 [OS: 25 December 1642]^[1] at Woolsthorpe Manor in Woolsthorpe-by-Colsterworth, a hamlet in the county of Lincolnshire. At the time of Newton's birth, England had not adopted the Gregorian calendar and therefore his date of birth was recorded as Christmas Day, 25 December 1642. Newton was born three months after the death of his father, a prosperous farmer also named Isaac Newton. Born prematurely, he was a small child; his mother Hannah Ayscough reportedly said that he could have fit inside a quart mug (≈ 1.1 litres). When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabus Smith, leaving her son in the care of his maternal grandmother, Margery Ayscough. The young Isaac disliked his stepfather and maintained some enmity towards his mother for marrying him, as revealed by this entry in a list of sins committed up to the age of 19: "Threatening my father and mother Smith to burn them and the house over them."^[11] Although it was claimed that he was once engaged,^[12] Newton never married.

Newton in a 1702 portrait by Godfrey Kneller

Isaac Newton (Bolton, Sarah K. Famous Men of Science. NY: Thomas Y. Crowell & Co., 1889)

From the age of about twelve until he was seventeen, Newton was educated at The King's School, Grantham (where his alleged signature can still be seen upon a library window sill).[1]^{[citation needed]} He was removed from school, and by October 1659, he was to be found at Woolsthorpe-by-Colsterworth, where his mother, widowed by now for a second time, attempted to make a farmer of him. He hated farming.^[13] Henry Stokes, master at the King's School, persuaded his mother to send him back to school so that he might complete his education. Motivated partly by a desire for revenge against a schoolyard bully, he became the top-ranked student.^[14] The Cambridge psychologist Simon Baron-Cohen considers it "fairly certain" that Newton had Asperger syndrome.^[15]

In June 1661, he was admitted to Trinity College, Cambridge as a sizar – a sort of work-study role.^[16] At that time, the college's teachings were based on those of Aristotle, whom Newton supplemented with modern philosophers, such as Descartes, and astronomers such as Copernicus, Galileo, and Kepler. In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became infinitesimal calculus. Soon after Newton had obtained his degree in August 1665, the university temporarily closed as a precaution against the Great Plague. Although he had been undistinguished as a Cambridge student,^[17] Newton's private studies at his home in Woolsthorpe over the subsequent two years saw the development of his theories on calculus,^[18] optics and the law of gravitation. In 1667, he returned to Cambridge as a fellow of Trinity.^[19] Fellows were required to become ordained priests, something Newton desired to avoid due to his unorthodox views. Luckily for Newton, there was no specific deadline for ordination and it could be postponed indefinitely. The problem became more severe later when Newton was elected for the prestigious Lucasian Chair. For such a significant appointment, ordaining normally could not be dodged. Nevertheless, Newton managed to avoid it by means of a special permission from Charles II (see "Middle years" section below).

Middle years[link]

Mathematics[link]

Newton's work has been said "to distinctly advance every branch of mathematics then studied".^[20] His work on the subject usually referred to as fluxions or calculus, seen in a manuscript of October 1666, is now published among Newton's mathematical papers.^[21] The author of the manuscript De analysi per aequationes numero terminorum infinitas, sent by Isaac Barrow to John Collins in June 1669, was identified by Barrow in a letter sent to Collins in August of that year as:^[22]

Mr Newton, a fellow of our College, and very young ... but of an extraordinary genius and proficiency in these things.

Newton later became involved in a dispute with Leibniz over priority in the development of infinitesimal calculus. Most modern historians believe that Newton and Leibniz developed infinitesimal calculus independently, although with very different notations. Occasionally it has been suggested that Newton published almost nothing about it until 1693, and did not give a full account until 1704, while Leibniz began publishing a full account of his methods in 1684. (Leibniz's notation and "differential Method", nowadays recognised as much more convenient notations, were adopted by continental European mathematicians, and after 1820 or so, also by British mathematicians.) Such a suggestion, however, fails to notice the content of calculus which critics of Newton's time and modern times have pointed out in Book 1 of Newton's Principia itself (published 1687) and in its forerunner manuscripts, such as De motu corporum in gyrum ("On the motion of bodies in orbit"), of 1684. The Principia is not written in the language of calculus either as we know it or as Newton's (later) 'dot' notation would write it. But his work extensively uses an infinitesimal calculus in geometric form, based on limiting values of the ratios of vanishing small quantities: in the Principia itself Newton gave demonstration of this under the name of 'the method of first and last ratios'^[23] and explained why he put his expositions in this form,^[24] remarking also that 'hereby the same thing is performed as by the method of indivisibles'.

