For First year book and James Randi must meet for discussion with Dr. Peel. See e mail from him for details

Transcription

1 For First year book and James Randi must meet for discussion with Dr. Peel. See e mail from him for details James Randi dinner tonight at North Campus Diner, meet after class today First year book Coffee at the Stamp 3 pm tomorrow 1 No SAB next week Conflicts with National Geographic excursion If signed up for excursion and can t make it let us know by 3 PM tomorrow (have people on wait list) Still a few slots open on Greenbank trip Leonids is last excursion! Watch e mail for voting on charity 2 1

2 If missed deadline for student interviews\talks\chats We still want to see you Will only get partial credit Which is better than no credit! Potential Service Day make up evening of Friday 2 November 3 Next Project Deadline Rough draft of paper Due Thursday 1 November 4 2

3 How big is the Universe? Is this an impractical question? Intellectual curiosity? Our place in the grand scheme of things? Does the answer to this question affect your attitude towards life? Spiritual/religious question? Is this a practical question? Economic Political 5 Bound the problem Could be infinite in size Could be finite in size If it is infinite: Don t have to worry about a boundary We can t be at the center (boo) If it is finite: We could be at the center (yea) Have to worry about the boundary (maybe) Could have no boundary, but then can we be at the center? 6 3

4 The smallest the Universe can be is? The size of the Earth Moon, Sun, Planets, Stars just things up in the atmosphere Even if don t buy that need the size of the Earth and the distance to the Sun to get the distance to the closest stars 7 Earth Earth 8 4

5 Earth Sun Earth 9 Do you always have a no shadow point? Infinite sized Earth Finite sized Earth 10 5

6 Sun Flat Earth infinite size Sun Flat Earth finite size 11 Can you determine the size of the Earth? If not, can you bound the size? Can you find the distance to the Sun? Does it matter how far away the Sun is? Do you need a no shadow point? Can you find the size of the Sun? 12 6

7 Do you always have a no shadow point? Can you determine the size of the Earth? If not, can you bound the size? Does it matter how far away the Sun is? Do you need a no shadow point? Can you find the distance to the Sun? Can you find the size of the Sun? 13 Greek, born in 276 BCE in Cyrene, now Shahhat, Libya Studied in Athens and Alexandria in Egypt Became the director of the Library in Alexandria Died in 197 BCE in Alexandria He became blind in his old age Said to have committed suicide by starvation 14 7

8 If you take intro astronomy will probably be taught that he was best known for his accurate calculation of the Earth s circumference Within 10 15% of modern day value Noticed that on the first day of summer, the noon sun was reflected in a well dug at Syene (modern Aswan) On the same day, and at the same time, the Sun was south of overhead by 1/50 th of a full circle (7.2º) at Alexandria 15 Huh? Hint: Sun is so far from the Earth that the rays from the Sun striking the Earth can be thought of as parallel lines 16 8

9 Two Parallel Lines 1 What can you say about angles A and B? B A 17 Two Parallel Lines 2 B A 18 9

10 Two Parallel Lines 3 Alexandria Zenith B A SUN Well at Syene 19 Ta Da 7.2 º = Distance from A to S 360 º Circumference of the Earth Circumference of the Earth = 360 AS Notice do not use! Alexandria 7.2 B Zenith Think in ratios! A SUN Well at Syene 20 10

11 Final Test: The Question Which angle do you Want? D Gnomon C Shadow 21 Final Test: The Answer 22 11

12 Is the Earth Flat or Round? 23 Is the Earth Flat or Round? Alexandria SUN Well at Syene NO! Because the Sun s rays are parallel, if the world was flat when the Sun was directly overhead at Syene, it would also be directly overhead at Alexandria 24 12

13 Near Sun & Flat Earth: 1. Distance to Sun 2. Size of Sun 3. Size of Sun to minimum size of the Earth Far Sun & Round Earth: 1. Size of the Earth 25 No (hidden) assumptions? 26 13

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15 That the angles were the same? Went to school and studied Euclid Same as you That the Sun s rays could be assumed to be parallel? Went to school and studied Aristarchus of Samos Not same as you Introductory astronomy books skip this part, i.e. you are not supposed to be smart enough to question this 29 Lived from 310 to 230 BCE Thirty four years old when Eratosthenes born Generation between Euclid and Archimedes Exponent of a Sun centered universe Only surviving work: On the Sizes and Distances of the Sun and Moon 30 15

