Description
Calculate signed meridian arc between two geodetic latitudes by 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 signed meridian arc between two geodetic latitudes by numerical quadrature.
When to use this tool
Use this tool when you need to calculate signed meridian arc between two geodetic latitudes by numerical quadrature.
How to use the tool and how it works
- Enter semiMajorMeters, flattening, startLatitudeDegrees, endLatitudeDegrees using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.signedDistanceMeters, using the stated boundary, ordering, sign and absence conventions.
Integrate meridian curvature from the equator to each endpoint using 1,024-panel composite Simpson quadrature, then subtract the start arc from the end arc.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. |
| flattening | Dimensionless ordinary flattening f=(a-b)/a, from zero through 0.02; supply f rather than inverse flattening. | Finite numeric value satisfying the stated comparisons. |
| startLatitudeDegrees | Geodetic start latitude in degrees, north positive, within ±90°. | Finite numeric value satisfying the stated comparisons. |
| endLatitudeDegrees | Geodetic end latitude in degrees, north positive, within ±90°. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.signedDistanceMeters | End-minus-start meridian arc in meters, positive northward. |
{
"input": {
"semiMajorMeters": 10,
"flattening": 0,
"startLatitudeDegrees": 0,
"endLatitudeDegrees": 30
},
"output": {
"result": {
"signedDistanceMeters": 5.235987755982988
}
}
}Limitations and assumptions
- The distance is signed northward and assumes one ellipsoid and meridian. This is numerical integration, not a longitude-varying geodesic or orthometric height difference.
- 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
- Meridian Arc Length Inverse Problem Solver
Invert a signed equator-relative meridian arc with bounded bisection and explicit residual evidence.
- Rectifying Latitude Meridian Arc Fraction Converter
Convert geodetic latitude to rectifying latitude using numerically integrated meridian distance.