“Newton” By William Blake Ch 5 Pg. 91-95

“Newton” By William Blake 1800Ch 5 pg. 91-95 Lecture 3Isaac Newton & the Newtonian Age“If I have ever made any valuable discoveries, it has been owing more topatient attention, than to any other talent.” - Newton

Newton Born 1642 (the year ofGalileo’s death). The world he was born intowas one ruled bymysticism. Philosophy/Science weresimilar, Newton was thelast “Philosoper/Scientist” The world was notgenerally regarded as“solvable”. By the time of his death, hewould have answered ancientphilosophical questions:– The nature of light– Motion & time Invented calculus Discovered gravity Explained planetary motions& Keplers Laws Found time to invent a newkind of telescope, studytheology, alchemy, andchemistry.

The time of Newton “Gravity” solemn. Amood, not a force! People thought: Lightthings and heavy thingsseparated themselves“naturally” up & down. Time was hard tomeasure. Concept of motion wasnot well-defined. Aristotle: Things “inmotion” include:––––An apple ripeningA dog runningA child growingA spinning top.

Newton’s impact: Invented terms ��“reaction”“momentum”“inertia”“to feel the force ofgravity” Quantified the world Invented calculus. Made us all “Newtonians”:– We believe the Universe issolvable– We seek to explain trends inweather, society, humanbehavior, etc.– Before Newton, this was notgenerally the case.

The time of Newton Most of the mathematical truths that people had discovered over historyhad been forgotten and then discovered, again and again, by cultures farfrom each other. It was still possible for one person to comprehend all of human knowledge!Only recently has this changed. (It is said that Thomas Jefferson knew allthere was to know). Newton, as a youth, *rediscovered* most of mathematics known tohumankind, and then invented calculus to help him understand motion. “The landscape has been so totally changed (by Newton) that it is veryhard to get hold of what it was like before” - H. Bondi.See Gleick’s “Isaac Newton”, Vintage 2003

Newton atCambridge Curriculum:Trinity College at CambridgeEntered June, 1661– Aristotle was the singleauthority in logic, ethics,and rhetoric, cosmology, &mechanics. Studied on his own(Newton’s tutor was alinguist) He was poor, sodeveloped his own shorthand to save on papercosts. Wrote in tiny script.See Gleick’s “Isaac Newton”, Vintage 2003

Aristotle’s “Motion” Motion included: pushing, pulling, carrying,twirling, combing, separating, waxing andwaning. Light things and heavy things separatedthemselves naturally by moving up and down. This all-embracing idea of motion left littleroom for the difference between velocity andacceleration. No room for quantifying thingswith numbers.

Influence of Galileo Newton found references toGalileo’s work. (Galileo haddied the year Newton wasborn). Galileo: all bodies fall at thesame rate.– Not the same *speed*, butthe same rate– Galileo created a conceptof uniform acceleration– This explicitly defiedAristotle Newton asked:– How and why doessomething’s velocitychange?See Gleick’s “Isaac Newton”, Vintage 2003

1664: Plague & Isolation In 1664 colleges in Cambridge shut down because of the Plague -It would eventually kill one out of every six in London.Newton went home, made himsellf a small study, and beganreading, taking notes, and doing research.‒ Read Euclid’s “Elements” (Geometry). Read Descartes, etc. Thought a lot about the concept of infinity.Wanted to understand curvature, and the rate of bending of linesand trajectories.Goal “to resolve Problems by motion”– In order to do this, he invented math that was continuous, not discrete.That is, he invented calculus.See Gleick’s “Isaac Newton”, Vintage 2003

Newton’s Calculus Calculus:– Mathematics that allowsone to deal withinfinitesimals andinfinities.– Keeps track of howlines of curve andchange– Area under curves– Slopes of lines

Newton’s CalculusZeno’s paradox:– Zeno was a famousgreek philosopher 480BC. Zeno: If space isinfinitely divisible, aperson can never get towhere he/she is going.Motion itself isimpossible, andtherefore must be anillusion! Calculus helps usunderstand how to“sum up” a series ofinfinitely smallpieces and have itadd up to a finitenumber. (Someinfinities are biggerthan others )

Newton’s Laws of MotionNewton derived laws that showed how objects move-- on Earth and in space -- Starting point of modern physics.1) Bodies in motion tend to remain in motion– Bodies move at constant speed unless acted on byan outside force.– This property is called “inertia”.2) F ma : Force mass x acceleration3) “For every action there is an equal and oppositereaction” If I push on the wall, the wall pushes back

Thinking about gravity What do apples Have to do with orbits?

