Earth Shadow Tapering: Why Does It Happen?

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The discussion centers on the phenomenon of Earth's shadow tapering, which occurs because the Sun is an extended light source rather than a point source. This results in a shadow that is not uniform, leading to a tapered appearance. The tapering effect is contrasted with how Venus casts a shadow during its transit, where only a small spot is visible on Earth. Clarifications were made regarding the implications of point versus extended light sources on shadow thickness. Understanding these principles helps explain the nature of shadows in astronomical contexts.
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The Earth casts a shadow. Why does this shadow taper?
 
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Venus also casts a shadow. On Earth we just see a small spot when Venus transits the Sun.
 
Because the Sun is not a point source of light but an extended object. Does that answer your question or have I misunderstood what taper means here?
 
Drakkith said:
Because the Sun is not a point source of light but an extended object. Does that answer your question or have I misunderstood what taper means here?
You mean if it were a point source, the shadow would not tapper (thinned) . So would it get thicker?
 
comparing a flat solar panel of area 2π r² and a hemisphere of the same area, the hemispherical solar panel would only occupy the area π r² of while the flat panel would occupy an entire 2π r² of land. wouldn't the hemispherical version have the same area of panel exposed to the sun, occupy less land space and can therefore increase the number of panels one land can have fitted? this would increase the power output proportionally as well. when I searched it up I wasn't satisfied with...
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