Because of this, the Principia has been called "a book dense with the theory and application of the infinitesimal calculus" in modern times^[25] and "lequel est presque tout de ce calcul" ('nearly all of it is of this calculus') in Newton's time.^[26] His use of methods involving "one or more orders of the infinitesimally small" is present in his De motu corporum in gyrum of 1684^[27] and in his papers on motion "during the two decades preceding 1684".^[28]

Newton had been reluctant to publish his calculus because he feared controversy and criticism.^[29] He was close to the Swiss mathematician Nicolas Fatio de Duillier. In 1691, Duillier started to write a new version of Newton's Principia, and corresponded with Leibniz.^[30] In 1693 the relationship between Duillier and Newton deteriorated, and the book was never completed.

Starting in 1699, other members of the Royal Society (of which Newton was a member) accused Leibniz of plagiarism, and the dispute broke out in full force in 1711. The Royal Society proclaimed in a study that it was Newton who was the true discoverer and labelled Leibniz a fraud. This study was cast into doubt when it was later found that Newton himself wrote the study's concluding remarks on Leibniz. Thus began the bitter controversy which marred the lives of both Newton and Leibniz until the latter's death in 1716.^[31]

Newton is generally credited with the generalised binomial theorem, valid for any exponent. He discovered Newton's identities, Newton's method, classified cubic plane curves (polynomials of degree three in two variables), made substantial contributions to the theory of finite differences, and was the first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations. He approximated partial sums of the harmonic series by logarithms (a precursor to Euler's summation formula), and was the first to use power series with confidence and to revert power series.

He was appointed Lucasian Professor of Mathematics in 1669 on Barrow's recommendation. In that day, any fellow of Cambridge or Oxford was required to become an ordained Anglican priest. However, the terms of the Lucasian professorship required that the holder not be active in the church (presumably so as to have more time for science). Newton argued that this should exempt him from the ordination requirement, and Charles II, whose permission was needed, accepted this argument. Thus a conflict between Newton's religious views and Anglican orthodoxy was averted.^[32]

Optics[link]

A replica of Newton's second Reflecting telescope that he presented to the Royal Society in 1672^[33]

From 1670 to 1672, Newton lectured on optics.^[34] During this period he investigated the refraction of light, demonstrating that a prism could decompose white light into a spectrum of colours, and that a lens and a second prism could recompose the multicoloured spectrum into white light.^[35] Modern scholarship has revealed that Newton's analysis and resynthesis of white light owes a debt to corpuscular alchemy. ^[36] .

He also showed that the coloured light does not change its properties by separating out a coloured beam and shining it on various objects. Newton noted that regardless of whether it was reflected or scattered or transmitted, it stayed the same colour. Thus, he observed that colour is the result of objects interacting with already-coloured light rather than objects generating the colour themselves. This is known as Newton's theory of colour.^[37]

From this work, he concluded that the lens of any refracting telescope would suffer from the dispersion of light into colours (chromatic aberration). As a proof of the concept, he constructed a telescope using a mirror as the objective to bypass that problem.^[38] Building the design, the first known functional reflecting telescope, today known as a Newtonian telescope,^[38] involved solving the problem of a suitable mirror material and shaping technique. Newton ground his own mirrors out of a custom composition of highly reflective speculum metal, using Newton's rings to judge the quality of the optics for his telescopes. In late 1668^[39] he was able to produce this first reflecting telescope. In 1671, the Royal Society asked for a demonstration of his reflecting telescope.^[40] Their interest encouraged him to publish his notes On Colour, which he later expanded into his Opticks. When Robert Hooke criticised some of Newton's ideas, Newton was so offended that he withdrew from public debate. Newton and Hooke had brief exchanges in 1679–80, when Hooke, appointed to manage the Royal Society's correspondence, opened up a correspondence intended to elicit contributions from Newton to Royal Society transactions,^[41] which had the effect of stimulating Newton to work out a proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector (see Newton's law of universal gravitation – History and De motu corporum in gyrum). But the two men remained generally on poor terms until Hooke's death.^[42]

Newton argued that light is composed of particles or corpuscles, which were refracted by accelerating into a denser medium. He verged on soundlike waves to explain the repeated pattern of reflection and transmission by thin films (Opticks Bk.II, Props. 12), but still retained his theory of ‘fits’ that disposed corpuscles to be reflected or transmitted (Props.13). Later physicists instead favoured a purely wavelike explanation of light to account for the interference patterns, and the general phenomenon of diffraction. Today's quantum mechanics, photons and the idea of wave–particle duality bear only a minor resemblance to Newton's understanding of light.

