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. Diameter of Earth INITIAL Shadow Length S 1 OBSERVATIONS: --------------------- = --- = -----; Arclength = L = 950,000 meters Pillar Height P 8.0 S P L 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.

3. Diameter of Moon NEWSolar Eclipse – Moon shadow tapers to a point on Earth OBSERVATIONS:Lunar Eclipse – Earth shadow tapers to width of 2.5 Moon Diameters 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.

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

5. Distance Between Earth and Sun NEW OBSERVATIONS:SEM Angle = 87 Degrees EMS Angle = 90 Degrees 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.

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

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): Dia Earth = 13,000 Km Dia Moon = 3,600 KmL Earth-Moon = 390,000 Km Dia Sun = 1,400,000 KmL Earth-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) Measurement Accepted Value (Km) Estimated Value (Km) Relative Error (%) Dia Earth 13,000 Dia Moon 3,600 L Earth-Moon 390,000 L Earth-Sun 150,000,000 Dia Sun 1,400,000