On the Breadth of Earth’s Shadow Of Lunar Eclipse - A New Approach To Students’ Understanding Of Aristarchus’s “Hypothesis 5”

The ancient Greek astronomer Aristarchus was the first astronomer to make a reasonable estimate of the distances of the sun and moon from the earth. In his treatise, “On the Sizes and Distances of the Sun and the Moon”, he proposed the “hypothesis 5” saying, "That the breadth of the shadow is two moons" in a lunar eclipse, without any argument. It may be estimated by measuring the size of the arc of Earth’s shadow (umbra) projecting on the lunar surface or other means. By studying how students interact with these concepts, we now present a new method to do the evaluation, showing that according to the time of the first contact and the third contact as well as the positions of the two contact points on lunar surface, the ratio of the breadth of Earth’s shadow to lunar diameter can be found to have a consistent value of around 2.85. The procedure can be designed to be a middle school science experiment to help students understand the motions of the Earth and Moon.