Some elementary but surprising facts about the Sun's path at sunset

Area of Science:

• Astronomy
• Earth Science
• Physics

Background:

• The apparent path of the Sun across the sky varies seasonally.
• Solar noon elevation differs significantly between summer and winter solstices.

Purpose of the Study:

• To investigate the angle of the Sun's path with the horizon at sunset.
• To determine if this angle changes seasonally despite varying solar noon elevations.

Main Methods:

• Geometric analysis of the Sun's apparent path.
• Calculation of sunset path angles at the horizon for different latitudes.
• Comparison of these angles between summer and winter solstices.

Main Results:

• The angle between the horizon and the Sun's path at sunset is constant throughout the year for any given latitude.
• For 43° north latitude, the Sun's noon elevation varies by 47°, but the sunset path angle variation is only 5°.

Conclusions:

• Contrary to intuitive assumptions based on noon elevation, the sunset horizon angle is invariant with season.
• This geometric property of solar paths has implications for understanding seasonal light and shadow patterns.