During the entire total phase of the solar eclipse, a bright prominence was visible near the equator of the Sun.

During the entire total phase of the solar eclipse, a bright prominence was visible near the equator of the Sun. Estimate its minimum size if the full phase bandwidth was 150 km and it was observed near the zenith.

In the problem statement, it is said that a total solar eclipse is observed near the zenith. In this case, we can assume that the centers of the Sun, Moon and Earth are on the same line, and the full phase strip width is equal to the diameter of the lunar shadow spot running along the Earth’s surface. Let us denote it through d, the distance from the center of the Earth to the Sun and the Moon through L and l, respectively, and the radius of the Earth through R. It can be seen from the figure that the prominence will be visible from the entire shadow region if it is visible from its most distant point A. From the equality of the vertical angles marked in the figure, we find that the size of the prominence must be not less than the value D, for which.
Substituting the numerical values ​​R = 6378 km, l = 384400 km and L = 149.6 million km, we get D = 59200 km, which is almost five times the diameter of the Earth! However, solar prominences are often observed during the entire total phase of a solar eclipse, indicating the enormous size of these formations.

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