PhysicsLAB: The Size of the Moon

After determining the circumference of the Earth, the Greeks utilized their observations of lunar eclipses to determine the size of the Moon. Lunar eclipses occur when the Sun, Earth, and Moon are exactly aligned and the Earth blocks the rays of the Sun from striking the Moon. To help visualize this event, watch this video showing the lunar eclipse of November 8th, 2003, taken in Grimbergen, Belgium. During totality, the red illumination of the Moon is due to the refraction of long wavelengths of red light by the Earth's atmosphere. If the Earth were to have no atmosphere, then the Moon would have been totally black.

Originally the Greeks compared the time it took the Moon to enter into the shadow of the Earth to the time it took it to leave the shadow. Later it was done by examining a sketch of the Moon as the shadow of the Earth partially covered It. By examining the curvature of the shadow we can find the ratio of the size of the Moon compared to the Earth. The ratio can be found by locating the center of the Earth’s shadow.

Refer to the following information for the next four questions.

For this activity you will need a compass, protractor, and centimeter ruler.

Using the picture given above, make two points on the edge of the shadow of the Earth.
Construct a tangent line to each point on the shadow’s curvature - this is a line which will just barely touch a curve at one point.
Construct a normal line at each point - this is a line that is perpendicular to the tangent line.
The two normal lines will cross; this represents the center of the Earth’s shadow.
Clearly illustrate your tangent and normal lines on your sketch.

Measure the radius of the Earth's shadow in centimeters.

Measure the radius of the Moon in centimeters.

Determine the size of the Moon as a percentage of the size of the Earth.

If the average radius of the Earth is 6378 km and the average radius of the Moon is 1737 km (link), what is your percent error for the percentage you calculated in the previous question?