Halliday, Resnick & Walker — Measurement: Problem 60

Noctilucent clouds. Soon after the huge 1883 volcanic explosion of Krakatoa Island (near Java in the southeast Pacific), silvery, blue clouds began to appear nightly in the Northern Hemisphere early at night. The explosion was so violent that it hurled dust to the mesosphere, a cool portion of the atmosphere located well above the stratosphere. There water collected and froze on the dust to form the particles that made the first of these clouds. Termed noctilucent clouds ("night shining"), these clouds are now appearing frequently (Fig. 1.6a), signaling a major change in Earth’s atmosphere, not because of volcanic explosions, but because of the increased production of methane by industries, rice paddies, landfills, and livestock flatulence. The clouds are visible after sunset because they are in the upper portion of the atmosphere that is still illuminated by sunlight. Figure 1.6b shows the situation for an observer at point A who sees the clouds overhead 38 min after sunset. The two lines of light are tangent to Earth’s surface at A and B, at radius r from Earth’s center. Earth rotates through angle $\theta$ between the two lines of light. What is the height H of the clouds?