Transcript Pearl on Newton`s Principia

Newton’s Principia
Presentation by: Sean Pearl
• 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
http://www.bbc.co.uk/history/discovery/revolutions/launch_
ani_cosmology.shtml
(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
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
Popular view of Scientific method (view initiated by Bacon):
Observation, Hypothesis, Prediction, Confirmation
Newton’s 4 Rules of Reasoning in Philosophy
1. We are to admit no more causes of natural things than such as are both true
and sufficient to explain their appearances.
2. Therefore to the same natural effects we must, as far as possible, assign the
same causes.
3. 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.
4. 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.
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)
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
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
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
“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/de
mo1202.mpg
“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/d
emo1201.mpg
“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/dem
o1203.mpg
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