Description
Convert geocentric latitude and radius using Bowring initialization followed by bounded refinement.
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.
Convert geocentric latitude and radius using Bowring initialization followed by bounded refinement.
When to use this tool
Use this tool when you need to convert geocentric latitude and radius using Bowring initialization followed by bounded refinement.
How to use the tool and how it works
- Enter semiMajorMeters, flattening, geocentricLatitudeDegrees, geocentricRadiusMeters using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.latitudeDegrees, result.longitudeDegrees, result.ellipsoidalHeightMeters, result.iterations, result.residualMeters, result.converged, using the stated boundary, ordering, sign and absence conventions.
Construct [r cos(theta),0,r sin(theta)] from geocentric latitude and radius, use a Bowring initial latitude, then refine by up to 32 iterations and report the ECEF reconstruction residual.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. |
| geocentricLatitudeDegrees | Radius-vector latitude in degrees, within ±90°, rather than geodetic normal latitude. | Finite numeric value satisfying the stated comparisons. |
| geocentricRadiusMeters | Distance from ellipsoid center in meters, from a/2 through 10⁹. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.latitudeDegrees | Resulting geodetic latitude in degrees, or null on direct-geodesic nonconvergence. |
| result.longitudeDegrees | Resulting east-positive longitude in [−180,180) degrees, or null on direct-geodesic nonconvergence. |
| result.ellipsoidalHeightMeters | Signed ellipsoidal height in meters on the supplied model. |
| result.iterations | Number of bounded numerical iterations performed. |
| result.residualMeters | Final reconstruction or arc residual in meters under the stated algorithm; arc residual is signed, vector residual a magnitude. |
| result.converged | Whether the operation’s stated iteration or reconstruction criterion succeeded; inspect null values and residual/reason evidence. |
{
"input": {
"semiMajorMeters": 10,
"flattening": 0,
"geocentricLatitudeDegrees": 0,
"geocentricRadiusMeters": 10
},
"output": {
"result": {
"latitudeDegrees": 0,
"longitudeDegrees": 0,
"ellipsoidalHeightMeters": 0,
"iterations": 1,
"residualMeters": 0,
"converged": true
}
}
}Limitations and assumptions
- Radius is between a/2 and 10⁹ m. Longitude is fixed to the zero meridian because no longitude input is provided. The actual implementation refines Bowring’s estimate rather than returning only a closed-form approximation.
- 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
- Geodetic from ECEF XYZ Iterative Converter
Convert ECEF coordinates to geodetic latitude, longitude and ellipsoidal height with bounded iteration and a reconstruction residual.
- Geodetic to Geocentric Latitude Converter
Convert geodetic latitude to surface geocentric latitude on an explicit ellipsoid.