Problem 11 - Astronomy Journey to the Cosmic Frontier

Question

Suppose you and your roommate had built a monument with piles of rocks to mark the azimuths of sunrise at the solstices. How could you determine where to place a pile of rocks to mark the azimuth of sunrise at the equinoxes? (Note, there are several correct answers to this question.)

Step-by-Step Solution

Answer

Place the rock pile between the existing solstice markers, exactly in the middle.

Step 1: Understand the Solstice Sunrise Azimuths

The azimuth is the angle from the north in a clockwise direction. During solstices, the sun rises at its extreme northern or southern points along the horizon. Determine the sunrise azimuth angles for summer and winter solstices using your existing monuments.

Step 2: Concept of Equinox Sunrise

During equinoxes, the sun rises exactly in the east. This occurs because the Earth's axis is tilted neither towards nor away from the sun, causing equal day and night.

Step 3: Midpoint Calculation

The position where the sun rises during the equinoxes falls exactly between its positions during the solstices. Compute the midpoint of the summer and winter solstice sunrise azimuths to find the azimuth for the equinoxes.

Step 4: Placement of an Equinox Marker

Using the midpoint azimuth calculated in Step 3, place the pile of rocks at this azimuth from your central point to mark the equinox sunrise.

Key Concepts

Solstice Sunrise Azimuth

The term "Solstice Sunrise Azimuth" refers to the precise direction along the horizon where the sun rises during the solstices. Solstices occur twice a year when the Earth's poles point directly towards or away from the sun.
This results in the longest and shortest days of the year, known as the summer and winter solstices, respectively. The azimuth is measured as an angle from the north in a clockwise fashion. For instance, during the summer solstice in the Northern Hemisphere, the sun rises at its most northern point, which is usually around an azimuth of 60 degrees.

• Summer Solstice: In the Northern Hemisphere, this occurs around June 21st, when the sun reaches its highest or most northern sunrise position.
• Winter Solstice: Around December 21st, the sun rises at its southernmost point, with azimuths generally pointing around 120 degrees from north.

These specific directions help in constructing monuments or markers that can indicate the azimuth of sunrises during different times of the year.

Earth's Axis Tilt

The tilt of Earth's axis plays a crucial role in the seasons and the position of the sun in the sky. The Earth is tilted at an angle of approximately 23.5 degrees from the perpendicular to its orbital plane.
This tilt is responsible for the variation in sunlight received at different latitudes and during different times of the year.

• Because of this tilt, the Northern Hemisphere experiences summer when it tilts towards the sun, and the sun appears higher in the sky.
• Conversely, during winter, the Northern Hemisphere tilts away from the sun, resulting in lower sun paths and shorter days.
• At the equinoxes, the tilt aligns such that both hemispheres receive approximately equal sunlight.

Understanding Earth's tilt is vital for recognizing how the sun's path changes and influences the equinox and solstice sunrises.

Sunrise Midpoint Calculation

To determine the equinox sunrise azimuth, you calculate the midpoint between the summer and winter solstice sunrise azimuths.
This is because, during the equinoxes, the sun rises exactly due east, sitting right between its northern and southernmost positions.

• Suppose the summer solstice sunrise azimuth is at 60 degrees.
• And the winter solstice sunrise azimuth is at 120 degrees.
• The equinox sunrise azimuth would be the average of these two angles: \( \frac{60 + 120}{2} = 90 \, degrees\ \).

This calculation demonstrates that at the equinox, the sun rises at an azimuth of 90 degrees from the north, pointing directly east.