Equation of Time Minutes Value Day-of-Year Approximation Calculator
Explicit trigonometric EOT approximation B=2pi(day-81)/364, minutes apparent-minus-mean solar time; not precision ephemeris.
Description
Equation of Time Minutes Value Day-of-Year Approximation Calculator: return approximate minutes.
The equation of time describes a difference between apparent solar time and mean solar time. A day-of-year approximation is a simplified seasonal model.
This tool returns approximate minutes. 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.
For integer days 1–366, set B to 2π(day-81)/364 and return 9.87 sin(2B) minus 7.53 cos(B) minus 1.5 sin(B), in minutes.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| dayOfYear | Day of year. | Integer; from 1 to 366 inclusive |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.approximateMinutes | Approximate minutes; use the stated units and sign convention. |
{
"input": {
"dayOfYear": 81
},
"output": {
"result": {
"approximateMinutes": -7.53
}
}
}Limitations and assumptions
- This is the tool's approximation, not a high-precision ephemeris, local-clock correction or longitude conversion.
- 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.
References
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