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How to Calculate Day Length

Day Length Formula:

\[ Day\ Length = 2 \times \frac{\arccos(-\tan(\phi) \tan(\delta))}{15} \]

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1. What is Day Length Calculation?

Day length calculation determines the duration of daylight hours at a specific location on Earth for a given day of the year. It's based on the latitude of the location and the solar declination angle.

2. How Does the Calculator Work?

The calculator uses the day length formula:

\[ Day\ Length = 2 \times \frac{\arccos(-\tan(\phi) \tan(\delta))}{15} \]

Where:

Explanation: The formula calculates the hour angle from sunrise to sunset and converts it to hours of daylight.

3. Importance of Day Length Calculation

Details: Day length calculations are essential for agriculture, astronomy, solar energy planning, and understanding seasonal variations in daylight hours.

4. Using the Calculator

Tips: Enter latitude between -90° and 90° (negative for southern hemisphere), and solar declination between -90° and 90°. Both values must be valid 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. It varies throughout the year between approximately ±23.5°.

Q2: How does latitude affect day length?
A: Day length variation increases with latitude. Near the equator, day length remains relatively constant throughout the year, while polar regions experience extreme variations.

Q3: What are typical day length values?
A: At the equator, day length is approximately 12 hours year-round. At higher latitudes, it can range from 0 hours (polar night) to 24 hours (midnight sun).

Q4: When is the formula not accurate?
A: The formula provides theoretical values and doesn't account for atmospheric refraction, twilight, or terrain features that might obstruct sunlight.

Q5: How accurate is this calculation?
A: The calculation provides a good theoretical approximation of day length, but actual observed day length may vary due to atmospheric conditions and local topography.

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