Description
Return signed meridian distance radius times latitude and derivative equal to radius.
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 signed meridian distance radius times latitude and derivative equal to radius.
When to use this tool
Use Meridian Distance Latitude Sensitivity when you need a stated spherical geographic term or angular conversion.
How to use the tool and how it works
- Enter radius, latitudeRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read distance, latitudeDerivative. Use the output convention below.
Require positive radius and latitudeRadians within ±π/2. Return signed meridian distance radius times latitude and derivative equal to radius.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| radius | Radius in the common length unit, with its geometric role defined above. | Required. Finite number; strictly above 0. |
| latitudeRadians | Latitude Radians Unit: rad. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| distance | Distance in the stated common unit and geometric model. | Required. Finite number. |
| latitudeDerivative | Latitude Derivative | Required. Finite number. |
{
"input": {
"radius": 10,
"latitudeRadians": 0.5
},
"output": {
"distance": 5,
"latitudeDerivative": 10
}
}Limitations and assumptions
- Distance is measured from the equator on a sphere; derivative has length per radian. This is not ellipsoidal meridian distance or geodesic routing.
- 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
- Latitude Parallel Circumference Radius Sensitivity
Return derivative equal to 2π times cosine latitude.
- Pole Distance From Latitude
Return 90 minus latitude for the north pole or 90 plus latitude for the south pole.