In his Hypothesis of Light of 1675, Newton posited the existence of the ether to transmit forces between particles. The contact with the theosophist Henry More, revived his interest in alchemy. He replaced the ether with occult forces based on Hermetic ideas of attraction and repulsion between particles. John Maynard Keynes, who acquired many of Newton's writings on alchemy, stated that "Newton was not the first of the age of reason: He was the last of the magicians."^[43] Newton's interest in alchemy cannot be isolated from his contributions to science.^[5] This was at a time when there was no clear distinction between alchemy and science. Had he not relied on the occult idea of action at a distance, across a vacuum, he might not have developed his theory of gravity. (See also Isaac Newton's occult studies.)

In 1704, Newton published Opticks, in which he expounded his corpuscular theory of light. He considered light to be made up of extremely subtle corpuscles, that ordinary matter was made of grosser corpuscles and speculated that through a kind of alchemical transmutation "Are not gross Bodies and Light convertible into one another, ...and may not Bodies receive much of their Activity from the Particles of Light which enter their Composition?"^[44] Newton also constructed a primitive form of a frictional electrostatic generator, using a glass globe (Optics, 8th Query).

In an article entitled "Newton, prisms, and the 'opticks' of tunable lasers^[45] it is indicated that Newton in his book Opticks was the first to show a diagram using a prism as a beam expander. In the same book he describes, via diagrams, the use of multiple-prism arrays. Some 278 years after Newton's discussion, multiple-prism beam expanders became central to the development of narrow-linewidth tunable lasers. Also, the use of these prismatic beam expanders led to the multiple-prism dispersion theory.^[45]

Mechanics and gravitation[link]

Newton's own copy of his Principia, with hand-written corrections for the second edition

In 1679, Newton returned to his work on (celestial) mechanics, i.e., gravitation and its effect on the orbits of planets, with reference to Kepler's laws of planetary motion. This followed stimulation by a brief exchange of letters in 1679–80 with Hooke, who had been appointed to manage the Royal Society's correspondence, and who opened a correspondence intended to elicit contributions from Newton to Royal Society transactions.^[41] Newton's reawakening interest in astronomical matters received further stimulus by the appearance of a comet in the winter of 1680–1681, on which he corresponded with John Flamsteed.^[46] After the exchanges with Hooke, Newton worked out a proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector (see Newton's law of universal gravitation – History and De motu corporum in gyrum). Newton communicated his results to Edmond Halley and to the Royal Society in De motu corporum in gyrum, a tract written on about 9 sheets which was copied into the Royal Society's Register Book in December 1684.^[47] This tract contained the nucleus that Newton developed and expanded to form the Principia.

The Principia was published on 5 July 1687 with encouragement and financial help from Edmond Halley. In this work, Newton stated the three universal laws of motion that enabled many of the advances of the Industrial Revolution which soon followed and were not to be improved upon for more than 200 years, and are still the underpinnings of the non-relativistic technologies of the modern world. He used the Latin word gravitas (weight) for the effect that would become known as gravity, and defined the law of universal gravitation.

In the same work, Newton presented a calculus-like method of geometrical analysis by 'first and last ratios', gave the first analytical determination (based on Boyle's law) of the speed of sound in air, inferred the oblateness of the spheroidal figure of the Earth, accounted for the precession of the equinoxes as a result of the Moon's gravitational attraction on the Earth's oblateness, initiated the gravitational study of the irregularities in the motion of the moon, provided a theory for the determination of the orbits of comets, and much more.

