Sunlight that reaches Earth is blocked by Earth from traveling any farther, so that the region on the side of Earth facing away from the Sun is in shadow. The portion of this region in complete shadow is the umbra, and the portion in partial shadow is the penumbra. The Sun's radius is \(7.0 \times 10^{5} \mathrm{~km}\), Earth's radius is \(6.4 \times 10^{3} \mathrm{~km}\), and the Sun-Earth distance is \(1.5 \times 10^{8} \mathrm{~km}\).

(a) What is the shape of the umbra? Of the penumbra? 

\((b)\) Consider an observer in space on the side of Earth facing away from the Sun-that is, in the shadow region. Does this observer see the Sun when he is in the umbra? When he is in the penumbra?