Rise/Set Hour Angle Formula
Geometricrissethourangleatanarccosrelationfromindependentactualdec/latitude/crossingaltitude,retainsnever/alwaysflags,nodateephemeris. Actual independent model/unit/frame/epoch/calibration and applicable measurement established;not precise ephemeris,forecast,geodesy operation,identity or safety approval.
Description
Rise and set geometry can be formulated as crossings of a caller-selected altitude.
Rise and set geometry can be formulated as crossings of a caller-selected altitude.1
This tool returns the corresponding hour-angle magnitude and whether that boundary is crossed, with no calendar ephemeris or civil-time conversion.
When to use Rise/Set Hour Angle Formula
Use this tool to apply the stated rise/set hour angle formula operation with an explicit input and unit basis.
How to use Rise/Set Hour Angle Formula and how it works
- Establish the measurement basis and units described above.
- Enter actualLatitudeDegrees, actualDeclinationDegrees, callerIndependentCrossingAltitudeDegrees and run the tool.
- Read result.hourAngleDegrees, result.condition using the output meanings below.
- If input is rejected, correct the stated type, range, ordering or alignment issue and rerun; review successful results under the declared convention.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualLatitudeDegrees | Latitude Degrees. Units, ordering and applicable branch are specified in the algorithm. | number | required; finite; further conditions in the algorithm |
| actualDeclinationDegrees | Declination Degrees. Units, ordering and applicable branch are specified in the algorithm. | number | required; finite; further conditions in the algorithm |
| callerIndependentCrossingAltitudeDegrees | Crossing Altitude Degrees. Units, ordering and applicable branch are specified in the algorithm. | number | required; finite; further conditions in the algorithm |
Require latitude and declination strictly within ±90 degrees and crossing altitude within ±90 inclusive. Compute x from the altitude equation; x>1 returns 0 and never-reaches-altitude, x<−1 returns 180 and always-above-altitude, otherwise return acos(x) in degrees and crossing, including tangency.
x=(sin h−sinφ sinδ)/(cosφ cosδ); H=acos(x) on the crossing branch Apply the declared units, ordering and branch conditions.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the declared output fields. | object |
| result.hourAngleDegrees | Nonnegative hour-angle magnitude in degrees, with condition describing noncrossing sentinels. | number |
| result.condition | Branch label describing geometric crossing or noncrossing, as explained in the algorithm. | string |
{
"input": {
"actualLatitudeDegrees": 0,
"actualDeclinationDegrees": 0,
"callerIndependentCrossingAltitudeDegrees": 0
},
"output": {
"result": {
"hourAngleDegrees": 90,
"condition": "crossing"
}
}
}Limitations and assumptions
The output applies the declared operation to the values you supply. Establish the measurement basis, units, coefficients and any caller-selected rules before interpreting it. The tool does not independently collect or verify observations or decide whether a model or reference applies.
Supply explicit required fields with the documented types and dense aligned arrays. Unknown fields, wrong types and nonfinite numbers are rejected. Branch-specific constraints are explained above. A returned boolean, signed difference or tied result follows the stated convention; an input error instead means the required input contract was not satisfied. Very large inputs or outputs may be rejected by shared resource limits.
Alternative or Complementary methods
For a related operation, use Daylight Duration Latitude Calculator. Geometric daylight uses the solar center crossing an ideal zero-altitude horizon.
For a related operation, use Civil Twilight End Hour Angle. Civil twilight conventionally uses the solar center six degrees below a geometric horizon.
References
-
Rise/Set Hour Angle Formula — tool.io
Similar or alternative tools
- Daylight Duration Latitude Calculator
Geometric daylight uses the solar center crossing an ideal zero-altitude horizon.
- Civil Twilight End Hour Angle
Civil twilight conventionally uses the solar center six degrees below a geometric horizon.