What can we learn from a Solar Eclipse?

In the last page, we said that the shadow of the Earth tapers by one Moon diameter (i.e., the shadow of the Earth is one Moon diameter smaller than the actual size of the Earth) at the distance of the Moon. How do we know this? From our observations of a solar eclipse.

Have you ever witnessed a total solar eclipse? Maybe you have not. They are particularly rare occurrences. Why? Consider the diagram below:

The Earth moves around the Sun, and the Moon moves around the Earth. But the orbit of the Moon around the Earth is tilted with respect to the orbit of the Earth around the Sun. This means that the Moon does not always lie in the same plane as the Earth and the Sun. Therefore, in order for a solar eclipse to occur, the Moon must be between the Earth and the Sun, and it must be in the same plane as the Earth in the Sun.

We know that during a total solar eclipse only a small region of the Earth is able to view the eclipse. In fact, the diameter of this region at any instant during the total solar eclipse is approxiamtely 200 km. Compared to the diameter of the Moon (approxiamtely 3700 km) the size of the region is approxiamtely 0.05 times the size of the Moon. In other words, the size of the shadow (created by the Moon during a total solar eclipse) is significantly smaller than the actual size of the Moon. Furthermore, we can even say that the shadow created by the Moon tapers by one Moon diameter by the time the shadow reaches Earth.

Consider the diagram below:

The Sun emits light in all directions. The diagram above only shows two sample light rays. These light rays, however, enable us to imagine the positions of the Earth, Moon, and Sun (and the subsequent shadow that produces a total solar eclipse). The two light rays that converge in a point on the Earth represent the light rays that cause the total solar eclipse. Note the small region on Earth that will be able to view the eclipse. We can say that the shadow created by the Moon tapers by one Moon diameter by the time the shadow reaches Earth.

By applying similar reasoning to a lunar eclipse, we can say that the the shadow of the Earth also tapers by one Moon diameter, since the orbit of the Moon around the Earth is approximately circular (and thus the distance between the Moon and the Earth is the same in both cases). Consider the diagram below which shows the positions of the Earth, Moon, and Sun during a lunar eclipse:

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