Lecture 6 Chapter 3. The Copernican Revolution

Transcription

1 Lecture 6 Chapter 3 The Copernican Revolution

2 From the last lecture Question!"#$%&#$'($)"*+"$("#$&,,-$.*/#/$0#1#-0/$,-$*(/$ 1"'/#$21"'/#$,3$("#$&,,-$0#1#-0/$,-$("#$.#4'%5#$1,/*%,-/$,3$("#$67-8$9,,-$:$;'.("<$! If the Sun sets at 6pm, when does a full Moon rise?!! 6 pm. The side of the Moon we see if facing the Sun, so when the Sun is setting, the Moon is rising. Another way of looking at it:! The moon and Sun rising times are 12 hrs apart. Sun rose at 6 am! Moon at 6pm.

3 chapter 2 Learning Goals 1 Describe how some ancient civilizations attempted to explain the heavens in terms of Earth-centered models of the universe. 2. Explain how the observed motions of the planets led to our modern view of a Sun-centered solar system. 3. Describe the major contributions of Galileo and Kepler to our understanding of the solar system. 4. State Kepler's laws of planetary motion. 5. Explain how astronomers have measured the true size of the solar system. 6. Explain how the law of gravitation enables us to measure the masses of astronomical bodies.

4 Goal 1 1 Describe how some ancient civilizations attempted to explain the heavens in terms of Earth-centered models of the universe.

5 Ancient civilizations observed the skies Many built structures to mark astronomical events Summer solstice sunrise at Stonehenge:

6 Alignment Astronomy Egyptian pyramids.! Use circumpolar stars ( Indestructibles ) to align the base of the pyramids due north. This was associated with eternity in the afterlife. Stonehenge.! Main axis is aligned with the rising of the Sun on the summer solstice.

7 Birth of Astronomy! Need to understand day, night, seasons (hunter-gatherers, agriculture)!!"#$%&'()"%"*+&%(,-+-.*(!(/.0".+-.(-1(23"()&%".4&'

8 Birth of Astronomy!!"#$%$&'()*+,)-$.'*#)-"*(&+()! Celestial objects were considered divine, some events like eclipses were believed to be omens announcing the fate of countries and their rulers.)

9 Predictive Astronomy: Mayans Mayans didn t understand fractions, BUT measured the lunar cycle and solar tropical year precisely - (lunar cycle repeats every 149 new moons in 4400 days) 4400 days/149 = days! less than difference with modern day value! Solar tropical year: Mayan measurement: !

10 The recognition and identification of events is different from understanding their causes This is not science

11 What Is Science? careful, disciplined, logical search for knowledge, obtained by examination of the best available evidence and always subject to correction and improvement upon discovery of better evidence 1.! Unprejudiced 2.! Falsifiable 3.! Explain current observations and predict new ones.

12 Pseudo-science 1.! Non falsifiable (meaning the theory CANNOT be proved right or wrong by available data) OR 2.! It doesn t explain all observations, results are not reproducible

13 ABOUT SCIENCE Multiple hypothesis can equally well explain observations, how do we choose? 1.! If we are lucky, predictions from one will prove it wrong, if not 2.! Use Ockham s Razor ( keep it simple ) Ockham s Razor entities should no be multiplied unnecessarily

14 ABOUT SCIENCE For example: A.! Planets move in ellipses with the Sun in one focus because of an attractive force between the Sun and the planets B.! Planets move in ellipses with the Sun in one focus because of an attractive force between the Sun and the planets generated by powerful aliens Which one will you choose?

15 ABOUT SCIENCE Both explain the motion of the planets, but we choose A A.! Planets move in ellipses with the Sun in one focus because of an attractive force between the Sun and the planets B.! Planets move in ellipses with the Sun in one focus because of an attractive force between the Sun and the planets generated by powerful aliens WHY?

