Sunrise Calculation

Sunrise Azimuth Formula:

\[ AZ = \arccos(\sin(lat) \times \sin(dec) + \cos(lat) \times \cos(dec) \times \cos(HA)) \]

Azimuth (AZ):

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1. What is Sunrise Azimuth Calculation?

The sunrise azimuth calculation determines the compass direction (in degrees from North) where the sun rises, based on the observer's latitude, the sun's declination, and the hour angle.

2. How Does the Calculator Work?

The calculator uses the azimuth equation:

\[ AZ = \arccos(\sin(lat) \times \sin(dec) + \cos(lat) \times \cos(dec) \times \cos(HA)) \]

Where:

\( AZ \) — Azimuth in degrees (compass direction of sunrise)
\( lat \) — Observer's latitude in degrees
\( dec \) — Sun's declination in degrees
\( HA \) — Hour angle in degrees

Explanation: The equation calculates the angle between the north direction and the point on the horizon where the sun rises, accounting for the observer's location and the sun's position.

3. Importance of Azimuth Calculation

Details: Knowing the sunrise azimuth is crucial for astronomy, navigation, architecture (for building orientation), and solar panel placement. It helps predict where the sun will appear on the horizon at different times of the year.

4. Using the Calculator

Tips: Enter latitude (-90 to 90), declination (-23.44 to 23.44), and hour angle (typically 0 at sunrise). All values must be in degrees. The calculator handles the conversion to radians internally.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of possible azimuth values?
A: Azimuth ranges from 0° (North) through 90° (East), 180° (South), to 270° (West). Sunrise azimuth is typically between 0° and 180°.

Q2: How does latitude affect sunrise azimuth?
A: At higher latitudes, the sunrise azimuth varies more dramatically throughout the year. At the equator, sunrise is always nearly due east.

Q3: What is solar declination?
A: The angle between the rays of the sun and the plane of the Earth's equator, varying between -23.44° and +23.44° through the year.

Q4: What is the hour angle at sunrise?
A: At sunrise, the hour angle is typically close to zero (solar noon being the reference point).

Q5: Can this be used for sunset azimuth?
A: Yes, the sunset azimuth would be 360° minus the sunrise azimuth for symmetrical conditions.