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2-5 Renaissance “naissance” = “birth”

2-5 Renaissance “naissance” = “birth”. The belief that the cosmos is ultimately understandable slowly emerges again. Revival of art. The Birth of Venus, Botticeli, 1485. Rediscovery of perspective (and geometry). Delphic Sybil, Michelangelo,1510 - 1512. Rediscovery of light.

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2-5 Renaissance “naissance” = “birth”

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  1. 2-5 Renaissance“naissance” = “birth” The belief that the cosmos is ultimately understandable slowly emerges again

  2. Revival of art The Birth of Venus, Botticeli, 1485

  3. Rediscovery of perspective (and geometry)

  4. Delphic Sybil, Michelangelo,1510 - 1512

  5. Rediscovery of light Lady with an ermine, Vinci

  6. The drape of the alb is basic

  7. More liberal period The creation of the planets, the Sun and the Moon, Michelangelo

  8. Rediscovery of sculpture Middle Age bas-relief Figures hardly stick out of the stone

  9. Gothic art

  10. David, Michelangelo Perfect knowledge of the human body Greek art

  11. A time of conquests and adventure Magellan’s travel around the Earth: 1519

  12. Europe was ready for the birth of modern science Young Frankenstein

  13. Giordano Bruno (1548 – 1600) Early champion of the heliocentric model: “the Sun, not the Earth, is the centre of the universe” Also believed: In the existence of inhabited planets That the universe is infinite But before all, dreamt of a radical reform of Christianity

  14. Bruno went to Rome to convince the Pope himself! ? 1600: Bruno was burnt by the Holy Inquisition Often portrayed by scientists as a martyr of science

  15. Nicolas Copernicus (1473 – 1543) Priest interested in mathematics and astronomy Understood that stellar parallax is not observed because stars are too far Goal: to predict the position of the planets

  16. Ptolemy’s geocentric model Very complex calculations !

  17. Copernicus proposed a simplified mathematicalmodel in which the Earth was orbiting the Sun

  18. Mars Earth Moon Jupiter Saturn Venus Mercury Sun

  19. A B A overtakes B. What does A see of B? B seems to be moving backward

  20. A B Now B overtakes A. What does A see of B? B is moving forward A: “B has moved back and forth”

  21. He could reproduce the retrograde motion of Mars in very simple manner Like in a car race, the Earth is sometimes overtaking Mars, giving us the impression that Mars is moving backward

  22. Copernicus also deduced that the nearer a planet is to the Sun, the greater its orbital speed Mercury orbits at a higher speed than Mars

  23. Which planet has the smallest orbital speed? Jupiter Earth Mercury

  24. Jupiter Earth Mercury

  25. Jupiter Earth Mercury

  26. Copernicus was a priest and had no intention to contradict the Scriptures He did not claim his model described the actual motion of the Earth. It was just a mathematical trick.

  27. Nevertheless, he chose to publish his De Revolutionibusafter his death His model: no better accuracy than Ptolemy’s => was not widely accepted until more than a century

  28. People were not ready to believe that the Earth was moving They argued that if the Earth were rotating, we would feel its motion

  29. Some even claimed that a rotating planet would fly into pieces

  30. At that time, logical reasoning had more weight than any observation or experiment Anyway astronomers had no telescope…

  31. Tycho Brahe (1546 – 1601) Born three years after Copernicus’ death

  32. Established a fine astronomical observatory on the North Sea island of Hven

  33. He made a continuous record of the position of the Sun, Moon and planets for almost 20 years Found that the predictions of Ptolemy’s model were inaccurate Tycho measuring the altitude of a celestial object, 1587

  34. Five planets orbiting around the Sun He believed in a modified geocentric model Sun Earth Moon All planets orbit around the Sun but the Earth!

  35. In 1597, Brahe’s patron the Danish King Frederick II died Brahe had to find a new job… He became court astronomer to the Emperor Rudolf of Bohemia, in Prague, Austria There he met a diligent assistant: Johannes Kepler

  36. Kepler (1571 - 1630) Theology student Became convinced that all the planets are actually orbiting the Sun

  37. Brahe was reluctant to give full access to data to Kepler, fearing his bright assistant would discover the secret of the universal motion When Brahe died, Kepler got full access to Brahe’s records, that he studied for more than 20 years At the age of 38, he finally published his first results

  38. Kepler’s first law

  39. The orbit of a planet is an ellipse ecliptic top view Sun planet

  40. How to draw an ellipse? Position of the Sun Focus Focus

  41. Eccentricity of an ellipse: e An ellipse which does not differ much from a circle is not “very eccentric” e is close to zero An ellipse which is very elongated has an eccentricity close to 1

  42. The eccentricity of the Earth’s orbit is 0.017. What is its shape?

  43. Very similar to a circle Caution: same orbit seen from two different points of view Top view Side view

  44. a: semimajor axis of an ellipse Semimajor axis

  45. Which of the following ellipses has the largest semimajor axis?

  46. Which of the following ellipses has the largest semimajor axis?

  47. Kepler’s second law A planet: Speeds up as it comes closer to the Sun Slows down as it moves away from the Sun Lowest speed Highest speed Sun

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