Born 1642 in Lincolnshire, England
1660: entered Trinity College, Cambridge
1665: graduated without distinction. This was a plague year, so he returned to Lincolnshire.
Newton had already discovered the binomial theorem; started work on "fluxions" (calculus).
Watching an apple fall, he wondered if the same force held the moon in orbit.
The gravitational force would have to supply the centripetal acceleration to keep
the moon in a circular orbit: a
But v = 2 * R
Newton used R
For comparison, the gravitational acceleration of an object close to the surface of the
earth is g = 980 cm/s
Newton guessed that an inverse power law should hold: for any object (mass M), the gravitation force is proportional to 1/(distance from centre of earth)^n. So if M is kept constant, the gravitational acceleration would also be proportional to 1/(distance from centre of earth)^n .
If so, g/a
= 60 for n = 1 , 3600 for n = 2 , 216000 for n = 3
Comparison with the "observed" value (3769) strongly suggests n = 2, but Newton was discouraged by the 5 % error ! Is the gravitation pull of the earth really the same as if its mass were all concentrated at the centre? It took Newton several years to prove this.
Later, Newton used a more accurate value for earth's radius, measured by Picard using Eratosthenes' method (variation of an celstial object's elevation with lattitude) but using star sightings rather than the sun, and obtained better agreement.
1668: developed the reflecting telescope. His first model had a 1" diam mirror and magnified up to 40 times. Today, all large instruments are of this type.
Newton believed, wrongly, that colour fringes (chromatic aberration) were inevitable in a refracting system. Besides chromatic effects, his reflecting telescope avoided light absorption in glass lenses (appreciable for the glass used at that time).
1669: at age 26, Newton was made Lucasian Professor of Mathematics in Cambridge (the post currently held by Stephen Hawking). He had to give 8 lectures/year, but these were not popular with students and not understood by most professors who dropped in to listen.
1671: built a 2" reflecting telescope and demonstrated it to King Charles II (an amateur physicist who founded the Royal Society - the most prestigious in Europe). Newton was elected a Fellow of Royal Society and communicated to them the results of his experiments on colours. Publication in the Royal Society's Transactions resulted in 12 letters; Newton felt that his privacy had been invaded.
Newton advocated a particle view of light, Hooke and Huygens a wave picture. We now know that both points of view are partially correct.
1684: Halley came to Cambridge to meet Newton. Hooke and Halley were convinced that gravity must decrease proportional to the square of distance and that this might explain the elliptical orbits of the planets, but could not prove it. Their colleague Wren offered a prize (a book worth up to 40 shillings) if either of them could produce a proof within 2 months, but neither succeeded.
Asked by Helley about the shape of planetary orbits if attractive force * 1/(distance)^2, Newton immediately came up with the correct answer: an ellipse. But he could not find the papers containing his derivation. While re-deriving the answer, he used his calculus (fluxions) to prove that a sphere has the same attractive force as a point mass.
1687: published Mathematical Principles of Natural Philosophy ("Principia"). Written in Latin; English translation 1729. Proofs by geometry not calculus, so that they could not be refuted. 400 copies were printed. Each had three volumes: general principles of dynamics; fluid mechanics and wave theory; application of dynamics to the mechanism of the heavens.
Hooke claimed prior discovery of certain details and tried to delay publication. The Royal Society withdrew its agreement to publish; Halley paid for publication and did all the proofreading.
The book is hard to read: Newton told a friend he "designedly made his Principia abstruse ... to avoid being baited by little smatterers in mathematicks". Yet it had a big impact; Britain was recovering from a period of war.
Often considered to be the greatest scientific work ever written. Ushered in the Age of Reason: the expectation that all problems could be solved by acceptance of a few axioms (based on careful observations) and skillful use of mathematics. It led to similar attempts in philosophy (John Locke) and economics (Adam Smith).
1. (Principle of Inertia): an object remains at rest or in uniform motion in a straight line, if not acted on by a force. (This redefined "natural motion", making it unnecessary to postulate a driving force for motion of the planets, such as Descartes' vortices; the planets move through space because nothing opposes their motion).
2. F = m a. This equation defines force in terms of mass and acceleration. (First clear distinction between mass and weight; mass = resistance to acceleration, related to inertia, weight=gravitational force on an object, usually due to the earth.) But is it a physical law or just a definition ? Definition of force or mass ?
If taken as a definition of force, F = ma arguably has no physical content. However, it can be taken as an "organizing principle" which clarifies our concept of force and motion. For example, it is a vector equation; it tells us to look for a force in the direction of a, towards the centre of circle in the case of uniform circular motion or towards one focus in the case of an ellipse. Also, it says that force is related to the second derivative of displacement, not the 10th for example.
3. For every action there is an equal and opposite reaction (sometimes called the
The third law implies that just as the sun exerts a force on planet, the planet exerts a force on the sun. So the sun moves (but only a little); both objects revolve around a common centre of mass.
Newton estimated G by considering moon/earth system and used the equation to
determine the masses of Jupiter and Saturn. Later (in 1798), Cavendish determined an
accurate value of G and therefore M
The Law of Universal Gravitation explained many things:
In fact, the Law of Gravitation can be derived from Kepler's 3rd Law.
