Declination Altitude Visibility
Compute geometric daily altitude extrema and visibility relative to a supplied horizon boundary, including both circumpolar and never-rising cases; refraction is excluded.
Description
An object's declination and observing latitude determine its daily geometric altitude extrema.
An object's declination and observing latitude determine its daily geometric altitude extrema. Comparing both with a supplied boundary distinguishes always above, never above and touching/crossing cases.1
Compute geometric daily altitude extrema and visibility relative to a supplied horizon boundary, including both circumpolar and never-rising cases; refraction is excluded.
When to use Declination Altitude Visibility
Use this tool to compute geometric daily altitude extrema and visibility relative to a supplied horizon boundary, including both circumpolar and never-rising cases; refraction is excluded.
Prepare the source, detector or coordinate measurements. Confirm frame, epoch, angular units, axis directions and the stated RA proper-motion convention before entering values.
How to use Declination Altitude Visibility and understand its results
- Prepare the source, detector or coordinate measurements. Confirm frame, epoch, angular units, axis directions and the stated RA proper-motion convention before entering values.
- Enter latitudeDegrees, declinationDegrees, altitudeBoundaryDegrees using the field table and calculation rules, then run the tool.
- Read minimumAltitudeDegrees, maximumAltitudeDegrees, visibility. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| latitudeDegrees | Latitude degrees | number | Required |
| declinationDegrees | Declination degrees | number | Required |
| altitudeBoundaryDegrees | Altitude boundary degrees | number | Required |
Enter latitude, declination and altitude boundary each within ±90 degrees. The tool converts both extrema through a clipped asin. It returns always-above only when the minimum is strictly greater, never-above only when the maximum is strictly less, and crosses-or-touches otherwise, including equality and a constant altitude on the boundary.
sinAltitude extrema=sinφ sinδ ± cosφ cosδ Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| minimumAltitudeDegrees | Minimum altitude degrees | number |
| maximumAltitudeDegrees | Maximum altitude degrees | number |
| visibility | Visibility | string |
{
"input": {
"latitudeDegrees": 60,
"declinationDegrees": 40,
"altitudeBoundaryDegrees": 0
},
"output": {
"minimumAltitudeDegrees": 9.99999999999999,
"maximumAltitudeDegrees": 70,
"visibility": "always-above"
}
}Limitations and assumptions
Refraction, terrain, daylight, weather and instrument limits are omitted. This does not calculate rise/set times or assess an observation's practical feasibility.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Equatorial Horizontal Coordinates: Transform geometric hour angle and declination to altitude and azimuth north-through-east; no refraction or time-to-hour-angle conversion is inferred. For a complementary task, use Kasten Young Optical Airmass: Evaluate Kasten–Young relative optical air mass for apparent altitude above the horizon; this is an atmospheric model approximation.
References
-
Declination Altitude Visibility — tool.io
Similar or alternative tools
- Equatorial Horizontal Coordinates
Transform geometric hour angle and declination to altitude and azimuth north-through-east; no refraction or time-to-hour-angle conversion is inferred.
- Kasten Young Optical Airmass
Evaluate Kasten–Young relative optical air mass for apparent altitude above the horizon; this is an atmospheric model approximation.