Theoretical Explanation: Solar System

1. Theoretical Explanation: Solar System www.assignmentpoint.com

2. The solar system Sun Planets Asteroids Comets Pluto Neptune Uranus Saturn Jupiter Mars Earth Venus Mercury Sun www.assignmentpoint.com

3. Historical figures in the Copernican Revolution Ptolemy – the geocentric model, that the Earth is at rest at the center of the Universe. Copernicus – published the heliocentric model. Galileo – his observations by telescope verified the heliocentric model. Kepler – deduced empirical laws of planetary motion from Tycho’s observations of planetary positions. Newton – developed the full theory of planetary orbits. www.assignmentpoint.com

4. The Copernican Revolution www.assignmentpoint.com

5. Nicolaus Copernicus • The Earth moves, in two ways. • It rotates on an axis (period = 1 day). • It revolves around the sun (period = 1 year). www.assignmentpoint.com

6. Where is this? Inscription: By reforming astronomy heinitiated modern science. www.assignmentpoint.com

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8. The heliocentric model The reasons for seasons – the Earth travels around the sun, and its axis of rotation is tilted by 23.5 degrees to the plane of the orbit. In July, the northern hemisphere is getting more sunlight than in January. www.assignmentpoint.com

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10. HEAVEN HELL www.assignmentpoint.com

11. The Copernican Model www.assignmentpoint.com

12. Galileo Galilei www.assignmentpoint.com

13. Galileo’s discoveries in Astronomy Galileo did not invent the telescope, but when he heard about the invention he figured out how to build telescopes. He had the best telescopes of his time. He was the first person to use telescopes to look at the heavenly bodies. He was first, so he made the discoveries. •  Craters and mountains on the moon •  Moons of Jupiter •  Phases of Venus •  The Milky Way consists of innumerable stars.  Sunspots move across the sun’s face. All of these favored the Copernican (heliocentric) model. www.assignmentpoint.com

14. Galileo’s sketch of the moon as seen from his telescope A photograph of the moon “What do you think of the foremost philosophers of this university? In spite of my oft repeated efforts and invitations, they have refused, with the obstinacy of a glutted adder, to look at the planets or Moon or my telescope.” (letter to Kepler) www.assignmentpoint.com

15. Galileo made many specific discoveries in astronomy, through observations by telescope. The general implications… ● The planets are objects like the Earth – masses – rather than some kind of special heavenly objects. Or, to put it another way, the Earth is just another planet. ● The planets, including Earth, travel around the sun. ● The Universe is a lot bigger than we can see by the naked eye. These ideas could be dangerous. www.assignmentpoint.com

16. The Trial of Galileo His Church decided that the heliocentric model was a heresy. But Galileo continued to argue in favor of the theory, and published his reasoning. The Inquisition in Rome accused him of heresy, and required him to answer. Found guilty of “suspicion of heresy,” Galileo recanted publicly. [A story, probably not true, is that he muttered “Eppur si muove” – “And yet, it does move.”] He was put under arrest and sentenced to prison. But because of his fame and age (70 years old at that time) he was allowed to serve under house arrest in Florence, for the remaining years of his life. www.assignmentpoint.com

17. Johannes Kepler (1571 – 1630) … discovered three empirical laws of planetary motion in the heliocentric solar system • Each planet moves on an elliptical orbit. • The radial vector sweeps out equal areas in equal times. • The square of the period is proportional to the cube of the radius. (needed for the CAPA) www.assignmentpoint.com

18. How did Kepler determine the planetary orbits? Compare the heliocentric model to naked-eye astronomy Mars The inner planet is Earth; the outer one is Mars. Plot their positions every month. Mars lags behind the Earth so its appearance with respect to the Zodiac is shifting. Earth The most complete data had been collected over a period of many years by Kepler’s predecessor, Tycho Brahe of Denmark. www.assignmentpoint.com

19. Astrology… a persistent superstition It’s all nonsense, of course. The motions of the planets are prescribed by natural laws of motion and gravity. How can their motion predict the future? www.assignmentpoint.com

20. Ellipse Geometry To draw an ellipse: Take a string. Tack down the two ends. Put a pencil in the string and pull the string taut. Move the pencil around keeping the string taut. An ellipse is the locus of points for which the sum of the distances to two fixed points is fixed. The two fixed points are called the focal points of the ellipse. www.assignmentpoint.com

21. Parameters of an elliptical orbit (a,e) ► Semi-major axis = a = one half the largest diameter ► Eccentricity = e = ratio of the distance between the focal points to the major diameter For example, this ellipse has a = 1 and e = 0.5. ► Perihelion and aphelion Perihelion = r2= 0.5 Aphelion = r1 = 1.5 www.assignmentpoint.com

22. Example. Determine a, e, r1, r2. www.assignmentpoint.com

23. Isaac Newton www.assignmentpoint.com

24. The observed solar system at the time of Newton Sun Mercury Venus Earth Mars Jupiter Saturn (all except Earth are named after Roman gods, because astrology was practiced in ancient Rome) Three outer planets discovered later… Uranus (1781, Wm Herschel) Neptune (1846 Adams; LeVerrier) Pluto (1930, Tombaugh) www.assignmentpoint.com

25. Gm m F 1 2 = = F a 2 r m Isaac Newton Newton solved the premier scientific problem of his time --- to explain the motion of the planets. To explain the motion of the planets, Newton developed three ideas: • The laws of motion • The theory of universal gravitation • Calculus, a new branch of mathematics “If I have been able to see farther than others it is because I stood on the shoulders of giants.” --- Newton’s letter to Robert Hooke, perhaps referring to Galileo and Kepler www.assignmentpoint.com

26. Newton’s Theory of Universal Gravitation Newton and the Apple Newton asked good questions  the key to his success. Observing Earth’s gravity acting on an apple, and seeing the moon, Newton asked whether the Earth’s gravity extends as far as the moon. (The apple never fell on his head, but sometimes a stupid person will say that, trying to be funny.) www.assignmentpoint.com