Early Scientific Measurements Aimed at determining sizes and

Diameter of Earth P L INITIAL Shadow Length S 1 OBSERVATIONS: ----------- = -----;

Diameter of Moon Scenario: During a solar eclipse, the shadow of the moon tapers

Distance Between Earth and Moon Scenario: When the moon is full, a small coin

Distance Between Earth and Sun Scenario: When the phase of the moon is a

Diameter of the Sun Scenario: When the light from the sun passes through a

Accuracy of These Measurements • The currently accepted values for the 5 quantities measured

• Illustrate the level of agreement between the currently accepted values and estimates

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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: Ø On each of the 5 measurement pages: q Label and complete the diagram q Illustrate how the diagram and the observations can be used to arrive at an estimate of the indicated quantity Ø On the last page q Determine the accuracy of these early measurements by comparing them to their currently accepted values Aristarchus of Samos

Diameter of Earth P L INITIAL Shadow Length S 1 OBSERVATIONS: ----------- = -----; Pillar Height P 8. 0 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. S Arclength = L = 950, 000 meters

Diameter of Moon 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. NEW Solar Eclipse – Moon shadow tapers to a point on Earth OBSERVATIONS: Lunar Eclipse – Earth shadow tapers to width of 2. 5 Moon Diameters

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 Dia Coin 1 NEW OBSERVATION: ------------- = ----Earth-Coin Distance L Earth-Coin 110

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

Diameter of the Sun 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. Sun Image Diameter Dia Sun Image 1 NEW OBSERVATION: --------------- = ----Earth-Paper Distance L Earth-Paper 110

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

• 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) Measurement Accepted Value (Km) Dia. Earth 13, 000 Dia. Moon 3, 600 LEarth-Moon 390, 000 LEarth-Sun 150, 000 Dia. Sun 1, 400, 000 Estimated Value (Km) Relative Error (%)