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Daylight Hours Formula:
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The Daylight Hours calculation estimates the duration of daylight based on latitude and solar declination. This astronomical formula calculates the time between sunrise and sunset for any given location and date.
The calculator uses the daylight hours formula:
Where:
Explanation: The formula calculates the hour angle at which the sun rises/sets and converts it to time duration, accounting for the spherical geometry of Earth's relationship with the sun.
Details: Accurate daylight calculation is crucial for agriculture, solar energy planning, architectural design, tourism, and understanding seasonal variations in different geographical locations.
Tips: Enter latitude and declination in radians. Remember to convert from degrees to radians if necessary (degrees × π/180). Ensure inputs are within valid mathematical ranges for trigonometric functions.
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. It varies throughout the year due to Earth's axial tilt.
Q2: How do I convert degrees to radians?
A: Multiply degrees by π/180 (approximately 0.0174533). For example, 45° = 45 × π/180 = 0.7854 radians.
Q3: What are typical declination values?
A: Declination ranges from approximately -23.45° to +23.45° (-0.409 to +0.409 radians), reaching extremes at solstices.
Q4: Why does the calculation sometimes fail?
A: The calculation fails when the argument to arccos is outside [-1,1], which occurs at polar regions during periods of midnight sun or polar night.
Q5: Can this be used for any date?
A: Yes, by using the appropriate solar declination for the specific date. Declination can be calculated using various astronomical formulas.