Problem 1 - Astronomy: At Play in the Cosmos

Question

How does the altitude of the Sun at noon on the same day in the Northern Hemisphere's summer compare for two observers at latitudes \(12^{\circ}\) north and \(54^{\circ}\) north, respectively? a. It is the same for both observers because they are in the same hemisphere, experiencing summer. b. It cannot be determined without knowing their longitudes. c. It is \(42^{\circ}\) higher for the observer at \(12^{\circ}\) north because of the difference in latitude. d. It is \(42^{\circ}\) higher for the observer at \(54^{\circ}\) north because of the difference in latitude. e. The relative altitude of the Sun cannot be determined for the two locations without knowing the exact date.

Step-by-Step Solution

Answer

c. It is \(42^{\circ}\) higher for the observer at \(12^{\circ}\) north.

Step 1: Understanding the Problem

We have to determine how the altitude of the Sun at noon varies for two observers at different latitudes in the Northern Hemisphere during summer. We know the latitudes are \(12^{\circ}\) north and \(54^{\circ}\) north.

Step 2: Knowing Key Facts

During summer in the Northern Hemisphere, the Sun is directly over the Tropic of Cancer on the summer solstice, around June 21. The Tropic of Cancer is at latitude \(23.5^{\circ}\) north.

Step 3: Calculate Sun's Noon Altitude at \(12^{\circ}\)

At noon on the summer solstice, the Sun's altitude is calculated as \(90^{\circ} - \) (latitude - Tropic of Cancer latitude). For \(12^{\circ}\), this is:\[90^{\circ} - (12^{\circ} - 23.5^{\circ}) = 90^{\circ} - (-11.5^{\circ}) = 101.5^{\circ}.\]Since \(90^{\circ}\) is the maximum for zenith, an altitude above \(90^{\circ}\) means the Sun is directly overhead or appears slightly to the north.

Step 4: Calculate Sun's Noon Altitude at \(54^{\circ}\)

For \(54^{\circ}\), the calculation is:\[90^{\circ} - (54^{\circ} - 23.5^{\circ}) = 90^{\circ} - 30.5^{\circ} = 59.5^{\circ}.\]

Step 5: Comparing the Altitude Difference

The Sun's altitude at \(12^{\circ}\) north is \(101.5^{\circ}\), while at \(54^{\circ}\) north it is \(59.5^{\circ}\). Therefore, the Sun is \(101.5^{\circ} - 59.5^{\circ} = 42^{\circ}\) higher in the sky at \(12^{\circ}\) north.

Key Concepts

Northern Hemisphere Summer

The Northern Hemisphere summer is characterized by the Earth's tilt toward the Sun, allowing sunlight to strike more directly over this hemisphere. This season typically spans from around June to September, peaking with the summer solstice around June 21.
The summer solstice is particularly significant because it marks the day when the Northern Hemisphere experiences the longest period of daylight and the Sun reaches its highest point in the sky at noon.

• The elevated position of the Sun during summer means that regions closer to the equator experience intense sunlight.
• This increased sunlight results in warmer temperatures and contributes to the characteristic climate of summer.

Understanding these basics can help explain why areas within the Northern Hemisphere experience such distinctive seasonal changes and how they affect local weather patterns.

Tropic of Cancer

The Tropic of Cancer is an important geographical latitude line located at approximately 23.5° north of the equator. This latitude marks the northernmost point on Earth where the Sun can be directly overhead at noon during the summer solstice in the Northern Hemisphere.
Here's why it's important:

• During a Northern Hemisphere summer solstice, the direct overhead Sun at noon occurs precisely at the Tropic of Cancer.
• This alignment results in the smallest shadow cast, signifying the Sun's zenith position.

The Tropic of Cancer serves as a useful marker for understanding Earth's solar dynamics. By delineating the limit of the Sun's vertical rays, it provides insights into why some regions experience very little shadow at certain times of the year while others see significant variation in sunlight angles.

Latitude Effect on Solar Position

Latitude plays a crucial role in determining the position of the Sun in the sky at any given time, especially noon. The effect of latitude on solar position becomes evident when comparing locations at different latitudes:

• At lower latitudes, closer to the equator, the Sun is generally higher in the sky, due to the direct nature of sunlight during summer months.
• Conversely, at higher latitudes, like those closer to the poles, the Sun's path is lower, leading to less direct sunlight and its angled position.

For instance, during the Northern Hemisphere summer, an observer at 12° north would see the Sun significantly higher compared to an observer at 54° north. This difference in solar altitude leads to varied energy received at the surface, influencing local climates and daylight length throughout different regions of the globe.