Star Count Limiting Magnitude Band
Independently same-sky-coverage catalog cumulative star count vs limiting magnitude, not universal naked-eye count. Matched piecewise-linear observational calibration with no extrapolation. Model only, not an ephemeris, measured stellar identity or observational guarantee.
Description
Visible-star counts depend on a defined sky sample and limiting-magnitude observations.
Visible-star counts depend on a defined sky sample and limiting-magnitude observations.1
A matched calibration is needed instead of assuming one universal star-count table. Use Star Count Limiting Magnitude Band to interpolate the supplied calibration.
When to use Star Count Limiting Magnitude Band
Use Star Count Limiting Magnitude Band to interpolate the supplied calibration. Choose a matched calibration, establish both axis units and supply strictly increasing sampled coordinates covering the query.
How to use Star Count Limiting Magnitude Band and understand its results
- Choose a matched calibration, establish both axis units and supply strictly increasing sampled coordinates covering the query.
- Enter Observed limiting magnitude star count coordinates, Independently matched limiting magnitude star count responses, Query limiting magnitude star count coordinate using the field table and validation rules below, then run the tool.
- Read Interpolated response, Local observed slope; interpret the units, signs, ordering and unknown-value placeholders described below.
- Correct reported input errors and rerun. Apply successful results according to their specific meanings and check the assumptions before using them in a decision.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| observedLimitingMagnitudeStarCountCoordinates | Observed limiting magnitude star count coordinates | array of number | Required; constraints below |
| independentlyMatchedLimitingMagnitudeStarCountResponses | Independently matched limiting magnitude star count responses | array of number | Required; constraints below |
| queryLimitingMagnitudeStarCountCoordinate | Query limiting magnitude star count coordinate | number | Required; constraints below |
Provide at least two aligned finite coordinates and responses, with strictly increasing coordinates, and query within the closed sampled range. The tool locates the segment, linearly interpolates its response and returns its response-per-coordinate slope. At an interior sample it uses the segment to the right; at the final endpoint it uses the last segment. Units come from the supplied calibration. No extrapolation or built-in time, temperature or performance table is supplied.
slope = (y[i+1]−y[i])/(x[i+1]−x[i]); response = y[i]+slope×(query−x[i]) Use the field order, units and branch conditions described above.
| Output field | Meaning | Value type |
|---|---|---|
| interpolatedResponse | Response interpolated in the caller’s response-axis units. | number |
| localObservedSlope | Response-axis units per coordinate-axis unit on the selected segment. | number |
{
"input": {
"observedLimitingMagnitudeStarCountCoordinates": [
1,
2,
3
],
"independentlyMatchedLimitingMagnitudeStarCountResponses": [
2,
4,
8
],
"queryLimitingMagnitudeStarCountCoordinate": 2.5
},
"output": {
"interpolatedResponse": 6,
"localObservedSlope": 4
}
}Limitations and assumptions
A matched calibration is needed instead of assuming one universal star-count table. Apply the exact scope and assumptions explained above.
All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse arrays fail validation. Domain-specific bounds, alignments and supported tokens are explained above; extremely large inputs or outputs can also be rejected. Input errors differ from successful false results, empty match lists and unknown-evidence placeholders.
Alternative or Complementary methods
Use Limiting Magnitude From Aperture for a related task: Limiting magnitude depends on observing conditions as well as aperture.
Use Bortle Class Sky Magnitude Lookup for a related task: Bortle descriptions and measured sky brightness are related but different quantities.
References
-
Star Count Limiting Magnitude Band — tool.io
Similar or alternative tools
- Limiting Magnitude From Aperture
Limiting magnitude depends on observing conditions as well as aperture.
- Bortle Class Sky Magnitude Lookup
Bortle descriptions and measured sky brightness are related but different quantities.