Newton made clear his heliocentric view of the solar system – developed in a somewhat modern way, because already in the mid-1680s he recognised the "deviation of the Sun" from the centre of gravity of the solar system.^[48] For Newton, it was not precisely the centre of the Sun or any other body that could be considered at rest, but rather "the common centre of gravity of the Earth, the Sun and all the Planets is to be esteem'd the Centre of the World", and this centre of gravity "either is at rest or moves uniformly forward in a right line" (Newton adopted the "at rest" alternative in view of common consent that the centre, wherever it was, was at rest).^[49]

Newton's postulate of an invisible force able to act over vast distances led to him being criticised for introducing "occult agencies" into science.^[50] Later, in the second edition of the Principia (1713), Newton firmly rejected such criticisms in a concluding General Scholium, writing that it was enough that the phenomena implied a gravitational attraction, as they did; but they did not so far indicate its cause, and it was both unnecessary and improper to frame hypotheses of things that were not implied by the phenomena. (Here Newton used what became his famous expression Hypotheses non fingo).

With the Principia, Newton became internationally recognised.^[51] He acquired a circle of admirers, including the Swiss-born mathematician Nicolas Fatio de Duillier, with whom he formed an intense relationship. This abruptly ended in 1693, and at the same time Newton suffered a nervous breakdown.^[52]

Later life[link]

Isaac Newton in old age in 1712, portrait by Sir James Thornhill

In the 1690s, Newton wrote a number of religious tracts dealing with the literal interpretation of the Bible. Henry More's belief in the Universe and rejection of Cartesian dualism may have influenced Newton's religious ideas. A manuscript he sent to John Locke in which he disputed the existence of the Trinity was never published. Later works – The Chronology of Ancient Kingdoms Amended (1728) and Observations Upon the Prophecies of Daniel and the Apocalypse of St. John (1733) – were published after his death. He also devoted a great deal of time to alchemy (see above).

Newton was also a member of the Parliament of England from 1689 to 1690 and in 1701, but according to some accounts his only comments were to complain about a cold draught in the chamber and request that the window be closed.^[53]

Newton moved to London to take up the post of warden of the Royal Mint in 1696, a position that he had obtained through the patronage of Charles Montagu, 1st Earl of Halifax, then Chancellor of the Exchequer. He took charge of England's great recoining, somewhat treading on the toes of Lord Lucas, Governor of the Tower (and securing the job of deputy comptroller of the temporary Chester branch for Edmond Halley). Newton became perhaps the best-known Master of the Mint upon the death of Thomas Neale in 1699, a position Newton held for the last 30 years of his life.^[54][55] These appointments were intended as sinecures, but Newton took them seriously, retiring from his Cambridge duties in 1701, and exercising his power to reform the currency and punish clippers and counterfeiters. As Master of the Mint in 1717 in the "Law of Queen Anne" Newton moved the Pound Sterling de facto from the silver standard to the gold standard by setting the bimetallic relationship between gold coins and the silver penny in favour of gold. This caused silver sterling coin to be melted and shipped out of Britain. Newton was made President of the Royal Society in 1703 and an associate of the French Académie des Sciences. In his position at the Royal Society, Newton made an enemy of John Flamsteed, the Astronomer Royal, by prematurely publishing Flamsteed's Historia Coelestis Britannica, which Newton had used in his studies.^[56]

Personal coat of arms of Sir Isaac Newton^[57]

In April 1705, Queen Anne knighted Newton during a royal visit to Trinity College, Cambridge. The knighthood is likely to have been motivated by political considerations connected with the Parliamentary election in May 1705, rather than any recognition of Newton's scientific work or services as Master of the Mint.^[58] Newton was the second scientist to be knighted, after Sir Francis Bacon.

Towards the end of his life, Newton took up residence at Cranbury Park, near Winchester with his niece and her husband, until his death in 1727.^[59] His half-niece, Catherine Barton Conduitt,^[60] served as his hostess in social affairs at his house on Jermyn Street in London; he was her "very loving Uncle,"^[61] according to his letter to her when she was recovering from smallpox.

Newton died in his sleep in London on 31 March 1727 [OS: 20 March 1726],^[1] and was buried in Westminster Abbey. Newton, a bachelor, had divested much of his estate to relatives during his last years, and died intestate. After his death, Newton's hair was examined and found to contain mercury, probably resulting from his alchemical pursuits. Mercury poisoning could explain Newton's eccentricity in late life.^[62]

After death[link]

Fame[link]

French mathematician Joseph-Louis Lagrange often said that Newton was the greatest genius who ever lived, and once added that Newton was also "the most fortunate, for we cannot find more than once a system of the world to establish."^[63] English poet Alexander Pope was moved by Newton's accomplishments to write the famous epitaph:

Nature and nature's laws lay hid in night;
God said "Let Newton be" and all was light.