16 ABOUT SCIENCE Ockham s Razor: Keep it simple!!!! B is not discarded because:! it sounds absurd! we don t like it or! we don t believe in the existence of alien beings B is discarded because the statement about aliens is unnecessary to describe the observe motion of the planets. That planets move in elliptical orbits does not provide evidence in favor or against the existence of powerful aliens.

17 Scientific Models! Physical model to explain the workings of nature! Models apply known laws of nature to explain observations! Key aspects of a scientific model!! models explain what is seen!! models predict observations accurately!! simplify your understanding of nature! Validity of models is tested by checking how well predictions fit the best & new observations! Scientific models are not static but evolve when new & better observations become available

18 !! models explain what is seen!! models predict observations accurately!! simplify your understanding of nature

19 The Greeks and Astronomy had a major role in the birth of modern science

20 Modeling the Cosmos: Early Greeks! Greeks enjoyed philosophy which to them meant the attempt to understand all things in nature.! Tools: Direct observation, highly developed mathematical skills (geometry & trigonometry), and logic.! Starting point: Idea of Earth as center was simple and reinforced philosophical and religious systems that taught the unique role of humans in the universe.! Any model of the cosmos will have to explain:! Motion of the Sun! Motion of the stars! Motion of the Moon! Motions of the 5 planets visible to the unaided eye: Mercury, Venus, Mars, Jupiter & Saturn

21 ! Any model of the cosmos will have to explain:! Motion of the Sun! Motion of the stars! Motion of the Moon! Motions of the 5 planets visible to the unaided eye: Mercury, Venus, Mars, Jupiter & Saturn

22 Ancient astronomers observed: Sun Moon Stars Five planets: Mercury, Venus, Mars, Jupiter, Saturn Greek science was preserved through the dark ages by muslim astronomers

23 Naked Eye Planets Mercury! Closest to the Sun! Fastest moving planet God of commerce Messenger to the Gods

24 Venus! The evening star! Brightest object in the sky Goddess of love

25 Earth? Sun and Moon

26 Mars has large variations on brightness! The red planet. Mars Mars, God of War by Diego Rodriguez de Silva y Velazques

27 ! Largest planet Jupiter Abduction of Ganymede by Rubens Jupiter and Callisto by Rubens

28 The rings were not known to the ancients Saturn! Planet with the largest ring system Saturn (ca. 18th century) - Arabic illustration showing agricultural activities under direction of Saturn, God of agriculture?

29 Planets, Gods & Days of Week! English names for most of the days of the week come from names by Teutonictribes from Germany! Tuesday : Tiw - god of war! Wednesday: Woden - god of day & night! Thursday: Thor - god of thunder - head god! Friday: Fria - goddess of spring

30 Aristotle & A Spherical Earth! Aristotle ( B.C.) showed by proof that the earth was spherical: Painting of Aristotle by Rembrandt 1! He observed that the Earth s shadow is curved during a lunar eclipse The shapes that the Moon itself shows are of every kind -straight, gibbous, and concave - but in eclipses the outline is always curved: and since it is the interposition of the Earth that makes the eclipse, the form of this line will be caused by the form of the Earth s surface which is therefore spherical Aristotle s treatise On the Heavens Composite image of successive pictures taken during a lunar eclipse showing the Earth shadow.

31 Aristotle & A Spherical Earth 2! Aristotle learned from travelers that the height of the Pole star above the horizon varies as you travel from North to South! Going North: Polaris gets higher with respect to the horizon! Going South: Polaris gets lower with respect to the horizon! Go far enough south -- Polaris no longer visible!!earth must be spherical! Flat Earth Spherical Earth

32 Aristotle & Geocentric Model! He pointed out that the motions in the sky could be explained! by a rotating celestial sphere or! a rotating Earth, but he rejected the idea of a moving Earth

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35 Beyond the tenth sphere is, as the words in the periphery say in Latin, "The Kingdom of Heaven, the Abode of God and of the Elect."!