16 Lunar eclipses caused by Moon passing through Earth s Shadow Only occur at full moon Moon Earth Sun Don t happen every month, orbital plane of the Moon tilted 5º with respect to Sun s Earth 1 Sun Comes from Size of Sun in the sky is 2 degrees Bounds the Earth Moon distance! Moon not further than 28.5 Earth diameters away Moon not closer than 1 lunar diameter 32 16

17 F B A 2 Earth E 1 D Moon C By observations during a lunar eclipse he determined that the size of the Earth s shadow at the Moon s orbit was 2 lunar diameters And then a miracle occurs Size of the Sun and the Moon in the sky are about the same 33 For similar triangles, ratios of sides is persevered on all sides: A C DE EF 3 CE = 28.5 CE AE 1 2 2e 2d 1e D 1c 1d E CE F 2c E 1 B C 34 17

18 Lunar Eclipse F B Earth E D Moon 9.5 C Note all distances in units of Earth diameters 35 Reality 36 18

19 Size of Sun in the sky is really ½ degree 108 Earth 1 Sun Know he later changed it from 2 degrees to ½ degree At Moon s orbit shadow cone is 2 ½ lunar diameters

20 Earth Sun Distance 1 Moon Sun 9.5 A Earth 40 Sound theory But it is a hard observation to do In real life angle A is 89.83º Too close to 90º for naked eye observation To get an idea of real scale of problem, imagine a scale drawing with 1 million miles = 1 inch Earth Moon distance = ¼ inch Earth Sun distance = 93 inches = 7 feet 9 inches 41 20

21 What he got instead was: Earth Sun distance = 19 Earth Moon distance Earth Sun distance = 180 Earth diameters Note all distances in units of: Earth Diameters (absolute value not known) Once Eratosthenes figures this out: Know the Earth Moon distance in absolute units Know the Earth Sun distance in absolute units Know the sizes of the Moon and Sun in absolute 42 units Synergistic One absolute measurement gives you a lot more Still true today Relative measurement between things is easy Which is hotter Which is bigger Etc. Relative measurement to an absolute standard easy Determination of absolute standard hard 43 21

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23 Does this affect your world view? 46 Source Moon Earth Distance Earth Sun Distance Aristarchus Hipparchus 33 2/3 1,245 Posidonius 26 1/5 6,545 Ptolemy 29 1/2 605 Reality 30 1/5 11,726 Note all distances in units of Earth diameters 47 23

24 Source Earth Sun Distance (Earth Diameter) Earth Sun Distance (Miles) Minimum Volume of the Universe The Earth 1 7, Aristarchus 180 1,430, Hipparchus 1,245 9,860, Posidonius 6,545 51,900, Ptolemy 605 4,790, Reality 11,726 92,900, Source Earth Sun Distance Velocity (mi/hr) Aristarchus Hipparchus 1, Posidonius 6, Ptolemy Reality 11,

25 The Gnomon: It s Multicultural 50 How can you explain that? The same size gnomon On the same day Casts different shadow lengths at two different places Well how about The Earth is flat and the Sun is close It s a consistent model with the data Can get the Earth Sun Distance and size of the Sun 51 25

26 True for all problem sets They do count towards your grade (see syllabus) SHOW ALL WORK! Right answer with no derivation = ½ possible points Group work OK, even encouraged, BUT Max 5 people per group Only one set (with full name, first and last) per person Must know what each person does 52 Employ one person as a number checker Vertical Distance Slant Distance No Shadow Shadow 53 26

27 So now you know the size of the world, the distance to the moon, etc. So what?

28 What Why How 56 The educated class at the time of Columbus knew that the world was round The problem really was that if you used Eratosthenes determination of the circumference before Columbus could reach China he would run out of supplies 57 28

29 So the argument about funding Columbus was An argument about the distance to travel Size of the Earth & the size of Asia An argument about risk vs. payoff Size of the Earth Ptolemy had the Earth being smaller than Eratosthenes Columbus went even smaller than that 58 Size of Asia and Marco Polo Know that Columbus had a copy of Marco Polo Don t know if he had it prior to his first voyage Marco Polo It s a fun read Mix of fact and fiction Written in collaboration Does not have a distance in it for the Europe Asia land mass, has instead how many days it took Had an overestimate for the distance of China to Japan By the time of Columbus, over a 100 years old 59 29

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31 Fact or Fiction? 62 So Columbus used A very small size of the Earth (wrong) A large size for the Asia land mass (wrong) A large size for the distance from China to Japan (wrong) Even then some evidence that he fudged those numbers to make the voyage seem possible (wrong) Four wrong s make a right? 63 31

32 An argument about risk vs. payoff So he dies, what do you lose? But what if he is right, what do you gain? When do you play the lottery? And while not right, it worked! 64 32