Newton himself had been rather more modest of his own achievements, famously writing in a letter to Robert Hooke in February 1676:

If I have seen further it is by standing on the shoulders of giants.^[64]

Two writers think that the above quote, written at a time when Newton and Hooke were in dispute over optical discoveries, was an oblique attack on Hooke (said to have been short and hunchbacked), rather than – or in addition to – a statement of modesty.^[65][66] On the other hand, the widely known proverb about standing on the shoulders of giants published among others by 17th-century poet George Herbert (a former orator of the University of Cambridge and fellow of Trinity College) in his Jacula Prudentum (1651), had as its main point that "a dwarf on a giant's shoulders sees farther of the two", and so its effect as an analogy would place Newton himself rather than Hooke as the 'dwarf'.

In a later memoir, Newton wrote:

I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.^[67]

Albert Einstein kept a picture of Newton on his study wall alongside ones of Michael Faraday and James Clerk Maxwell.^[68] Newton remains influential to today's scientists, as demonstrated by a 2005 survey of members of Britain's Royal Society (formerly headed by Newton) asking who had the greater effect on the history of science, Newton or Einstein. Royal Society scientists deemed Newton to have made the greater overall contribution.^[69] In 1999, an opinion poll of 100 of today's leading physicists voted Einstein the "greatest physicist ever;" with Newton the runner-up, while a parallel survey of rank-and-file physicists by the site PhysicsWeb gave the top spot to Newton.^[70]

Commemorations[link]

Newton statue on display at the Oxford University Museum of Natural History

Newton's monument (1731) can be seen in Westminster Abbey, at the north of the entrance to the choir against the choir screen, near his tomb. It was executed by the sculptor Michael Rysbrack (1694–1770) in white and grey marble with design by the architect William Kent. The monument features a figure of Newton reclining on top of a sarcophagus, his right elbow resting on several of his great books and his left hand pointing to a scroll with a mathematical design. Above him is a pyramid and a celestial globe showing the signs of the Zodiac and the path of the comet of 1680. A relief panel depicts putti using instruments such as a telescope and prism.^[71] The Latin inscription on the base translates as:

Here is buried Isaac Newton, Knight, who by a strength of mind almost divine, and mathematical principles peculiarly his own, explored the course and figures of the planets, the paths of comets, the tides of the sea, the dissimilarities in rays of light, and, what no other scholar has previously imagined, the properties of the colours thus produced. Diligent, sagacious and faithful, in his expositions of nature, antiquity and the holy Scriptures, he vindicated by his philosophy the majesty of God mighty and good, and expressed the simplicity of the Gospel in his manners. Mortals rejoice that there has existed such and so great an ornament of the human race! He was born on 25 December 1642, and died on 20 March 1726/7. — Translation from G.L. Smyth, The Monuments and Genii of St. Paul's Cathedral, and of Westminster Abbey (1826), ii, 703–4.^[71]

From 1978 until 1988, an image of Newton designed by Harry Ecclestone appeared on Series D £1 banknotes issued by the Bank of England (the last £1 notes to be issued by the Bank of England). Newton was shown on the reverse of the notes holding a book and accompanied by a telescope, a prism and a map of the Solar System.^[72]

A statue of Isaac Newton, looking at an apple at his feet, can be seen at the Oxford University Museum of Natural History.

In popular culture[link]

Religious views[link]

Newton's tomb in Westminster Abbey

According to most scholars, Newton was a monotheist who believed in biblical prophecies but was Antitrinitarian.^[6][73] 'In Newton's eyes, worshipping Christ as God was idolatry, to him the fundamental sin'.^[74] Historian Stephen D. Snobelen says of Newton, "Isaac Newton was a heretic. But ... he never made a public declaration of his private faith—which the orthodox would have deemed extremely radical. He hid his faith so well that scholars are still unravelling his personal beliefs."^[6] Snobelen concludes that Newton was at least a Socinian sympathiser (he owned and had thoroughly read at least eight Socinian books), possibly an Arian and almost certainly an anti-trinitarian.^[6] In an age notable for its religious intolerance, there are few public expressions of Newton's radical views, most notably his refusal to receive holy orders and his refusal, on his death bed, to receive the sacrament when it was offered to him.^[6]

In a view disputed by Snobelen,^[6] T.C. Pfizenmaier argues that Newton held the Arian view of the Trinity rather than the Western one held by Roman Catholics, Anglicans and most Protestants.^[75] Although the laws of motion and universal gravitation became Newton's best-known discoveries, he warned against using them to view the Universe as a mere machine, as if akin to a great clock. He said, "Gravity explains the motions of the planets, but it cannot explain who set the planets in motion. God governs all things and knows all that is or can be done."^[76]

Along with his scientific fame, Newton's studies of the Bible and of the early Church Fathers were also noteworthy. Newton wrote works on textual criticism, most notably An Historical Account of Two Notable Corruptions of Scripture. He placed the crucifixion of Jesus Christ at 3 April, AD 33, which agrees with one traditionally accepted date.^[77] He also tried unsuccessfully to find hidden messages within the Bible.

