Description
Calculate linear eccentricity in meters from a semimajor axis and dimensionless first eccentricity.
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 linear eccentricity in meters from a semimajor axis and dimensionless first eccentricity.
When to use this tool
Use this tool when you need to calculate linear eccentricity in meters from a semimajor axis and dimensionless first eccentricity.
How to use the tool and how it works
- Enter semiMajorMeters, eccentricity using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.linearEccentricityMeters, using the stated boundary, ordering, sign and absence conventions.
Multiply semiMajorMeters by dimensionless eccentricity to obtain linear eccentricity in meters.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. |
| eccentricity | Dimensionless first eccentricity e from zero up to but excluding one, not e² or f. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.linearEccentricityMeters | a times first eccentricity, in meters. |
{
"input": {
"semiMajorMeters": 10,
"eccentricity": 0.1
},
"output": {
"result": {
"linearEccentricityMeters": 1
}
}
}Limitations and assumptions
- Semi-major axis lies from one through 10⁸ m and eccentricity in [0,1). Eccentricity is not flattening or squared eccentricity.
- 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
- Second Eccentricity Squared Calculator
Calculate second eccentricity squared from explicit oblate or spherical semiaxes.
- Ellipsoid Flattening from Axes Calculator f=(a-b)/a
Calculate ordinary geometric flattening from explicit oblate or spherical semiaxes.