Calculating Solar Azimuth Angle Based on Longitude, Latitude, and Time

Solar azimuth angle calculation is a common requirement in astronomy and geographic information systems (GIS), used to determine the sun's orientation at specific times and locations. The MATLAB implementation involves the following core approach:

Fundamental Principles: Solar azimuth calculation is based on astronomical patterns of Earth's rotation and revolution, requiring consideration of the observer's longitude, latitude, and specific time (including time zone). The key computational steps include:

Julian Day Conversion: Convert universal time to Julian Day, the standard time representation in astronomical calculations. Julian Day counts continuous days since noon on January 1, 4713 BC. In code implementation, this involves date-to-Julian conversion functions with precision handling for fractional days.

Solar Position Calculation: Based on Julian Day, compute solar parameters including mean anomaly, geometric mean longitude, and subsequently obtain the sun's apparent right ascension and declination. These parameters describe the sun's precise position on the celestial sphere. The algorithm typically uses trigonometric functions and iterative calculations for accuracy.

Local Hour Angle Computation: Calculate the sun's hour angle relative to the local meridian based on observer longitude and time. This step requires time zone correction and accounts for Earth's rotation effects. Code implementation involves angular conversions and modulo operations for 24-hour cycle handling.

Azimuth Transformation: Finally, transform the sun's equatorial coordinates to the horizontal coordinate system to obtain the solar azimuth angle. The azimuth is typically measured from true north (0°) increasing eastward. This involves spherical trigonometry calculations using sine and cosine laws.

Implementation Key Points: - Time zone processing: Requires UTC to local time conversion algorithms - Coordinate transformation: Includes matrix operations for equatorial-to-horizontal coordinate conversion - Precision control: Numerical stability handling for trigonometric computations - Seasonal corrections: Accounts for Earth's orbital eccentricity and other astronomical factors

Application Scenarios: This calculation can be applied to solar panel orientation optimization, architectural daylighting design, photography lighting planning, and other fields. By inputting specific coordinates and time, users can obtain the sun's exact azimuth at that moment, providing data support for related applications.

Important Considerations: - Results require magnetic declination correction based on actual location - Azimuth changes rapidly near sunrise/sunset times - Polar day/night phenomena may occur in high-latitude regions during specific seasons - Code should include edge case handling for extreme latitudes and special astronomical events