Newton wrote more on religion than he did on natural science. He believed in a rationally immanent world, but he rejected the hylozoism implicit in Leibniz and Baruch Spinoza. The ordered and dynamically informed Universe could be understood, and must be understood, by an active reason. In his correspondence, Newton claimed that in writing the Principia "I had an eye upon such Principles as might work with considering men for the belief of a Deity".^[78] He saw evidence of design in the system of the world: "Such a wonderful uniformity in the planetary system must be allowed the effect of choice". But Newton insisted that divine intervention would eventually be required to reform the system, due to the slow growth of instabilities.^[79] For this, Leibniz lampooned him: "God Almighty wants to wind up his watch from time to time: otherwise it would cease to move. He had not, it seems, sufficient foresight to make it a perpetual motion."^[80] Newton's position was vigorously defended by his follower Samuel Clarke in a famous correspondence. A century later, Pierre-Simon Laplace's work "Celestial Mechanics" had a natural explanation for why the planet orbits don't require periodic divine intervention.^[81]

Effect on religious thought[link]

Newton and Robert Boyle's mechanical philosophy was promoted by rationalist pamphleteers as a viable alternative to the pantheists and enthusiasts, and was accepted hesitantly by orthodox preachers as well as dissident preachers like the latitudinarians.^[82] The clarity and simplicity of science was seen as a way to combat the emotional and metaphysical superlatives of both superstitious enthusiasm and the threat of atheism,^[83] and at the same time, the second wave of English deists used Newton's discoveries to demonstrate the possibility of a "Natural Religion".

Newton, by William Blake; here, Newton is depicted critically as a "divine geometer".

The attacks made against pre-Enlightenment "magical thinking", and the mystical elements of Christianity, were given their foundation with Boyle's mechanical conception of the Universe. Newton gave Boyle's ideas their completion through mathematical proofs and, perhaps more importantly, was very successful in popularising them.^[84] Newton refashioned the world governed by an interventionist God into a world crafted by a God that designs along rational and universal principles.^[85] These principles were available for all people to discover, allowed people to pursue their own aims fruitfully in this life, not the next, and to perfect themselves with their own rational powers.^[86]

Newton saw God as the master creator whose existence could not be denied in the face of the grandeur of all creation.^[87][88][89] His spokesman, Clarke, rejected Leibniz' theodicy which cleared God from the responsibility for l'origine du mal by making God removed from participation in his creation, since as Clarke pointed out, such a deity would be a king in name only, and but one step away from atheism.^[90] But the unforeseen theological consequence of the success of Newton's system over the next century was to reinforce the deist position advocated by Leibniz.^[91] The understanding of the world was now brought down to the level of simple human reason, and humans, as Odo Marquard argued, became responsible for the correction and elimination of evil.^[92]

End of the world[link]

In a manuscript he wrote in 1704 in which he describes his attempts to extract scientific information from the Bible, he estimated that the world would end no earlier than 2060. In predicting this he said, "This I mention not to assert when the time of the end shall be, but to put a stop to the rash conjectures of fanciful men who are frequently predicting the time of the end, and by doing so bring the sacred prophesies into discredit as often as their predictions fail."^[93]

Enlightenment philosophers[link]

Enlightenment philosophers chose a short history of scientific predecessors — Galileo, Boyle, and Newton principally — as the guides and guarantors of their applications of the singular concept of Nature and Natural Law to every physical and social field of the day. In this respect, the lessons of history and the social structures built upon it could be discarded.^[94]

It was Newton's conception of the Universe based upon Natural and rationally understandable laws that became one of the seeds for Enlightenment ideology.^[95] Locke and Voltaire applied concepts of Natural Law to political systems advocating intrinsic rights; the physiocrats and Adam Smith applied Natural conceptions of psychology and self-interest to economic systems; and sociologists criticised the current social order for trying to fit history into Natural models of progress. Monboddo and Samuel Clarke resisted elements of Newton's work, but eventually rationalised it to conform with their strong religious views of nature.

