Description
Calculate a signed Laplace azimuth correction from latitude and the supplied eta deflection.
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 a signed Laplace azimuth correction from latitude and the supplied eta deflection.
When to use this tool
Use this tool when you need to calculate a signed Laplace azimuth correction from latitude and the supplied eta deflection.
How to use the tool and how it works
- Enter latitudeDegrees, etaArcseconds using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.azimuthCorrectionArcseconds, using the stated boundary, ordering, sign and absence conventions.
Calculate etaArcseconds×tan(latitude), converting latitude to radians. Return a signed azimuth correction in arcseconds under this stated Laplace sign convention.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. |
| etaArcseconds | Signed eta deflection component in arcseconds under the stated Laplace convention, magnitude≤300. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.azimuthCorrectionArcseconds | Signed eta×tan(latitude) correction in arcseconds. |
{
"input": {
"latitudeDegrees": 45,
"etaArcseconds": 1
},
"output": {
"result": {
"azimuthCorrectionArcseconds": 0.9999999999999999
}
}
}Limitations and assumptions
- Abs(eta)≤300 arcseconds and latitude magnitude≤89.9999°. The meridian-plane deflection component and observational sign convention must be supplied correctly; this is not a full astronomical/geodetic reduction.
- 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
- UTM Grid Convergence Angle gamma Calculator
Estimate local ellipsoidal grid convergence with a longitude series through third order.
- Reciprocal Azimuth Difference Blunder Flag Checker
Check local reciprocal azimuth agreement with signed wrapping and a caller-supplied tolerance.