“newton” by william blake ch 5 pg....

Lecture 3

Isaac Newton & the Newtonian Age

“If I have ever made any valuable discoveries, it has been owing more to patient attention, than to any other talent.” - Newton

“Newton” By William Blake ~1800

Ch 5 pg. 91-95 ++

Newton •  Born 1642 (the year of

Galileo’s death). •  The world he was born into

was one ruled by mysticism.

•  Philosophy/Science were similar, Newton was the last “Philosoper/Scientist”

•  The world was not generally regarded as “solvable”.

•  By the time of his death, he would have answered ancient philosophical questions: –  The nature of light –  Motion & time

•  Invented calculus •  Discovered gravity •  Explained planetary motions

& Keplers Laws •  Found time to invent a new

kind of telescope, study theology, alchemy, and chemistry.

The time of Newton

•  “Gravity” = solemn. A mood, not a force!

•  People thought: Light things and heavy things separated themselves “naturally” up & down.

•  Time was hard to measure.

•  Concept of motion was not well-defined.

•  Aristotle: Things “in motion” include: –  An apple ripening –  A dog running –  A child growing –  A spinning top.

Newton’s impact:

•  Invented terms and concepts: –  “mass” –  “action” –  “reaction” –  “momentum” –  “inertia” –  “to feel the force of

gravity”

•  Quantified the world •  Invented calculus. •  Made us all “Newtonians”:

–  We believe the Universe is solvable

–  We seek to explain trends in weather, society, human behavior, etc.

–  Before Newton, this was not generally the case.

•  Most of the mathematical truths that people had discovered over history had been forgotten and then discovered, again and again, by cultures far from 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 all

there was to know).

•  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

Newton at Cambridge

•  Curriculum: –  Aristotle was the single

authority in logic, ethics, and rhetoric, cosmology, & mechanics.

•  Studied on his own (Newton’s tutor was a linguist)

•  He was poor, so developed his own short-hand to save on paper costs. Wrote in tiny script.

Trinity College at Cambridge

Entered June, 1661


Aristotle’s “Motion” •  Motion included: pushing, pulling, carrying,

twirling, combing, separating, waxing and waning.

•  Light things and heavy things separated themselves naturally by moving up and down.

•  This all-embracing idea of motion left little room for the difference between velocity and acceleration. No room for quantifying things with numbers.

Influence of Galileo •  Newton found references to

Galileo’s work. (Galileo had died the year Newton was born).

•  Galileo: all bodies fall at the same rate. –  Not the same *speed*, but

the same rate –  Galileo created a concept

of uniform acceleration –  This explicitly defied

Aristotle

•  Newton asked: –  How and why does

something’s velocity change?


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 began reading, 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 lines

and 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.


Newton’s Calculus •  Calculus:

–  Mathematics that allows one to deal with infinitesimals and infinities.

–  Keeps track of how lines of curve and change

–  Area under curves –  Slopes of lines

Zeno’s paradox: –  Zeno was a famous

greek philosopher ~480BC.

•  Zeno: If space is infinitely divisible, a person can never get to where he/she is going. Motion itself is impossible, and therefore must be an illusion!

•  Calculus helps us understand how to “sum up” a series of infinitely small pieces and have it add up to a finite number. (Some infinities are bigger than others…)

Newton’s Calculus

Newton’s Laws of Motion

1)  Bodies in motion tend to remain in motion –  Bodies move at constant speed unless acted on by

an outside force. –  This property is called “inertia”.

2)  F=ma : Force = mass x acceleration 3)  “For every action there is an equal and opposite

reaction”   If I push on the wall, the wall pushes back

Newton derived laws that showed how objects move -- on Earth and in space -- Starting point of modern physics.

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

Newton’s Law of Gravity

Force of gravity is larger from a more massive object.

Every object in the Universe attracts every other object in the Universe. This force is Gravity.

Force of gravity is smaller from something farther away.

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 less massive, what would happen?

Newton’s Version of Kepler’s 3rd Law

Kepler’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 is proportional to R^3 in this limit => Kepler’s 3rd law.

Principia Mathematica •  Newton kept his ideas to himself until

publishing them in 1687 in his “Principia”. •  “Principia” is often claimed to be the

greatest work in the history of the physical sciences. –  Demonstrated that the motion of all bodies were

controlled by the same physical laws, both in the heavens 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, and show that it stayed blue when it passed through a second prism. –  Concluded that prisms

did not make color, but rather separates them.

–  white light was “made up of” the different colors.

Debates at the time… •  Voltaire: “For us (the French) it is the pressure of the

moon that causes the tides of the sea, for the English (Newton) it is the sea that gravitates towards the moon…”

•  Fundamental concepts up in the air: –  “For a Cartesian (following Descartes) light exist

in the air, for a Newtonian, it comes from the sun in (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 and

philosophy went separate ways after Principia. –  Newton took questions about the nature of things -

about what exists - away from “metaphysics” and assigned them to a new realm, physics.

•  By linking science & math, he made it possible for its facts and claims to be proved wrong.

•  That hypotheses can be proven wrong is the fundamental strength of science. It allows us to make progress, to dismiss theories that are lacking, and work towards building a more complete picture of the Universe.

Orbital speed of planets

K’s 3rd:

Speed of the orbit, v, is the distance around the orbit (2 pi R) divided by the time to go around (the period P):

Speed of orbit falls off with radius

Quotations & Life •  “I don’t know what I may seem to the world, but, as 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.”

•  Tomb @ Westminster Abbey: "Mortals! rejoice at so great an ornament to the human race!"

•  Alexander : "Nature and Nature's laws lay hid in night; God said, Let Newton be! and all was light."

“newton” by william blake ch 5 pg....

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