Counterfeiters[link]

As warden of the Royal Mint, Newton estimated that 20 percent of the coins taken in during The Great Recoinage of 1696 were counterfeit. Counterfeiting was high treason, punishable by the felon's being hanged, drawn and quartered. Despite this, convicting the most flagrant criminals could be extremely difficult. However, Newton proved to be equal to the task.^[96] Disguised as a habitué of bars and taverns, he gathered much of that evidence himself.^[97] For all the barriers placed to prosecution, and separating the branches of government, English law still had ancient and formidable customs of authority. Newton had himself made a justice of the peace in all the home counties - there is a draft of a letter regarding this matter stuck into Newton's personal first edition of his Philosophiæ Naturalis Principia Mathematica which he must have been amending at the time.^[98] Then he conducted more than 100 cross-examinations of witnesses, informers, and suspects between June 1698 and Christmas 1699. Newton successfully prosecuted 28 coiners.^[99]

One of Newton's cases as the King's attorney was against William Chaloner.^[100] Chaloner's schemes included setting up phony conspiracies of Catholics and then turning in the hapless conspirators whom he had entrapped. Chaloner made himself rich enough to posture as a gentleman. Petitioning Parliament, Chaloner accused the Mint of providing tools to counterfeiters (a charge also made by others). He proposed that he be allowed to inspect the Mint's processes in order to improve them. He petitioned Parliament to adopt his plans for a coinage that could not be counterfeited, while at the same time striking false coins.^[101] Newton put Chaloner on trial for counterfeiting and had him sent to Newgate Prison in September 1697. But Chaloner had friends in high places, who helped him secure an acquittal and his release.^[100] Newton put him on trial a second time with conclusive evidence. Chaloner was convicted of high treason and hanged, drawn and quartered on 23 March 1699 at Tyburn gallows.^[102]

Laws of motion[link]

The famous three laws of motion (stated in modernised form): Newton's First Law (also known as the Law of Inertia) states that an object at rest tends to stay at rest and that an object in uniform motion tends to stay in uniform motion unless acted upon by a net external force. The meaning of this law is the existence of reference frames (called inertial frames) where objects not acted upon by forces move in uniform motion (in particular, they may be at rest).

Newton's Second Law states that an applied force, Failed to parse (Missing texvc executable; please see math/README to configure.): \vec{F} , on an object equals the rate of change of its momentum, Failed to parse (Missing texvc executable; please see math/README to configure.): \vec{p} , with time. Mathematically, this is expressed as

Failed to parse (Missing texvc executable; please see math/README to configure.): \vec F = \frac{\mathrm{d}\vec p}{\mathrm{\mathrm{d}}t} \, = \, \frac{\mathrm{d}}{\mathrm{d}t} (m \vec v) \, = \, \vec v \, \frac{\mathrm{d}m}{\mathrm{d}t} + m \, \frac{\mathrm{d}\vec v}{\mathrm{d}t} \,.

If applied to an object with constant mass (dm/dt = 0), the first term vanishes, and by substitution using the definition of acceleration, the equation can be written in the iconic form

Failed to parse (Missing texvc executable; please see math/README to configure.): \vec F = m \, \vec a \ .

The first and second laws represent a break with the physics of Aristotle, in which it was believed that a force was necessary in order to maintain motion. They state that a force is only needed in order to change an object's state of motion. The SI unit of force is the newton, named in Newton's honour.

Newton's Third Law states that for every action there is an equal and opposite reaction. This means that any force exerted onto an object has a counterpart force that is exerted in the opposite direction back onto the first object. A common example is of two ice skaters pushing against each other and sliding apart in opposite directions. Another example is the recoil of a firearm, in which the force propelling the bullet is exerted equally back onto the gun and is felt by the shooter. Since the objects in question do not necessarily have the same mass, the resulting acceleration of the two objects can be different (as in the case of firearm recoil).

Unlike Aristotle's, Newton's physics is meant to be universal. For example, the second law applies both to a planet and to a falling stone.