36 Question! Imagine you lived at the time of Aristotle. What observations or evidence could you offer to support the idea of a stationary earth?!we do not feel the earth moving!if earth moved then objects thrown upward would not drop back to their point of departure

37 Question! Imagine you lived at the time of Aristotle. What observations or evidence could you offer to support the idea of a stationary earth?!we do not feel the earth moving!if earth rotated then objects thrown upward would not drop back to their point of departure!if earth moved about the Sun, then one should observe change in the apparent positions of the stars, stellar parallax

38 Stellar Parallax! Apparent shift in the position of the stars because of the motion of the observer.

39 Hipparchus (c. 150 B.C.)! Erected an observatory on Rhodes! compiled catalog of stellar coordinates entries! determined length of year to within 6 minutes! predicted lunar eclipses to within 1 hour! predicted the paths of totality for solar eclipses! Developed a geometrical, geocentric model of the universe

40 Run animation: geocentric model! Deferent & Epicycle Hipparchus! Deferent - a large circle, either centered on Earth or offset from Earth (eccentric)! Epicycle - smaller circle, centered on the circumference of the deferent! Combination of Epicycle & Deferent explained retrograde motion:! Planets fixed to the epicycle! Planets moved around epicycle which in turn moved around the deferent

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42 Ptolemy ( A.D.)! Added geometrical devices to the basic Hipparchus model to better explain the motions of the planets! Epicycle, Deferent, Eccentric & Equant Eccentric: Ptolemy made the deferent an eccentric (not centered on Earth)

43 Ptolemy Equant: Center of epicycle moves at a constant distance from the eccentric, but at a uniform angular rate from the equant.! Ptolemy never claimed his model described reality. It was a mathematical representation to predict the positions of the planets.! The model successfully predicted the observed motions of planets and was the absolute authority until the 17 th century.

44 Ptolemy Equant this can be used to give a very accurate description of motion in an ellipse

45 Earliest models had Earth at center of solar system Needed lots of complications to accurately track planetary motions For clarity only the tracks of Venus and Jupiter are shown

46 The predictions of the Ptolemaic system were excellent It needed better observations to bring about the downfall

47 Goal 2 2. Explain how the observed motions of the planets led to our modern view of a Sun-centered solar system. Goal 3 3. Describe the major contributions of Galileo and Kepler to our understanding of the solar system.

48 Copernicus ( )! Polish! Studied medicine and law! Wrote De Revolutionibus explaining his Heliocentric model.

49 Heliocentric Model

50 the Copernican Revolution 1. Earth is not at the center of everything. 2. Center of Earth is the center of Moon s orbit. 3. All planets revolve around the Sun. 4. The stars are very much farther away than the Sun. 5. The apparent movement of the stars around the Earth is due to the Earth s rotation. 6. The apparent movement of the Sun around the Earth is due to the Earth s rotation. 7. Retrograde motion of planets is due to Earth s motion around the Sun.!Predicted observations as well as Ptolemaic system. but not better!

51 Reaction to Copernicus!The book was an exercise in mathematical astronomy and not very popular.!it didn t improve predictions.!almost all astronomers rejected the idea of a moving Earth.!The church remained silent, since nobody paid attention to the book, it was easy to ignore. Copernicus dedicated the book to Pope Paul III and addressed the book only to astronomers. He delayed the publication of the book until his final days.

52 2.2 The Geocentric Universe Sun, Moon, and stars all have simple movements in the sky Planets: Move with respect to fixed stars Change in brightness Change speed Undergo retrograde motion Text

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54 This figure shows retrograde motion of Mars. 2.3 The Heliocentric Model of the Solar System Sun is at center of solar system. Only Moon orbits around Earth; planets orbit around Sun.

55 Model also accounts for change in brightness

56 Goal 3 3. Describe the major contributions of Galileo and Kepler to our understanding of the solar system.

57 5 minute break

58 Goal 3 3. Describe the major contributions of Galileo and Kepler to our understanding of the solar system.

59 Galileo Galilei ( )! Italian mathematician. Professor of mathematics and astronomy.! He accepted the Copernican model of the solar system.! 1609 he heard of the telescope and constructed his own, he run many tests to make sure the image seen by the telescope was accurate.! Used the telescope to observe the sky.! 1610 published The Sidereal Messenger with his discoveries.

