Sun Altitude And Azimuth Calculator

Sun Position Equations:

\[ \sin \alpha = \sin \delta \sin \varphi + \cos \delta \cos \varphi \cos H \] \[ Az = \cos^{-1}\left[\frac{\sin \delta \cos \varphi - \cos \delta \sin \varphi \cos H}{\cos \alpha}\right] \]

Altitude (α):

Azimuth (Az):

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1. What is Sun Altitude and Azimuth?

Sun altitude (α) is the angle between the sun and the horizontal plane, while azimuth (Az) is the compass direction from which the sunlight is coming. These coordinates define the sun's position in the sky at any given time and location.

2. How Does the Calculator Work?

The calculator uses astronomical equations:

\[ \sin \alpha = \sin \delta \sin \varphi + \cos \delta \cos \varphi \cos H \] \[ Az = \cos^{-1}\left[\frac{\sin \delta \cos \varphi - \cos \delta \sin \varphi \cos H}{\cos \alpha}\right] \]

Where:

\( \alpha \) — Sun altitude (degrees above horizon)
\( Az \) — Sun azimuth (degrees from north)
\( \delta \) — Solar declination (degrees)
\( \varphi \) — Observer's latitude (degrees)
\( H \) — Hour angle (degrees)

Explanation: These equations calculate the sun's position based on astronomical coordinates and time.

3. Importance of Sun Position Calculation

Details: Accurate sun position calculation is crucial for solar energy systems, architectural design, photography, navigation, and astronomical observations.

4. Using the Calculator

Tips: Enter declination, latitude, and hour angle in degrees. All values must be valid numerical inputs. Results are given in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is solar declination?
A: Solar declination is the angle between the rays of the sun and the plane of the earth's equator, varying throughout the year.

Q2: How is hour angle calculated?
A: Hour angle is the angular distance between the sun's current position and its position at solar noon, with 15 degrees per hour.

Q3: What are typical altitude values?
A: Altitude ranges from 0° at sunrise/sunset to 90° at zenith (directly overhead at equator on equinoxes).

Q4: How is azimuth measured?
A: Azimuth is typically measured clockwise from true north: 0°=north, 90°=east, 180°=south, 270°=west.

Q5: Are there limitations to these equations?
A: These equations provide theoretical positions and may not account for atmospheric refraction or local topography effects.