How to Calculate North or South Degrees of Sun Setting

Introduction

The north or south degrees of sun setting refer to the angular position of the sun relative to the north-south axis as it sets. This measurement is crucial for astronomers, navigators, and solar energy engineers who need precise information about solar positions.

Calculating these degrees involves understanding the sun's declination and the observer's latitude. The formula takes into account the time of year and the observer's location to provide accurate results.

Formula

The primary formula used to calculate the north or south degrees of sun setting is:

This formula calculates the angle between the sun's setting position and the north-south axis. The result can be positive (south of north) or negative (north of south).

Example Calculation

Let's calculate the north or south degrees of sun setting for an observer at 40°N latitude on the summer solstice (June 21).

1. Observer's latitude (φ) = 40°
2. Sun's declination (δ) = 23.5° (summer solstice)
3. Calculate using the formula: Degrees = arctan(cos(40°) * tan(23.5°))
4. First, convert degrees to radians: 40° = 0.6981 radians, 23.5° = 0.4102 radians
5. Calculate cos(40°) = 0.7660
6. Calculate tan(23.5°) = 0.4452
7. Multiply: 0.7660 * 0.4452 = 0.3416
8. Calculate arctan(0.3416) = 18.9°

The result is 18.9°, which means the sun sets 18.9° south of west from the observer's perspective.

Interpreting Results

The calculated degrees indicate how far the sun's setting position deviates from the true west direction. A positive value means the sun sets south of west, while a negative value indicates north of west.

This information is valuable for:

• Navigational purposes
• Solar panel orientation
• Shadow calculations
• Timekeeping devices