The longest duration of a total lunar eclipse (i.e.,how long the Moon is within the umbra)is 107 minutes.If it takes the Moon 57 minutes to move a distance equal to its own diameter against the background stars,how wide is Earth's umbra at the closest distance of the Moon's orbit?

Question

Quizplus · Accepted Answer

The total lunar eclipse lasts for 107 minutes, during which the Moon is within the Earth's umbra. We know that the Moon takes 57 minutes to move a distance equal to its own diameter against the background stars. This means that during the eclipse, the Moon would move through a distance of two diameters of its own against the background stars (since it would enter the umbra, cross its diameter, and exit it). Thus, the width of Earth's umbra would be approximately three times the Moon's diameter. Therefore, the answer is C, a little less than three times the Moon's diameter.

The Longest Duration of a Total Lunar Eclipse (I