1. What is the Daylight Length Formula?

The Daylight Length formula calculates the number of daylight hours at a specific location on Earth based on latitude and solar declination. This astronomical formula helps determine day length for any given date and location.

2. How Does the Calculator Work?

The calculator uses the daylight length formula:

Where:

• \( lat \) — Latitude in degrees (positive for north, negative for south)
• \( decl \) — Solar declination in degrees
• \( \frac{1}{15} \) — Conversion factor (15° per hour of Earth's rotation)
• \( \arccos \) — Inverse cosine function
• \( \tan \) — Tangent function

Explanation: The formula calculates the hour angle of sunrise/sunset and converts it to daylight hours, accounting for the Earth's spherical geometry and axial tilt.

3. Importance of Daylight Length Calculation

Details: Daylight length calculations are essential for agriculture, solar energy planning, architectural design, tourism, and understanding seasonal variations in climate and ecosystems.

4. Using the Calculator

Tips: Enter latitude in degrees (-90 to 90) and solar declination in degrees (-23.45 to 23.45). For accurate results, ensure inputs are within valid ranges and use appropriate declination values for specific dates.

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 due to Earth's axial tilt.

Q2: How do I find solar declination for a specific date?
A: Solar declination can be calculated using astronomical formulas or obtained from solar position calculators and almanacs for specific dates.

Q3: Why does daylight length vary throughout the year?
A: Daylight length varies due to Earth's 23.5° axial tilt and its revolution around the sun, causing seasonal changes in solar declination.

Q4: What are extreme cases of daylight length?
A: At polar circles (66.5° latitude), 24-hour daylight occurs at summer solstice; at poles, 6 months of continuous daylight followed by 6 months of darkness.

Q5: Is this formula accurate for all locations?
A: The formula provides theoretical daylight length; actual sunrise/sunset times may vary due to atmospheric refraction, elevation, and local topography.