60 2.4 The Birth of Modern Astronomy Telescope invented around 1600 Galileo built his own, made observations: Moon has mountains and valleys Sun has sunspots, and rotates Jupiter has moons (shown) Venus has phases

61 Geocentric vs. Heliocentric Model How can we distinguish between the models? Heliocentric: We should be able to observe phases on inferior planets, similar to the phases of the moon.

62 2.4 The Birth of Modern Astronomy Phases of Venus cannot be explained by geocentric model

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64 Galileo! Jupiter has 4 moons revolving about it with different periods.!!"#$%&'(%&)(*+&,-&./&),#01,*+2&./& "3*"4"*,(#&21(526&! 7+3,2&8.+2&195.,89&-9(2+2&#"$+&19+& )..36&!!..3&9(2&).,31("32:&;5(1+52:&4(##+%2& <,21&#"$+&=(5196&! >,32-.12:&?@#+)"29+2A:&.3&19+&>,36&B+& 2(C&19+&2-.12&).4"38&*(%&@%&*(%&.3#%& 1.&*"2(--+(5&(3*&5+(--+(5&C"19&(& -+5".*&./&(@.,1&(&).3196&

65 Galileo & A New Physics! Galileo realized the need to develop a new physics to replace that of Aristotle.! Objections to Heliocentric Model 1.! Moving Earth! objects on Earth (clouds, stones, etc would be left behind) 2.! An ellipse is not a perfect shape, the heavens are perfect and unchanging 3.! No stellar parallax

66 Describing Motion! speed rate at which an object moves, i.e. the distance traveled per unit time [m/s; mi/hr]! velocity an object s speed in a certain direction, e.g. 10 m/s moving east! acceleration a change in an object s velocity, i.e. a change in either speed or direction is an acceleration [m/s 2 ]

67 The Acceleration of Gravity! As objects fall, they accelerate.! The acceleration due to Earth s gravity is 10 m/s each second, or g = 10 m/s 2.! The higher you drop the ball, the greater its velocity will be at impact.

68 If the initial velocity is zero then s = (1/2) g t^2 s is the distance traveled in time t g is the acceleration due to gravity On Earth g is about 9.8 meter/second^2

69 Describing Motion! momentum object s mass! object s velocity! m! v! force causes a change in an object s momentum! If object s mass does not change, a force causes change in velocity

70 Is Mass the Same Thing as Weight?! mass the amount of matter in an object! weight a measurement of the gravitational force that acts upon an object.! Gravitational force downward is balanced by upward force of the ground the downward force pressing you against the ground is what you call your weight!

71 Galileo & A New Physics! Objections to Heliocentric Model 1.! Moving Earth! objects on Earth (clouds, stones, etc would be left behind) horizontal motion is natural, with no forces, objects would continue to move in a uniform way INERTIA

72 Inertia! Inertia is defined as the tendency of a body to oppose changes in velocity.! Galileo experimented with balls and incline planes to study inertia

73 Gravity!!"##$%&'$('%)*'"'%"*+,"#'-).)%' /+*'0),123'"%3'3+2'*)'&,"4$*5'! 6,"4$*5'"1*(')%'"##'/)3$2('$%'*72' ("-2'8"5'$%'*72'"/(2%12')0'"$,',2($(*"%12'),')*72,'0),12('!,"*2')0'"112#2,".)%'$('*72' ("-2'%)'-"92,'87"*'*72' -"(('! :;<2,$-2%*('8$*7'0"##$%&' )/=21*('

74 Galileo & A New Physics! Objections to Heliocentric Model 2. An ellipse is not a perfect shape, the heavens are perfect and unchanging!!"#$%&'(#%)*+(,-.('/0*1-%2,('$%3*.(#$,-4*'(5-( +$*(6$*,2*-'7(!8,959*%(.5'#%2*1"(%:(;/-'0%+'<()%/-+,5-'(%-(+$*( )%%-( (!(65)0*1:*#=%-'(%:($*,2*-9"(%>?*#+'7(

