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/demo1202.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/demo1201.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/demo1203.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