Description
Calculate the meridian-quadrant-preserving rectifying radius by bounded numerical quadrature.
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.
Calculate the meridian-quadrant-preserving rectifying radius by bounded numerical quadrature.
When to use this tool
Use this tool when you need to calculate the meridian-quadrant-preserving rectifying radius by bounded numerical quadrature.
How to use the tool and how it works
- Enter semiMajorMeters, semiMinorMeters using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.rectifyingRadiusMeters, using the stated boundary, ordering, sign and absence conventions.
Numerically integrate meridian curvature from equator to pole using composite Simpson quadrature with 1,024 panels. Return rectifyingRadius=2×quarterMeridian/π.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| semiMajorMeters | Equatorial semiaxis a in meters, 1–10⁸. It is a radius, not a diameter. | Finite numeric value satisfying the stated comparisons. |
| semiMinorMeters | Polar semiaxis b in meters, with 0.9a≤b≤a under the explicit-axis model. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.rectifyingRadiusMeters | Meridian-quadrant-preserving sphere radius in meters. |
{
"input": {
"semiMajorMeters": 10,
"semiMinorMeters": 10
},
"output": {
"result": {
"rectifyingRadiusMeters": 9.999999999999998
}
}
}Limitations and assumptions
- Axes use meters and require flattening at most 0.02. This radius preserves meridian-quadrant length; it is not the equal-area authalic radius or an exact analytic integration certificate.
- 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
Similar or alternative tools
- Authalic Radius R2 from Axes Calculator
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- Meridian Arc Length Degree Interval Calculator
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