The vector nature of the second law addresses the geometrical relationship between the direction of the force and the manner in which the object's momentum changes. Before Newton, it had typically been assumed that a planet orbiting the Sun would need a forward force to keep it moving. Newton showed instead that all that was needed was an inward attraction from the Sun. Even many decades after the publication of the Principia, this counterintuitive idea was not universally accepted, and many scientists preferred Descartes' theory of vortices.^[103]

Apple incident[link]

Reputed descendants of Newton's apple tree, at the Cambridge University Botanic Garden and the Instituto Balseiro library garden

Newton himself often told the story that he was inspired to formulate his theory of gravitation by watching the fall of an apple from a tree.^[104] Although it has been said that the apple story is a myth and that he did not arrive at his theory of gravity in any single moment,^[105] acquaintances of Newton (such as William Stukeley, whose manuscript account, published in 1752, has been made available by the Royal Society)^[106] do in fact confirm the incident, though not the cartoon version that the apple actually hit Newton's head. Stukeley recorded in his Memoirs of Sir Isaac Newton's Life a conversation with Newton in Kensington on 15 April 1726:^[107]

... We went into the garden, & drank tea under the shade of some appletrees, only he, & myself. amidst other discourse, he told me, he was just in the same situation, as when formerly, the notion of gravitation came into his mind. "why should that apple always descend perpendicularly to the ground," thought he to him self: occasion'd by the fall of an apple, as he sat in a comtemplative mood: "why should it not go sideways, or upwards? but constantly to the earths centre? assuredly, the reason is, that the earth draws it. there must be a drawing power in matter. & the sum of the drawing power in the matter of the earth must be in the earths centre, not in any side of the earth. therefore dos this apple fall perpendicularly, or toward the centre. if matter thus draws matter; it must be in proportion of its quantity. therefore the apple draws the earth, as well as the earth draws the apple."

John Conduitt, Newton's assistant at the Royal Mint and husband of Newton's niece, also described the event when he wrote about Newton's life:^[108]

In the year 1666 he retired again from Cambridge to his mother in Lincolnshire. Whilst he was pensively meandering in a garden it came into his thought that the power of gravity (which brought an apple from a tree to the ground) was not limited to a certain distance from earth, but that this power must extend much further than was usually thought. Why not as high as the Moon said he to himself & if so, that must influence her motion & perhaps retain her in her orbit, whereupon he fell a calculating what would be the effect of that supposition.

In similar terms, Voltaire wrote in his Essay on Epic Poetry (1727), "Sir Isaac Newton walking in his gardens, had the first thought of his system of gravitation, upon seeing an apple falling from a tree."

It is known from his notebooks that Newton was grappling in the late 1660s with the idea that terrestrial gravity extends, in an inverse-square proportion, to the Moon; however it took him two decades to develop the full-fledged theory.^[109] The question was not whether gravity existed, but whether it extended so far from Earth that it could also be the force holding the Moon to its orbit. Newton showed that if the force decreased as the inverse square of the distance, one could indeed calculate the Moon's orbital period, and get good agreement. He guessed the same force was responsible for other orbital motions, and hence named it "universal gravitation".

Various trees are claimed to be "the" apple tree which Newton describes. The King's School, Grantham, claims that the tree was purchased by the school, uprooted and transported to the headmaster's garden some years later. The staff of the [now] National Trust-owned Woolsthorpe Manor dispute this, and claim that a tree present in their gardens is the one described by Newton. A descendant of the original tree ^[110] can be seen growing outside the main gate of Trinity College, Cambridge, below the room Newton lived in when he studied there. The National Fruit Collection at Brogdale^[111] can supply grafts from their tree, which appears identical to Flower of Kent, a coarse-fleshed cooking variety.^[112]

Writings[link]

• Method of Fluxions (1671)
• Of Natures Obvious Laws & Processes in Vegetation (unpublished, c. 1671–75)^[113]
• De motu corporum in gyrum (1684)
• Philosophiæ Naturalis Principia Mathematica (1687)
• Opticks (1704)
• Reports as Master of the Mint (1701–25)
• Arithmetica Universalis (1707)
• The System of the World, Optical Lectures, The Chronology of Ancient Kingdoms, (Amended) and De mundi systemate (published posthumously in 1728)
• Observations on Daniel and The Apocalypse of St. John (1733)
• An Historical Account of Two Notable Corruptions of Scripture (1754)

See also[link]

	Book: Isaac Newton
Wikipedia books are collections of articles that can be downloaded or ordered in print.

Notes[link]

References[link]

Further reading[link]