Solar Declination Hour Angle Calculator
Sinusoidal day-of-year solar declination with geometric altitude hour angle; unattainable flagged, no ephemeris/refraction/rise-time guarantee.
Description
Solar Declination Hour Angle Calculator: return approximate declination degrees, altitude attainable, hour angle degrees.
Solar declination and hour angle describe geometric relationships between the Sun, observer latitude and altitude. A day-of-year approximation simplifies the solar model.
This tool returns approximate declination degrees, altitude attainable, hour angle degrees. Use the stated units and model convention when interpreting these fields.
When to use this tool
Use this tool when the supplied inputs match the specific operation described above and you need a repeatable result under its stated convention.
- Check the supported input and output contract against an existing calculation or observation.
- Use the complete example to confirm units, selector spelling and result interpretation.
How to use the tool and how it works
- Enter every field in the input table using the stated units and the exact supported selector spelling where applicable.
- Run the tool. Correct input errors before interpreting an output.
- Read the result fields below; use accompanying flags and the stated sign, boundary or model convention when interpreting a number.
Approximate declination with 23.44 sin[2π(day-81)/365]. Use the spherical altitude equation to derive a cosine argument, flag whether it lies in [-1,1], and take arccos only when attainable.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| dayOfYear | Day of year. | Integer; from 1 to 366 inclusive |
| latitudeDegrees | Latitude degrees. Degrees. | Finite number; from -89.9 to 89.9 inclusive |
| solarAltitudeDegrees | Solar altitude degrees. Degrees. | Finite number; from -90 to 90 inclusive |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.approximateDeclinationDegrees | Approximate declination degrees; use the stated units and sign convention. |
| result.altitudeAttainable | Whether the modeled cosine argument lies between -1 and +1. |
| result.hourAngleDegrees | Modeled angular magnitude in degrees; zero is a placeholder when altitudeAttainable is false. |
{
"input": {
"dayOfYear": 81,
"latitudeDegrees": 0,
"solarAltitudeDegrees": 0
},
"output": {
"result": {
"approximateDeclinationDegrees": 0,
"altitudeAttainable": true,
"hourAngleDegrees": 90
}
}
}Limitations and assumptions
- Read altitudeAttainable before hourAngleDegrees; zero is a placeholder when unattainable. Refraction, longitude and civil-clock time are not included.
- Every declared field is required and unexpected fields are rejected. Numeric inputs must be finite; input errors are distinct from a valid false result or an explicitly qualified output.
- Extremely large inputs and nonfinite or excessively large outputs are rejected. List positions reported by the tool use zero-based indices unless stated otherwise.
Alternative or Complementary methods
Check the underlying observations, units and conventions independently before using the result in a larger workflow. The tools listed below address nearby tasks; compare their inputs and scope before substituting one for this operation.
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