Newton’s Principia

1. Newton’s Principia Presentation by: Sean Pearl

2. History of Kinetics and Planetary Motion • Aristotelian Concept of an object’s natural place and thus a natural motion • Ptolemy – Geocentric Universe • Copernicus – Heliocentric (not accepted yet) • Brahe – Geocentric with the rest of planets revolving around sun • Kepler – Heliocentric universe with elliptical orbits • Galileo – Naturally accelerated motion, projectile motion (separation of components of motion), inertia • Galileo agreed with Copernican view of universe • Galileo on motion: all bodies heavy and fall to earth; change in motion important Overview of Planetary Theory http://www.bbc.co.uk/history/discovery/revolutions/launch_ani_cosmology.shtml

3. Biography of Isaac Newton (1642 – 1727) Born in Woolsthorpe, England on Christmas Day 1642 Age 12 – King’s School in Grantham 1661 – Attended Trinity College, Cambridge Discovered the Binomial Theorem while attending the university 1664 – 1665: Began work on “Fluxions” (Calculus) 1665 – 1667: chemistry, prisms, calculus, considered lunar forces 1669: De Analysi per Aequationes Numero Terminorum Infinitas Also became Lucasian professor at Trinity 1670 – 1671: De Methodis Serierum et Fluxionum 1672: Lecture Series, began rivalry with Robert Hooke 1679: Hooke posed problem of trying to determine the orbit of the planets, with a force varying inversely as the square of the distance from the sun Newton had proved that the orbit was an ellipse

4. Biography (cont.) Halley Encourage Newton to publish these results 1685 – 1686: Newton expanded this principle into his Principia 1693 – 1696: Major controversy with Gottfried Leibniz for invention of calculus Newton did not publish until his Optics in 1704, Leibniz published in 1684 “Tanquam ex ungue leonem” 1705: Knighted; first scientist in England so honored Died on March 20th, 1727 of gallstones

5. Newton's view on Science • Popular view of Scientific method (view initiated by Bacon): • Observation, Hypothesis, Prediction, Confirmation • Newton’s 4 Rules of Reasoning in Philosophy • We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. • Therefore to the same natural effects we must, as far as possible, assign the same causes. • The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever. • In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may e imagined, till such time as other phenomena occur, by which they may either be made more accurate or liable to exceptions.

6. With these principles: Orbits of planets about the sun are ellipses, equal areas in equal times Force of gravitation is inverse square Deduced Kepler’s 3 Laws from these observations, tidal effects of moon Hypotheses non fingo 3 different levels at which we must work: Mathematical, physical, and philosophical (causes of these laws)

7. Newton and Alchemy While at Trinity, Newton introduced to the philosophical treatise by the Neoplatonist Henry More Became aware of the Hermetic tradition that emphasized alchemy and magic 1678 – 1684: withdrew into isolation, became intensely interested in the Hermetic tradition and alchemy Believed matter could NOT organize into living forms on its own – required divine guidance, “vegetable spirit” He hoped to learn the secret of spirit of life through alchemy In Newton’s time: “spontaneous generation” was seen as a factual occurrence; i.e. Eels emerging from the mud or maggots from rotting flesh Believed that this process needed a trigger, such as the warmth of the sun or an act of God or both Alchemists quoted the Gospel according to John

8. Newton's Contribution Newton analyzed older alchemical literature and laid bare the hidden assumptions of alchemical theory regarding life and death Newton held that alchemical agents first “putrefied” and confounded an object into chaos, and that out of this chaos it THEN would generate the new forms When speaking of the orbit of the planets with Leibniz, he argued that the perturbations of the planets due to the interaction with other planets’ gravitational forces would eventually send the solar system into decay and that it would need God’s touch to renew it

9. Principia Prelude: Opens with definitions of mass, momentum, and force; states the 3 laws Book I – Motion of Bodies Some calculus concepts (limits) Motion of body about a fixed force center … (now known as constant angular momentum in time) Motion of bodies in conic sections – proves Kepler’s 3rd Law Equation of motion determines orbit Discussion of central force problem purely hypothetical, neither conditions nor results related to the actual physical world Book III – The System of the World Applies problem to natural phenomena, deduces gravity as inverse square His Universal Law of Gravitation Discusses Kepler’s Laws and slight departures due to gravitation

10. Newton's 1st Law “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.” Galileo had said that it is not the motion of bodies that was important, but the changes in motion This was formularized in the 1st Law, which basically states that a body resists changes in motion; also known as the Law of Inertia http://bednorzmuller87.phys.cmu.edu/demonstrations/mechanics/newtonslaws/demo1202.mpg

11. Newton's 2nd Law “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 acts.” Galileo had introduced the framework, but Newton was the one who introduced the concept of forces formally that produce changes in motion Simplest possible mathematical law (product of the two) used to equate forces with change in momentum (however, F = ma never mentioned in his Principia) http://bednorzmuller87.phys.cmu.edu/demonstrations/mechanics/newtonslaws/demo1201.mpg

12. Newton's 3rd Law “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.” Newton quote http://bednorzmuller87.phys.cmu.edu/demonstrations/mechanics/newtonslaws/demo1203.mpg

13. Orbit of Planets Used throwing a rock as an example for planetary orbit (connected the pull of the earth on the moon to the earth on a rock) Generalized this principle to the sun pulling on the planets and the moon pulling back on the earth (tides) Newton, as opposed to Kepler, looked to radial forces diverting the motion of the planets rather than tangential forces Dealt with infinitesimal arc elements, but asserted continuous forces; beginning of the groundwork for his calculus Force treated as discrete impulses at equal intervals of time; used smaller and smaller time units until the lines approached a curve (limits) Universal Law of Gravitation: Pendulum with the same weight of varying objects