Rocket building social tonight in CCC 1200 Right after class Required if going to rocket launch on Sunday Rocket launch this Sunday 7 April Bus departs at 11:45am from Cambridge Hall Horseshoe Please eat before you get on the bus Quick bus ride over to NASA for community rocket launch Return by 3:30pm 1 Life as a Twisted Biologist lecture this Wednesday Last excursion Must find Dr. Peel before and after lecture Will be a discussion date TBD (probably over dinner) SAB next week 2 1
Registering for next term CPSP218D Read e mails from Sarah Elaine 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 4 2
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? 5 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 6 3
Earth Earth 7 Earth Sun Earth 8 4
Do you always have a no shadow point? Infinite sized Earth Finite sized Earth 9 Sun Flat Earth infinite size Sun Flat Earth finite size 10 5
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? 11 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? 12 6
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 13 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 14 7
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 15 Two Parallel Lines 1 What can you say about angles A and B? B A 16 8
Two Parallel Lines 2 B A 17 Two Parallel Lines 3 Alexandria Zenith B A SUN Well at Syene 18 9
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 19 Final Test: The Question Which angle do you Want? D Gnomon C Shadow 20 10
Final Test: The Answer 21 Is the Earth Flat or Round? 22 11
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 23 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 24 12
No (hidden) assumptions? 25 26 13
27 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 28 14
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 29 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 30 15
28.5 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 31 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 Size of the Sun and the Moon And then a miracle occurs in the sky are about the same 32 16
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 9.5 28.5 F 2c E 1 B C 33 Lunar Eclipse 5 28.5 F B Earth E D Moon 9.5 C Note all distances in units of Earth diameters 34 17
Reality 35 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 36 18
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Earth Sun Distance 1 Moon Sun 9.5 A Earth 39 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 40 20
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 41 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 42 21
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Does this affect your world view? 45 Source Moon Earth Distance Earth Sun Distance Aristarchus 9.5 180 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 46 23
Source Earth Sun Distance (Earth Diameter) Earth Sun Distance (Miles) Minimum Volume of the Universe The Earth 1 7,920 2.08 10 12 Aristarchus 180 1,430,000 1.22 10 19 Hipparchus 1,245 9,860,000 4.02 10 21 Posidonius 6,545 51,900,000 5.84 10 23 Ptolemy 605 4,790,000 4.61 10 20 Reality 11,726 92,900,000 3.36 10 24 47 Source Earth Sun Distance Velocity (mi/hr) Aristarchus 180 1.87 10 5 Hipparchus 1,245 1.29 10 6 Posidonius 6,545 6.79 10 6 Ptolemy 605 6.27 10 5 Reality 11,726 1.22 10 7 48 24
The Gnomon: It s Multicultural 49 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 50 25
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 51 Employ one person as a number checker Vertical Distance Slant Distance No Shadow Shadow 52 26
So now you know the size of the world, the distance to the moon, etc. So what? 53 54 27
What Why How 55 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 56 28
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 57 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 58 29
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Fact or Fiction? 61 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? 62 31
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! 63 32