75 Galileo & A New Physics! Objections to Heliocentric Model 3. No stellar parallax!milky Way made out of stars, stars farther than expected! parallax too small to be measured

76 Galileo & the Inquisition! Warned to stop teaching the Copernican model in 1616! Publishes Two Chief World Systems with approval of Church in Comparison of Geocentric & Heliocentric models

77 The Dialogue! Dialogue: takes form of a conversation between 3 philosophers:!salviati: brilliant philosopher who argues for the Copernican system!simplicio: a good humored fool who defends Geocentric model using the Pope s favorite arguments!sagredo: 3rd philosopher, intelligent but uninformed.

78 !"#$%&%'(")! *(+,)-"./0)1)(/2,/&)!"#$%&%'(")345678)! *:-<,2)$"2,/)+,/+,=$-:)?($&,)-//,&=)! B%-:(.$,)+:-<,2)(");(/C%22,"):%&=)-:(".)D%=?)D(/E&)C0) F(+,/"%<$&)>)G,+:,/)! H,A(I,2);/(A):%&=)%")4J6K)! Church publicly forgave Galileo s crimes in 1992!!!

79 Goal 4 4. State Kepler's laws of planetary motion.

80 2.5 The Laws of Planetary Motion Kepler s laws were derived using observations made by Tycho Brahe

81 Tycho Brahe ( )!Danish nobleman!new improved observations were needed to renovate astronomy.!observed the sky for 20 years.!1572 new transient star : supernova! He didn t know what it was, but showed the new star was beyond the orbit of the moon and implied a change in the heavens.!1577 great comet was also beyond the orbit of the moon and its path carried it across the crystalline celestial spheres! there were no crystalline spheres.

82 Johanes Kepler ( )!Tycho s assistant and convinced Copernican (Heliocentric).!He used Tychos observations to find the true motion of the planets.

83 The eccentric orbit of Mars Had a key role in the development of Kepler s theories

84 2.5 The Laws of Planetary Motion 1. Planetary orbits are ellipses, Sun at one focus

85 More Precisely 2-1: Some Properties of Planetary Orbits Semimajor axis and eccentricity of orbit completely describe it Perihelion: closest approach to Sun Aphelion: farthest distance from Sun

86 Each planet moves in an ellipse with the Sun at one focus. The length of a line drawn from the Sun, to a planet and then to the empty focus, denoted by the dashed line, is always 2a, or twice the semi-major axis, a. The eccentricity, or elongation, of the planetary ellipse has been greatly overdone in this figure; planetary orbits look much more like a circle.

87 2.5 The Laws of Planetary Motion 2. Imaginary line connecting Sun and planet sweeps out equal areas in equal times

88 Areas A, B and C are equal

89 2.5 The Laws of Planetary Motion 3. Square of period of planet s orbital motion is proportional to cube of semimajor axis

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91 Kepler s Three Laws of Planetary Motion Law #1: Tells us the shape of a planet s orbit (ellipse, with Sun at one focus) Law #2: Tells us how the planet s speed depends on where it is in the orbit (planet moves faster as it nears the Sun) Law #3: Tells us how the planet s average speed depends on the size of the orbit (for bigger orbits, planets move more slowly)

92 5. Explain how astronomers have measured the true size of the solar system.

93 2.6 The Dimensions of the Solar System Astronomical unit: mean distance from Earth to Sun First measured during transits of Mercury and Venus, using triangulation

94 2.6 The Dimensions of the Solar System Now measured using radar: Ratio of mean radius of Venus s orbit to that of Earth is very well known

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96 Goal 6 6. Explain how the law of gravitation enables us to measure the masses of astronomical bodies.

97 Newton s laws of motion explain how objects interact with the world and with each other. 2.7 Newton s Laws