Description
Return their sum and height divided by surfaceRadius as relativeChange.
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 their sum and height divided by surfaceRadius as relativeChange.
When to use this tool
Use Latitude Height Radius Approximation when you need a stated spherical geographic term or angular conversion.
How to use the tool and how it works
- Enter surfaceRadius, height. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read radius, relativeChange. Use the output convention below.
Require positive surfaceRadius and surfaceRadius plus height greater than zero. Return their sum and height divided by surfaceRadius as relativeChange.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| surfaceRadius | Surface Radius | Required. Finite number; strictly above 0. |
| height | Height in the common length unit and direction stated above. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| radius | Radius in the common length unit, with its geometric role defined above. | Required. Finite number. |
| relativeChange | Relative Change | Required. Finite number. |
{
"input": {
"surfaceRadius": 6000000,
"height": 1000
},
"output": {
"radius": 6001000,
"relativeChange": 0.00016666666666666666
}
}Limitations and assumptions
- Height and radius share a length unit, with negative height allowed while the resulting radius remains positive. This radial approximation does not model latitude-dependent ellipsoid geometry despite the tool name.
- 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
- Geocentric Axis Z Component Sphere
Return z equal to radius times sine latitude.
- Meridian Distance Latitude Sensitivity
Return signed meridian distance radius times latitude and derivative equal to radius.