Jakarta, Indonesia is located at 106.8 ° Longitude, -6.1° Latitude.
Enter the solar-zenith angles for this city on each of the following dates.
Summer Solstice:
Autumn Equinox:
Winter Solstice:
Spring Equinox:
(Remember, all answers are positive. There are no negative angles.)
The Correct Answer and Explanation is :
The solar zenith angle (SZA) is the angle between the sun’s rays and the vertical direction at a specific location. It indicates how high the sun appears in the sky; a smaller SZA means the sun is higher overhead. Jakarta, Indonesia, is situated at approximately 6.1° South latitude.
The SZA at solar noon can be estimated using the formula:
SZA = |Latitude – Declination|
Here, the declination is the angle between the rays of the sun and the plane of the Earth’s equator, varying throughout the year as the Earth orbits the sun.
Summer Solstice (June 21):
On this date, the sun’s declination is approximately +23.44°, meaning it’s directly over the Tropic of Cancer. For Jakarta:
SZA = |(-6.1°) – (+23.44°)| = | -29.54° | = 29.54°
This indicates the sun is 29.54° away from being directly overhead at noon.
Autumn Equinox (September 23):
During an equinox, the sun’s declination is 0°, as it’s directly over the equator. For Jakarta:
SZA = |(-6.1°) – 0°| = | -6.1° | = 6.1°
The sun is just 6.1° away from the zenith at noon, appearing almost directly overhead.
Winter Solstice (December 21):
On this day, the sun’s declination is approximately -23.44°, over the Tropic of Capricorn. For Jakarta:
SZA = |(-6.1°) – (-23.44°)| = | -6.1° + 23.44° | = 17.34°
The sun is 17.34° away from being directly overhead at noon.
Spring Equinox (March 21):
Similar to the autumn equinox, the sun’s declination is 0°. For Jakarta:
SZA = |(-6.1°) – 0°| = | -6.1° | = 6.1°
Again, the sun is just 6.1° from the zenith at noon.
These calculations show that during the equinoxes, Jakarta experiences the sun almost directly overhead at noon, resulting in minimal shadows and intense sunlight. At the summer solstice, the sun is slightly farther from the zenith, while during the winter solstice, it’s a bit closer compared to the summer solstice. This variation affects the intensity and distribution of sunlight, influencing factors like climate, energy generation, and daily human activities.
Understanding the SZA is crucial for optimizing solar panel installations, as panels should be angled to maximize exposure to sunlight. It also aids in architectural design, agriculture, and even in planning outdoor events, ensuring that structures and activities align with the sun’s position for maximum efficiency and comfort.