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Early Scientific Measurements

Explore the power of mathematics in science through early measurements by Greek geographers and mathematicians aimed at determining sizes and relative positions of celestial bodies. The handout provides diagrams and observations to estimate quantities and compares them to currently accepted values.

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Early Scientific Measurements

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  1. Early Scientific Measurements Aimed at determining sizes and relative positions of dominant celestial bodies (Earth/Moon/Sun) Performed by Greek Geographers and Mathematicians in 365-240 BC Effectively illustrate power of mathematics in science Instructions to complete handout: On each of the 5 measurement pages: Label and complete the diagram Illustrate how the diagram and the observations can be used to arrive at an estimate of the indicated quantity On the last page Determine the accuracy of these early measurements by comparing them to their currently accepted values Aristarchus of Samos

  2. Scenario: At local noon on an equinox light rays from the sun do cast a shadow for an upright pillar that is not located at the equator, but on the equator no shadow is cast. Diameter of Earth P S L INITIAL Shadow Length S 1 OBSERVATIONS: --------------------- = --- = -----; Arclength = L = 950,000 meters Pillar Height P 8.0

  3. Scenario: During a solar eclipse, the shadow of the moon tapers to a point on the surface of the earth. However, during a lunar eclipse, the shadow of the earth tapers to 2.5 moon diameters. Diameter of Moon NEW Solar Eclipse – Moon shadow tapers to a point on Earth OBSERVATIONS: Lunar Eclipse – Earth shadow tapers to width of 2.5 Moon Diameters

  4. Distance Between Earth and Moon Scenario: When the moon is full, a small coin can be located an appropriate distance from our eye to perfectly block out the moon. Coin Diameter DiaCoin 1 NEW OBSERVATION: -------------------------- = ------------ = ----- Earth-Coin Distance LEarth-Coin 110

  5. Distance Between Earth and Sun Scenario: When the phase of the moon is a perfect “quarter” the Earth-Moon-Sun angle will be 90 degrees, resulting in the three celestial bodies lying at the vertices of a right triangle. NEW OBSERVATIONS: SEM Angle = 87 Degrees EMS Angle = 90 Degrees

  6. Scenario: When the light from the sun passes through a pin hole in a piece of paper and shines on the ground, a set of similar triangles is created. Diameter of the Sun Sun Image Diameter DiaSun Image 1 NEW OBSERVATION: ------------------------------ = --------------- = ----- Earth-Paper Distance LEarth-Paper 110

  7. Accuracy of These Measurements • The currently accepted values for the 5 quantities measured by these early scientists are as follows (to two significant digits): DiaEarth = 13,000 Km DiaMoon = 3,600 Km LEarth-Moon = 390,000 Km DiaSun = 1,400,000 Km LEarth-Sun = 150,000,000 Km • Absolute and Relative Error are often used to quantify the level of agreement between estimates and accepted values:

  8. Illustrate the level of agreement between the currently accepted values and estimates of early scientists by completing the following table (remember: 1 Km = 1000 m)

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