4. RENAISSANCE PERIOD (1400-1650)

Background: conditions were favourable for new ideas and `free thought' - the cultural renaissance in Europe was at its height. The protestant reformation had begun; it was an era of new exploration $\rightarrow$ A TIME OF GREAT INTELLECTUAL STIMULATION!

4.1 Copernicus (1473-1543)

• Polish physician and lawyer; Catholic canon
• revived Aristarchus' heliocentric model
• showed that retrograde motion of the planets could be explained with this model
• measured planetary distances in a similar geometric way Aristarchus did for the Earth/Moon/Sun.

Copernicus published his work in ``De revolutionibus orbium coelestium'' (on the revolutions of the celestial orbits) in 1543 - the year he died. In 1616, the Catholic Church placed it on the Index of Prohibited Books, but this had little effect on its distribution throughout Europe (in fact, it probably helped).

Copernicus' model could do no better job than Ptolemy's in predicting positions of the planets $\Rightarrow$ Not clear why he persevered with it!! Yet again, aesthetics heavily swayed Copernicus - it was simpler than Ptolemy's and it had a ``fixed symmetry'' to it - spacing of planets fixed by observations (unlike Ptolemy's spheres).

Copernicus' model slow to be accepted:

- no better than Ptolemy's

- still the problem of stellar parallax with heliocentric model

- motion of celestial objects across sky $\rightarrow$ mind-set on Earth being at centre of motion

- no sensation of Earth moving

By this time there was a growing recognition of the Universe: the stars were recognised as other Suns with other worlds around them. New scientific open-mindedness and the aesthetic appeal of a simpler system led to a gradual acceptance of Copernicus' view. The key points were:

• Earth rotates daily on its axis
• Earth revolves yearly around the Sun
• Planets circle the Sun
• earth wobbles (precesses) as it rotates
• solid, planet-bearing spheres retained
• sphere containing fixed stars stationary
• planets ordered according to their periods of revolution: radius of sphere proportional to period.

What about other `Copernicans'??............

4.2 Tycho Brahe (1546-1601)

• Danish astronomer who inaugurated the era of precision in astronomical measurement, reaching the limits of what could be done with the naked eye (resolve to $\sim 1/60$degree).
• Built the best ever instrumnets to precisely track the motions of the planets (funded by King Frederick II of Denmark).
• His data were later to be crucial in confirming Copernicus' heliocentric model.
• Never fully accepted Copernican model; sought a compromise with the old Ptolemaic system - 5 known planets revolving around the Sun, which, with the planets, circled the (stationary) Earth.

4.3 Kepler (1571-1630)

• Tycho Brahe's assistant - inherited his superb data on planetary motions.
• Accepted outright the Copernican theory - its simplicity must have been God's plan!
• Formulated 3 (famous) laws:

  1.

  planets travel on ELLIPTICAL orbits (rather than circles)

  2.

  P²=a³ where P = period of orbit and a= half the longest dimension of the ellipse

  3.

  planets sweep out equal areas in equal times ( $\Rightarrow$ planet travels faster as it comes close to the Sun).

Law 2 highly significant: the very first mathematical formula to describe the heavens correctly. By describing behaviour mathematically, the physical laws responsible for it could be established (later found to be gravity).

• Kepler pondered what FORCE might control the motions of planets - could it be MAGNETISM?
• His discoveries were rather ironic: obsessed by patterns & mathematical relations, he attempted to explain the separation of the planets in terms of geometrical figures (spheres, cubes), and their motion using the mathematical relations known to exist between different notes of the musical scale $\rightarrow$ ``Music of the Spheres''.

4.4 Galileo (1564-1642)

• His primary interest was in MOTION: falling bodies, swinging weights, planets.
• Was the first to use the newly invented telescope; key observations (made with a 20x magnification telescope) were:

  - Moon: discovered the existence of mountains

  - Sun: discovered `Sun spots' and noticed their positions changed from day to day. A sun which had blemishes & changed, contradicted the popular Aristotlian view that the heavens were perfect and immutable.

  - Jupiter: found 4 moons orbiting it - proved that there was at least some bodies in the heavens which did not orbit the earth!

  - Saturn: not perfectly round (but didn't resolve rings)

  - Milky Way: uncountable numbers of stars - many more than previously thought!

  - Venus: observed it went through a cycle of phases like the moon $\Rightarrow$ it must orbit the Sun like the moon orbits the Earth. [It was Galileo's Venus observation more than anything else which dealt the death blow to the old geocentric model.]

Galileo & Society: vocal supporter of the Copernican view and wrote and circulated his views widely and tactlessly. He was a friend of the Pope but was nonetheless brought before the Inquisition because his non-geocentric views were counter to the teachings of the Catholic church. He was made to recant his ``heresy'' and was put under house arrest for the remainder of his life. Only in 1992 did the Catholic church admit it had made a mistake in condemning Galileo for his ideas.

Galileo on Motion: inverted the popular idea that an object falling towards the earth was a natural motion and horizontal motion was forced. Instead he took the view that downward motion was the forced motion and horizontal motion was natural (tendency for body to remain in motion unless acted on by a force). It was Galileo who demonstrated that all objects irrespective of their mass had the same acceleration when falling under gravity (hence assocation with Leaning Tower of Posa experiment).

Galileo on Cosmology: paid little attention to Kepler's work on orbits of planets but a firm believer in the Copernican `order of the universe'. Contemplated that the universe was open and infinite (cf. Aristotlian view of a spherical & finite universe).