Description
Calculate first-order Cartesian polar-motion displacement under an explicit rotation convention.
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 first-order Cartesian polar-motion displacement under an explicit rotation convention.
When to use this tool
Use this tool when you need to calculate first-order Cartesian polar-motion displacement under an explicit rotation convention.
How to use the tool and how it works
- Enter ecefMeters, xpArcseconds, ypArcseconds using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.displacementMm, result.convention, using the stated boundary, ordering, sign and absence conventions.
Convert xp and yp arcseconds to radians and apply the declared infinitesimal active rotation omega=(−yp,−xp,0). Return 1,000 times [−xp Z, yp Z, xp X−yp Y] as Cartesian displacement in mm.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| ecefMeters | Three-element [X,Y,Z] geocentric Cartesian meter vector; individual magnitudes≤10⁹ and any radius restrictions stated above apply. | Dense list of at most 128 finite numbers, under the stated integer/range rules. |
| xpArcseconds | Signed polar-motion xp under the declared active-rotation convention, within ±1 arcsecond. | Finite numeric value satisfying the stated comparisons. |
| ypArcseconds | Signed polar-motion yp under the declared active-rotation convention, within ±1 arcsecond. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.displacementMm | Cartesian [dX,dY,dZ] displacement from the declared infinitesimal rotation, in millimeters. |
| result.convention | Explicit rotation convention retained with the output. |
{
"input": {
"ecefMeters": [
1000,
0,
0
],
"xpArcseconds": 1,
"ypArcseconds": 0
},
"output": {
"result": {
"displacementMm": [
0,
0,
4.84813681109536
],
"convention": "infinitesimal active rotation omega=(-yp,-xp,0)"
}
}
}Limitations and assumptions
- Input Cartesian coordinates are a three-element [X,Y,Z] meter vector with each magnitude at most 10⁹; xp and yp each lie within ±1 arcsecond. This explicit linearized convention is not the complete IERS celestial-to-terrestrial rotation chain.
- 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
- Helmert Transform Coordinate Rotation Applier
Apply a static small-angle seven-parameter Helmert transform with an explicit rotation-sign convention.
- ENU Local Tangent Plane Component Converter
Rotate an ECEF displacement into local east, north and up at a supplied origin direction.