Why does Earth's shadow taper?

The correct answer is based on the relative sizes and distances between the Earth and the Sun. The Sun is significantly larger than the Earth, about 109 times in diameter and about 330,000 times in mass. Due to this vast difference in size, the shadow cast by the Earth, particularly during events like a lunar eclipse, takes on a tapered shape.

When the Earth blocks sunlight, the shadow consists of two main parts: the umbra, where total shadow occurs, and the penumbra, where partial shadow exists. As light radiates from the Sun, it spreads out in all directions. The shadow starts at the surface of the Earth and narrows as it extends into space. This tapering happens because the finite size of the light source (the Sun) results in less light reaching the edges of the shadow. Essentially, the larger the light source in relation to the object casting the shadow, the more pronounced this tapering effect becomes.

This phenomenon can also be visualized during solar eclipses, where the shadow of the Moon on the Earth can vary in width, depending on the distances involved, but the fundamental reason remains the same: the large size of the Sun compared to Earth leads to this unique shadow shape.