Sunrise/Sunset & Sun Position Calculator
Understanding Sun Calculations
This calculator estimates sunrise, sunset, twilight times, and the Sun's position (azimuth and altitude) for a given date, time, and location. These calculations are based on astronomical formulas that model the Earth's orbit and rotation.
Key Concepts:
- Solar Declination (δ): The angle between the rays of the Sun and the plane of the Earth's equator. It varies throughout the year from approximately -23.45° (winter solstice) to +23.45° (summer solstice).
- Equation of Time (EoT): The difference between apparent solar time (time by a sundial) and mean solar time (time by a clock). It arises because of the Earth's elliptical orbit and axial tilt. Max variation is about ±16 minutes.
- Hour Angle (H): The angular distance of the Sun east or west of the local meridian due to Earth's rotation. It is 0° at solar noon, negative in the morning, and positive in the afternoon.
- Azimuth (Az): The Sun's compass direction, measured clockwise from North (0° = North, 90° = East, 180° = South, 270° = West).
- Altitude/Elevation (h): The Sun's angle above (or below) the horizon. 0° is on the horizon, 90° is directly overhead (zenith).
- Sunrise/Sunset: Defined as when the upper limb of the Sun is on the horizon. For calculation, this is often approximated as when the center of the Sun is about -0.833° below the geometric horizon (accounting for atmospheric refraction and the Sun's semi-diameter).
- Twilights: Periods of partial illumination before sunrise and after sunset.
- Civil Twilight: Sun's center is 0° to -6° below the horizon. Brightest form of twilight.
- Nautical Twilight: Sun's center is -6° to -12° below the horizon. Horizon and brighter stars visible.
- Astronomical Twilight: Sun's center is -12° to -18° below the horizon. Sky is dark enough for most astronomical observations.
General Calculation Approach:
- Calculate Julian Day for the date.
- Determine solar coordinates like declination and the Equation of Time.
- Calculate the hour angle for sunrise/sunset events using the desired solar altitude (e.g., -0.833° for sunrise/set, -6° for civil twilight, etc.).
- Convert these hour angles to local times, adjusting for solar noon and the Equation of Time.
- For sun position at a specific time, calculate the current hour angle and then use spherical trigonometry to find azimuth and altitude.
Note: These calculations are approximations. Actual times can vary slightly due to local atmospheric conditions, elevation, and precise definitions. Timezones are based on your browser's local settings.