Newton’s Law of GravityEvery object in the Universe attracts every other objectin the Universe. This force is Gravity.Force of gravity is larger from a more massive object.Force of gravity is smaller from something farther away.

Newton’s Law of GravityEvery object in the Universe attracts every other objectin the Universe. This force is Gravity.Force of gravity is larger from a more massive object.Force of gravity is smaller from something farther away.

Newton’s Law of GravityEvery object in the Universe attracts every other objectin the Universe. This force is Gravity.Force of gravity is larger from a more massive object.Force of gravity is smaller from something farther away.

Newton’s Law of GravityEvery object in the Universe attracts every other objectin the Universe. This force is Gravity.Force of gravity is larger from a more massive object.Force of gravity is smaller from something farther away.

How does the Earth’s gravity tug on the ball as it orbits?

How does the Earth’s gravity tug on the ball as it orbits?

How does the Earth’s gravity tug on the ball as it orbits?

How does the Earth’s gravity tug on the ball as it orbits?

How does the Earth’s gravity tug on the ball as it orbits?

How does the Earth’s gravity tug on the ball as it orbits?

If the Earth were to get more massive, what would happen?

If the Earth were to get more massive, what would happen?

If the Earth were to get less massive, what would happen?

Newton’s Version of Kepler’s 3rd LawKepler’s 3rd Law:Newton derived:Newton’s version applied to all objects orbiting each other -not just planets about sun, but moon about earth, etc.For sun mass m1 and planet m2, m1 m2 and P 2 isproportional to R 3 in this limit Kepler’s 3rd law.

Principia Mathematica Newton kept his ideas to himself untilpublishing them in 1687 in his “Principia”. “Principia” is often claimed to be thegreatest work in the history of the physicalsciences.– Demonstrated that the motion of all bodies werecontrolled by the same physical laws, both in theheavens and on earth.– Explained motions of planets and comets,Kepler’s laws.– Presented the Law of Gravity

Newton and Light What was light? Newton used a prism to“isolate” blue light, andshow that it stayed bluewhen it passed througha second prism.– Concluded that prismsdid not make color, butrather separates them.– white light was “made upof” the different colors.

Debates at the time Voltaire: “For us (the French) it is the pressure of themoon that causes the tides of the sea, for theEnglish (Newton) it is the sea that gravitates towardsthe moon ” Fundamental concepts up in the air:– “For a Cartesian (following Descartes) light existin the air, for a Newtonian, it comes from the sunin (eight) minutes”.Now, we are all Newtonians. (We see the world the way he did.)-Light comes from the Sun.-The Moon tugs at the Earth.-The same Universal laws exist throughout the Universe.

Newton: architect of modern science Principia marked a fork in the road: science andphilosophy went separate ways after Principia.– Newton took questions about the nature of things about what exists - away from “metaphysics” andassigned them to a new realm, physics. By linking science & math, he made it possible for itsfacts and claims to be proved wrong. That hypotheses can be proven wrong is thefundamental strength of science. It allows us to makeprogress, to dismiss theories that are lacking, and worktowards building a more complete picture of theUniverse.

Orbital speed of planetsSpeed of the orbit, v, is the distance around the orbit (2 pi R)divided by the time to go around (the period P):K’s 3rd:Speed of orbit falls off with radius

Quotations & Life “I don’t know what I may seem to the world, but, as to myself, Iseem to have been only like a boy playing on the sea-shore,and diverting myself in now and then finding a smoother pebbleor a prettier shell than ordinary, whilst the great ocean of truthlay all undiscovered before me.” Tomb @ Westminster Abbey: "Mortals! rejoice at so great anornament to the human race!" Alexander : "Nature and Nature's laws lay hid in night; Godsaid, Let Newton be! and all was light."

Newton, as a youth, *rediscovered* most of mathematics known to humankind, and then invented calculus to help him understand motion. “The landscape has been so totally changed (by Newton) that it is very hard to get hold of what it was like before” - H. Bondi. The time of Newton See Gleick’s “Isaac Newton”, Vintage 2003