Visualizing the Lunar Eclipse - Ratio of Moon and Earth Shadow

Introduction:

Please bring yourself back to the time of our Greek ancestors when they questioned facts about the Moon and the Earth, such as their sizes.[br]Then, they thought of observing the time for the first and second phases of the lunar eclipse.[br]Please discover these ancient observations through this GeoGebra build.

How to Use the GeoGebra Applet for Exploration and Discovery?

Before 1st Phase: Move the slider to move the Moon from point B until it touches the Earth's shadow at (5,0). Note the time.[br][br]First Phase: Move the slider to move the Moon fully into the Earth's shadow as a complete circle. Note the time as t1.[br][br]Second Phase: Move the slider to shift the Moon across the Earth's shadow until it reaches the opposite edge. Note the time as t2.[br][br]First Phase + Second Phase = Total Eclipse Phase[br][br]Now, find the ratio of the First Phase time t1[br]to the Second Phase time t2.[br][br]Finally, by using the total eclipse time, determine the ratio of the Moon's diameter to the Earth's diameter.[br][br]The Earth's shadow diameter is ____ times the Moon's diameter.[br]

Source of Inspiration and Reference:

Sizes of the Moon and the Earth

What did the Greek ancestors use to estimate the sizes of the Moon and the Earth?

D) Using telescopes C) Comparing the brightness of stars A) Observing solar eclipses B) Measuring the time phases of a lunar eclipse

Ratio of t1 and t2

If the time for the first phase of the lunar eclipse is t1, and the time for the second phase is t2, what is the correct ratio given in this build?

A) t2=2×t1 C) t2=3 * t1 B) t2=5/2 * t1 D) t2=1/2 * t1

Ratio of the Moon’s diameter to the Earth’s diameter

How does observing a lunar eclipse help in determining the ratio of the Moon’s diameter to the Earth’s diameter?

C) By tracking the Moon’s surface features D) By observing the Moon’s color changes B) By measuring how long the Moon takes to pass through the Earth's shadow A) By comparing the brightness of the Moon during different phases

Approximate ratio of the Earth's diameter to the Moon's diameter

Based on the observations in this GeoGebra build, what is the approximate ratio of the Earth's shadow diameter to the Moon's diameter?

A) 1:4 C) 1:6 B) 1:2.5 D) 1:10

Textbook Reference and Source of Inspiration:

Bondoc, J. M. F., Villa, J. C. S., & Pawilen, G. T. (Eds.). (2024). [i]History of mathematics[/i]. Rex Marketing Publisher.