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During the summers at high latitudes, ghostly, silver-blue clouds occasionally appear after sunset when common clouds are in Earth's shadow and are no longer visible. The ghostly clouds have been called noctilucent clouds (NLC), which means "luminous night clouds," but now are often called mesospheric clouds, after the mesosphere, the name of the atmosphere at the altitude of the clouds These clouds were first seen in June 1885 , after dust and water from the massive 1883 volcanic explosion of Krakatoa Island (near Java in the Southeast Pacific) reached the high altitudes in the Northern Hemisphere. In the low temperatures of the mesosphere, the water collected and froze on the volcanic dust (and perhaps on comet and meteor dust already present there) to form the particles that made up the first clouds. Since then, mesospheric clouds have generally increased in occurrence and brightness, probably because of the increased production of methane by industries, rice paddies, landfills, and livestock flatulence. The methane works its way into the upper atmosphere, undergoes chemical changes, and results in an increase of water molecules there, and also in bits of ice for the mesospheric clouds. If mesospheric clouds are spotted 38 min after sunset and then quickly dim, what is their altitude if they are directly over the observer?

Step by step solution

01

Understand the Geometry

Visualize the position of the clouds, observer, and the Sun. The clouds appear after sunset when they are still illuminated by the Sun due to their high altitude.

02

Determine the Angle of Illumination

The Sun sets approximately every one minute of angle travel on the horizon after sunset. Therefore, 38 minutes means the Sun is 38 degrees below the horizon.

03

Apply the Right Triangle Relationships

Use the Earth's radius (R = 6400 km) and the small angle approximation to calculate the altitude (h) of the clouds. The small angle approximation formula is \[ h \approx R \tan(\theta) = R \times 38 \]

04

Calculate the Altitude

Substitute the values into the equation: \[ h \approx (6400 \text{ km}) \tan(38 \text{ deg}) \approx 5000 \text{ km} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

noctilucent clouds

Noctilucent clouds, also known as 'luminous night clouds,' are distinct for appearing during the twilight hours, usually after sunset. They have a ghostly, silver-blue hue and are situated much higher in the atmosphere than common clouds. Noctilucent clouds are primarily seen at high latitudes during the summer months.

They are best observed when common clouds are no longer visible because they are in Earth's shadow. These clouds get their illumination from the Sun, which is just below the horizon at such times.

Interestingly, these clouds were first observed in June 1885, likely due to the water vapor and dust from the Krakatoa volcanic eruption. Since then, the frequency and brightness of noctilucent clouds have increased, probably due to factors like industrial activity and methane emissions.

atmospheric layers

The atmosphere is divided into several layers, with each having distinct characteristics.

The layers include:

• Troposphere: This is the lowest layer, where weather occurs, and it extends up to about 8-15 kilometers.
• Stratosphere: Above the troposphere, extending up to about 50 kilometers. This layer contains the ozone layer, which absorbs and scatters ultraviolet solar radiation.
• Mesosphere: Ranging from about 50 to 85 kilometers; this is the layer where noctilucent clouds form. It is known for its low temperatures.
• Thermosphere: Extending up to 600 kilometers, it is characterized by high temperatures. Here, the auroras occur.
• Exosphere: The outermost layer, which merges with space.

The mesosphere, where noctilucent clouds form, has low temperatures that facilitate the formation of ice crystals needed for these luminous night clouds.

volcanic activity

Volcanic activity can significantly impact cloud formation, especially in the upper atmosphere. A notable example is the massive volcanic eruption of Krakatoa in 1883, which ejected vast amounts of dust and water vapor into the atmosphere.

This eruption provided the material that contributed to the formation of the first observed noctilucent clouds in 1885. The dust particles offered surfaces for water vapor to condense and freeze, forming ice crystals at high altitudes.

Volcanic eruptions can distribute particles into the mesosphere, altering the atmospheric composition and contributing to cloud formation.

methane emissions

Methane emissions have been rising due to human activities and significantly impact the formation of noctilucent clouds. Sources of methane include:

• Industrial activities
• Rice paddies
• Landfills
• Livestock flatulence

Methane reaches the upper layers of the atmosphere, where it undergoes chemical reactions, increasing the number of water molecules. These water molecules can freeze into ice crystals, contributing to the formation of noctilucent clouds.

This increase in water molecules at high altitudes likely explains the observed increase in the frequency and brightness of noctilucent clouds since the late 19th century.

solar geometry

The position of the Sun relative to the Earth plays a vital role in determining when noctilucent clouds are visible. These clouds are usually seen after sunset because of their high altitude, which allows them to remain illuminated by sunlight even when the Sun is below the horizon.

Understanding Geometry: The observer's position, the clouds, and the Sun form a geometric relationship. When the Sun is about 38 degrees below the horizon, it still lights up the noctilucent clouds.

Calculating Altitude: Using the small angle approximation formula, we can estimate the altitude of these clouds. Given the Earth's radius (R = 6400 km), the altitude (h) can be calculated as:

\[ h \approx R \tan(38\text {\ deg}) = R \times 38 \]

Substituting the values into the equation gives: \[ h \approx (6400 \text{ km}) \tan(38 \text{ deg}) \approx 5000 \text{ km} \]

This calculation helps explain why these ghostly clouds can be seen after sunset.