What causes the shape of the shadows in the eclipse diagrams?
[Note that the eclipse diagrams I showed, e.g. like the ones in Figures 2.25 and 2.26, are not at all to scale! In reality they are far, far more elongated, but they must be compressed in order to show the main features.] Consider Figure 2.25. Suppose you are looking at the Sun from the region on the right, and the Earth (or whatever object) is in the way. You can draw lines from the outer edges of the Sun to the nearest outer edges of the Earth, and extend the lines to the right of the Earth to make a narrowing triangle. If you are inside this triangle on the right of the Earth, then you can’t see the Sun at all: every line of sight to the Sun is blocked by the Earth. This region is called the umbra. But you can also draw lines from the edges of the Sun to the opposite edges of the Earth, too, making an expanding triangle. This is the penumbra. If you are within this region, you still have some lines of sight to the Sun, and the Sun’s light is not completely blocked.
