The limiting ecliptic geocentric latitude of the center of the lunar disk for the beginning (end) of the lunar eclipse

The limiting ecliptic geocentric latitude of the center of the lunar disk for the beginning (end) of the lunar eclipse is determined by the formula P = p3t + pl, where p3t, pl are the angular radii of the earth’s shadow and the moon. For which eclipse is this formula applicable: for penumbra, partial or total shadow? How is this formula written for the other two types of eclipses?

This formula determines the beginning of a partial shadow eclipse. For a penumbra eclipse, in the formula for the limiting ecliptic latitude of the center of the lunar disk, instead of the angular radius of the earth’s shadow, it is necessary to take the angular radius of the earth’s penumbra.

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