For a stable circular orbit, force on a planet is: F = M
The tides (bulges on both sides of Earth, towards and away from the sun)
Precession of the earth's rotational axis. Forces on the two bulges are unequal, leading to a torque which ought to restore the axis to being perpendicular to ecliptic plane. However, system behaves like a gyroscope or spinning top: instead of moving in the direction one might expect, axis of rotateion moves in a perpendicular direction, i.e. it precesses about the perpendicular P. The precession rate very low: period T = 26,000 years.
How observed? At vernal equinox, sun should rise due east and set due west, midsummer's day rise at certain point. Monuments and temples were built to demonstrate this. But over the years, the positions of the stars and sun (at a particular season) were found to vary. This effect was discovered by Hipparchus (130 BC) by comparing the position of sunrise at vernal equinox with the constellations, so it is known as precession of the equinox.
Irregularities in the moon's orbit due to precession: the plane of the orbit is not perpendicular to earth's axis of rotation etc.
Irregularities in the motions of the planets: perturbations, a result of their mutual attractions, which make the orbits slightly non-elliptical. Since the mass of planets is much less than the sun (even Jupiter/Sun = 1/1000), these deviations are small but observable. In fact, irregularities in the orbit of planet Uranus (discovered in late 18 century) led to the discovery of Neptune.
In 1930's, the economist John Maynard Keynes purchased a trunk full of Newton's papers at an auction; to his surprise, he found it full of notes on alchemy and biblical prophecy, with floor plans of the Temple at Jerusalem reconstructed from Hebrew texts.
From biblical chronology, Newton calculated the day of creation, obtaining a result not very different from Kepler. (Bishop Ussher, in a famous proclamation, gave the moment of creation as midnight of 23 October, 4004 BC)
1692: Newton suffered a nervous breakdown, possibly caused by mercury poisoning from his alchemy experiments. Spent 2 years in isolation, writing strange letters to his friends, but recovered.
1696: a Swiss mathematician challenged European scholars to solve two problems. Newton forwarded his answers anonymously, but was easily identified.
1687: elected Member of Parliament. Records show that he never made a formal speech.
1696: appointed Warden of the Mint, and in 1699 Master of the Mint (considered an honour and carrying a generous salary; Newton left 30,000 pounds on his death). Resigned his professorship and reorganised the production of money; attacked the problem of counterfeiting by interrogating suspects, sending many to the gallows.
1703: President of the Royal Society; re-elected each year until his death.
1704: wrote Opticks (in English, but soon translated into Latin so that Europeans could read it).
1713: second edition of Principia.
In words of Tom Ferris, Newton cast a long shadow. He may even have retarded science in Britain in the years after his death, by appearing to settle matters which should have been further investigated. Certainly, Newton used his influence to fill University posts with his proteges.
In a letter to Hooke (1676) he says "If I have seen further than other men, it is because I stood on the shoulders of giants". He avoided the "booby traps" of magnetism, Kepler's anima motrix and Descartes' vortices as explanations for motion of the planets; but substituted "action at a distance", which Leibniz described as "occult" and Huygens called "absurd". Newton agreed, calling action at a distance "so great an absurdity that I believe no man who has, in philosophical matters, a competent faculty of thinking, can ever fall into it".
At end of Principia, he says " I have not been able to discover the cause of those properties of gravity from phenomena, and so I frame no hypothesis". It might have remained a crank idea, except for the fact that Newton was able to express it in precise mathematical terms and demonstrate that his theory fitted the observed behaviour of the heavens: the motions of the moon and planets.
Followers of Descartes argued that the vortex model provided an explanation of gravity and was therefore a better theory. But it did not lead to quantitative predictions, and survived only 50 years after Newton (even in continental Europe). After a while, people stopped asking about the cause of gravity.
Another problem which Newton foresaw was that under the action of universal gravity, the universe should collapse; the stars should rush together to form an implosion. We now know that this will not happen in the "near" future because the universe is expanding.
Principia: "The orbit of any one planet depends on the combined action of all the
planets, not to mention the action of all of these on each other. But to consider
simultaneously all these causes of motion and to define these motions by exact
laws allowing of convenient calculation exceeds, unless I am mistaken, the force
of the entire human intellect." Here, Newton identifies the "many body problem"
which remains unsolved analytically.
However, it can be treated numerically (by computer calculation). Given sufficient knowledge of initial conditions (displacement and velocity) of a system of particles and a mathematical description of their interactions (gravity being one), the behaviour of a system can in principle be predicted. Extending this idea to the entire universe leads to the idea of determinism, loosely related to materialism: the belief that only matter has real existence.
Many philosophers have felt that the determinism inherent in Newton's description denies the possibility of free will. Voltaire: "It would be very singular that all nature, all the planets, should obey eternal laws but that there should be a small animal, five feet high, who in contempt of these laws could act as he pleased".
Newton did not consider that his theory had diminished the role of the God in the Universe; he had discovered laws, but their authorship remained a mystery. At the end of the Principia, he says "this most beautiful system of the sun, planets and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being".
In fact, Newton believed that divine intervention was occasionally necessary to correct the planetary orbits, otherwise interaction of the planets would make the solar system unstable. Later, Laplace showed that the solar system would be stable, in spite of the perturbations. (The sun is slowly loosing mass but the planetary orbits are expected to increase by less than 1% before the sun becomes a white dwarf, 10 billion years in the future).