Description
Return radius times one minus signed sine latitude for cap height inside result.
Spherical geography models Earth with one radius and angular coordinates. Surface arcs, polar heights, circle radii, and area fractions are different derived quantities; an ideal spherical result does not include ellipsoid or terrain effects.
Return radius times one minus signed sine latitude for cap height inside result.
When to use this tool
Use Geography: Spherical Cap Latitude Height when you need a stated spherical geographic term or angular conversion.
How to use the tool and how it works
- Enter latitudeDegrees, sphereRadius, pole. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Require latitude in degrees within [-90, 90], positive radius, and north or south pole. Return radius times one minus signed sine latitude for cap height inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| latitudeDegrees | Latitude Degrees Unit: deg. | Required. Finite number. |
| sphereRadius | Sphere Radius | Required. Finite number. |
| pole | Pole | Required. Text; one of "north", "south". Implementation limit: 8192 Unicode code points and 16384 UTF-16 code units. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the calculated members; expand to inspect the fields below. | Required. Object. |
| result.capHeight | Cap Height | Calculated result member: number. |
{
"input": {
"latitudeDegrees": 0,
"sphereRadius": 2,
"pole": "north"
},
"output": {
"result": {
"capHeight": 2
}
}
}Limitations and assumptions
- Height is measured along the sphere's polar axis from the selected pole to the latitude plane, not a surface arc or an ellipsoidal altitude.
- Outputs are nested inside result. Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use ellipsoidal geodesy or a suitable terrain model when spherical assumptions are inadequate. Keep angular units, physical length units, latitude definition, and reference radius explicit.
References
Similar or alternative tools
- Spherical Cap Latitude Area Fraction
Return the north-cap whole-sphere area fraction (1-sin latitude)/2 and its south-cap complement.
- Latitude Height Radius Approximation
Return their sum and height divided by surfaceRadius as relativeChange.