Description
Check spherical Cassini–Soldner scale along a meridian and identify the central-meridian case.
Geodesy distinguishes a mathematical reference ellipsoid, a realized coordinate datum and the physical gravity field. Geodetic latitude follows the ellipsoid normal; geocentric latitude follows a radius from the center. Ellipsoidal height, orthometric height and geoid undulation are separate signed quantities. Keep the declared ellipsoid, coordinate axes, angular units and time scale with a result.
Check spherical Cassini–Soldner scale along a meridian and identify the central-meridian case.
When to use this tool
Use this tool when you need to check spherical Cassini–Soldner scale along a meridian and identify the central-meridian case.
How to use the tool and how it works
- Enter latitudeDegrees, longitudeDifferenceDegrees using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.meridianScale, result.onCentralMeridian, result.model, using the stated boundary, ordering, sign and absence conventions.
Calculate the differential scale along a meridian for spherical Cassini–Soldner using latitude and longitude difference from the central meridian. Return scale, an exact-zero central-meridian flag and the spherical model label.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| latitudeDegrees | Geodetic latitude in degrees, north positive; the operation’s pole restrictions apply. | Finite numeric value satisfying the stated comparisons. |
| longitudeDifferenceDegrees | Signed east-positive longitude minus central-meridian longitude in degrees; the operation-specific local range applies. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.meridianScale | Dimensionless spherical Cassini–Soldner scale along a meridian. |
| result.onCentralMeridian | Whether longitudeDifferenceDegrees is exactly zero. |
| result.model | Name of the stated historical/spherical model, retained as context. |
{
"input": {
"latitudeDegrees": 0,
"longitudeDifferenceDegrees": 0
},
"output": {
"result": {
"meridianScale": 1,
"onCentralMeridian": true,
"model": "spherical Cassini-Soldner differential"
}
}
}Limitations and assumptions
- Latitude lies within ±85° and longitude difference within ±30°. The central meridian has scale one; this checker is spherical, gives meridian-direction scale only, and is not a full ellipsoidal Cassini–Soldner implementation.
- All quantities are finite and retain the units stated for this operation. Ellipsoid-parameter tools use semi-major axis 1–10⁸ m and dimensionless flattening 0–0.02; explicit-axis tools use 0.9a≤b≤a unless a tighter bound is stated. These tools do not fetch datums, geoid grids, satellite observations or Earth-orientation updates.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Numeric results must be finite. Large physical magnitudes are allowed by the output evidence checks, while integer fields and source schemas retain their exactness rules. Source indexes are zero-based. Floating-point residues can remain even where an ideal formula gives an exact zero.
Alternative or Complementary methods
Use a coordinate transform for a change of representation and explicit datum parameters for a change of reference frame. Preserve model and convergence metadata, and use observation and datum information appropriate to a real survey before interpreting a computed tolerance as accuracy.
References
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