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Chapter 1 About Science

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Scientific Measurement Size of Earth Size of the Moon Distance to the Moon Distance to the Sun Size of the Sun Mathematics – The Language of Science Scientific Methods

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Scientific Observation and Measurement How do you know whether the earth is flat or round? Is there any evidence that we can see from here? Where would be the best place to find this evidence? Evidence: Best place – on a large body of water – large, flat, level surface Activity – watch a boat sail out over the horizon Observations – (Evidence for a curve surface) Boat disappears sailing out – bottom first Boat reappears sailing in – top first Climbing to a higher vantage point brings the boat back into view.

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Other Observations The Sun and moon are round so why not the earth? The shadow of the earth on the surface of the moon during an eclipse of the moon showed that the surface of the earth was round. When did people first figure out the earth was round? ~500 B.C. – Pythagoreans gave the similar shape reasoning (Induction argument) ~300 B.C. – Aristotle used the disappearing boat argument. Educated people knew the earth was round in the 3 rd century B.C. but didn’t know how to measure it.

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Size of Earth Eratosthenes (Egyptian director of the Library at Alexandria) – 1 st known calculation of the size of the earth. ~235 B.C. Eratosthenes performed a measurement in Alexandria, Egypt that allowed him to calculate the radius of the earth. Somehow, Eratosthenes came to know about the well in Aswan (where the big dam is located), south of Alexandria, where the sun shines straight down to the bottom of the well at noon on the summer solstice

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At the Summer Solstice the earth’s axis is tilted 23 0 toward the sun. This brings the sun directly overhead in Aswan at noon on this day. While not directly south of Alexandria is wasn’t far off. (This would effect Eratosthenes’ ability to synchronize “noon” in both locations.) Aswan, Aswan Lat. 24:06:55N (24.1152) Long. 33:00:47E (33.0131) Alexandria, Egypt Lat. 31 o 7' North Long. 29 o 54' East Aswan (anciently Syene) was on the Tropic of Cancer

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Earth’s Dimensions Polar radius 6,356.6 km Equatorial radius 6,378.2 km Equatorial circumference 40,075 km Surface area 510,900,000 sq. km Earth’s Dimensions Polar radius 6,356.6 km Equatorial radius 6,378.2 km Equatorial circumference 40,075 km Surface area 510,900,000 sq. km Caitlin, The correct tilt angle is 23 degrees 27 minutes, which is approximately 23.45 degrees. David R. Cook Atmospheric Research Section Environmental Research Division Argonne National Laboratory

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Do the math here On Jun 22 – summer soltice – “only day the sun shone down the well at noon” This synchronized the measurement in Alexandria d/H = Shadow / Height = 1/8 Angle ~7.2 0 or 7.2/360 = 1/50 of circumference The distance from Alexandira to Aswan D= 5000 statia ( =800km) Therefore Circumference = 5000 (50) = 250,000 stadia ( =40,000 km) or within 5% of the presently accepted value.

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The info needed to complete the next series of calculations Earth radius Moon radius Moon distance Distance to Sun Sun diameter Size of moon Use the size of shadows during eclipses of the sun and Moon Solar Eclipse – Moon between Sun and Earth (Moon shadow on Earth) Lunar Eclipse – Earth between Moon and Sun (Earth shadow on Moon) Size of the Moon

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Aristarchus in around 240 B.C. measured moon’s diameter and distance from earth. Presently accepted value of diam is 3640 km which is within 5% of Aristarchus’ value. Aristarchus in around 240 B.C. measured moon’s diameter and distance from earth. Presently accepted value of diam is 3640 km which is within 5% of Aristarchus’ value. Moon’s shadow on earth tapers to a point. It tapers by one moon diam. Hence the earth’s shadow must taper by one moon diam. During a lunar eclipse the earth’s shadow on the moon is 2.5 moon diam. Therefore the earth real diam is 3.5 x moon diam. Moon’s shadow on earth tapers to a point. It tapers by one moon diam. Hence the earth’s shadow must taper by one moon diam. During a lunar eclipse the earth’s shadow on the moon is 2.5 moon diam. Therefore the earth real diam is 3.5 x moon diam. Gives Earth diameter as 3.5 times Moon’s diameter

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Similar triangles give: Moon diam / Moon distance = 1/110 Early Greeks knew this. However, they needed Aristarchus’ measurement of the moon’s diameter to complete the calculation. Early Greeks knew this. However, they needed Aristarchus’ measurement of the moon’s diameter to complete the calculation. Distance to the Moon

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Distance to the Sun The coin on the window trick doesn’t work with the sun. The method needs a radius or diameter. It’s also dangerous to look at the sun Moon and sun subtend the same angle. This is observed. Remember the moon’s shadow tapered to a point during the solar eclipse. Same apparent size. Moon exactly covers sun The coin on the window trick doesn’t work with the sun. The method needs a radius or diameter. It’s also dangerous to look at the sun Moon and sun subtend the same angle. This is observed. Remember the moon’s shadow tapered to a point during the solar eclipse. Same apparent size. Moon exactly covers sun Half-lit moon determined geometry. Earth-moon distance known Measure angle x Calculate Earth –Sun distance Half-lit moon determined geometry. Earth-moon distance known Measure angle x Calculate Earth –Sun distance

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This is another way to determine the 1/110 ratio. Pin hole camera – with lenses and film (or CCD) you have today’s modern cameras. Camera Obscura – Camera (Room) Obscura (Dark) Size of the Sun

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Mathematics – The Language of Science Science and mathematics came together some four centuries ago. Physics is based on concepts and mathematics provides an efficient, unambiguous means of expressing the relationship between theses concepts. We will be emphasizing the understanding of the concepts of Physics. But we will use equations for their ability to summarize relationships.

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Mathematics In some cases we will use simple mathematics to estimate relative sizes to further aid in understanding the concepts. There is no math prerequisite for this course – all the math we will need will be developed right here. Similar triangles Ratios Estimation techniques A little trig

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Scientific Method Hypothesis Experiment Confirmation A Theory must explain currently known phenomena. A Theory must make predictions that can be tested. Goals: Theory as simple as possible Few or no adjustable constants

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CONCEPT - an abstract or generic idea generalized from particular instances. FACT - something that has actual existence. Or an actual occurrence HYPOTHESIS implies insufficient evidence to provide more than a tentative explanation. LAW implies a statement of order and relation in nature that has been found to be invariable under the same conditions. THEORY - a plausible or scientifically acceptable general principle or body of principles offered to explain phenomena Scientific Method

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As soon as a theory is established scientists start to investigate how far it can be stretched: smaller dimensions, larger dimensions, larger and smaller masses. Scientific Method

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Disagreements with established theory Initially attempt to modify the theory to fit in the new results Try to add new concepts to theory Discoveries are not always that orderly but can benefit from luck, accidents and a prepared mind. X-Rays were discovered when leaks in shielding exposed some nearby photographic plates. Cosmic Background Radiation was discovered when trying to eliminate electrical noise in telephone transmission equipment. Scientific Method

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The Rest of the Stuff The Scientific Attitude Rightness – Wrongness Honesty in Science. Pseudoscience Science, Art and Religion A little person opinion from the author Science and Technology Risk Assessment Physics – The Basic Science Some boasting by Hewitt

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Science and Technology Risk Assessment Physics – The Basic Science Some boasting by Hewitt

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