NOTES ON POST-MEDIEVAL SCIENCE

Some important scientists & discoveries:

I. Nicolaus Copernicus

Developed his heliocentric conception of the cosmos around 1510 but didn't publish it, probably for fear of criticism.

Wrote his famous defense of the heliocentric system, On the Revolutions of the Celestial Spheres in 1530, but it wasn't published until shortly before his death, in 1543.

Copernicus' system:

Earth rotates on its axis daily and orbits the sun yearly.

Kept the planetary spheres & the sphere of the fixed stars, but they are centered on the sun. The sphere of the fixed stars is stationary. The planets orbit the sun.

However, Copernicus' system was initially less accurate than the Ptolemaic system, and only slightly simpler.

The system was not accepted at first. There were only 10 Copernicans before 1600 (including Kepler & Galileo).

II. Tycho Brahe

Another astronomer, later in the 1500s.

The king of Denmark & Norway provided him funds to build an observatory, where he pursued his astronomical observations (until the next king took it away).

Brahe is known as a meticulous observer.

Discovered errors in the standard astronomical tables and corrected them.

Catalogued 700 stars. Made the most accurate measurements of stellar positions to date.

Proposed a compromise between Copernican & Ptolemaic astronomy: the planets orbit the sun, while the sun orbits the earth. The fixed stars also orbit the earth.

Provided data that enabled Kepler to formulate his laws.

III. Johannes Kepler

Kepler was Brahe's assistant at the end of Brahe's life (1600). Kepler lived into the early 1600s.

Accepted Copernican system. Initially he used circular orbits. Proposed that the sun emits a force that diminishes with distance and that pushes planets around in their orbits.

Later figured out that the orbits were elliptical.

Kepler's laws of planetary motion:

1. Planets move in elliptical orbits, with the sun at one focus.

2. A line drawn from the planet to the sun sweeps out equal areas in equal times.

3. R³/T² is a constant for all the planetary orbits, where R=the average distance from the sun and T=the orbital period.

Based on Brahe's data, Kepler found the Ptolemaic system to be in error, and his own system more accurate.

Heliocentric system was still not generally accepted when he died.

IV. Galileo Galilei

Lived into mid 1600s.

Famous physics discoveries:

Discovered the law that the period of a pendulum depends on the length of the string, and not on the weight on it. He is said to have discovered this while watching a pendulum in a cathedral, and using his pulse for a timer.

Famous story (probably apocryphal): he dropped a heavy and a light object from the Leaning Tower, in order to prove to his students that rate of fall was independent of weight, refuting Aristotle.

Studied motion. Discovered parabolic path of projectiles.

Astronomy:

Accepted Copernican system.

Built a telescope of 20x magnification. Discovered: craters on the moon, the phases of Venus, & 4 satellites of Jupiter.

The Copernican system had been pronounced heresy in 1616.

Nevertheless, in 1632, he published his Dialogue on the Two Chief World Systems. In it, he defended the Copernican system. Despite its approval by church censors, he was called to Rome to be tried for heresy (1633). He recanted, and was sentenced only to house arrest for the rest of his life.

Somehow, he went ahead and wrote another book, refuting Aristotelian physics, the Dialogues on Two New Sciences.

Died in 1642, the same year Newton was born.

The church forgave him in 1992.

V. Isaac Newton

Dec. 25, 1642 - 1727. Possibly the greatest scientist in history.

Discoveries/studies:

The 'method of fluxions' (differential calculus).

Studied light & colors.

The laws of motion.

The theory of gravity.

The binomial theorem.

Spent his later life studying theology.

More about Newton's biggest discoveries:

Study of the moon's orbit. Assumed there was an inverse square law of gravitation. Used this to argue that the moon is held in its orbit by the same force as terrestrial gravity.

In the Principia Mathematica (1687):

Newton's definitions:

There are 8 definitions:

1. Quantity of matter is a measure of matter that arises from its density and volume jointly.

2. Quantity of motion is a measure of motion that arises from the velocity and the quantity of matter jointly.

+ 6 more.

Laws of motion:

1. Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed.

2. A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.

3. To any action there is always an opposite and equal reaction; in other words, the actions of two bodies upon each other are always equal and always opposite in direction.

Theory of gravity: each particle of matter attracts every other particle. Attraction is proportional to mass, inversely proportional to distance squared. Newton proved results from this:

The gravitational force produced by a spherical body is as if the mass were concentrated at the center.

The gravitational force would produce an elliptical orbit.

It would also produce an orbit in which the orbiting object swept out equal areas in equal times.

The parallelogram law for the composition of forces.

Newton used geometrical methods, rather than fluxions, to avoid controversy about fluxions.

Didn't know how gravity worked, but he rejected 'action at a distance.'

Calculus:

Fluxions & fluents. Fluents are changing quantities; fluxions are their rates of change. Newton dealt with 2 kinds of problems:

"The relation of the fluents being given, to find the relation of their fluxions." (In modern terms: given y as a function of x, to find dy/dx.)

Given the relation of the fluxions, to find the relation of the fluents. (In modern terms: given dy/dx, to find y as a function of x.)

Newton was mainly concerned with motion and change over time, so he considered quantities that are mathematically related as changing over time.

Newton discovered that integration was the inverse operation of differentiation (a.k.a. 'the fundamental theorem of calculus')

Makes it possible to determine velocity function from acceleration

Newton's influence:

Came to be accepted first in Britain, then in the rest of Europe. France held out for several decades, in deference to Descartes.

About Newton's life:

Tried to avoid controversy; avoided publishing

Modest about his accomplishments:

"I do not know what I may appear to the world; but 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."

--I. Newton

Anti-social. Not very generous, as shown by his controversy with Leibniz.

Was completely focused on scientific work.

Generally a genius. Known for solving difficult problems posed by other scientists.