Description
Rescale a spherical arc distance for a new radius at fixed central angle.
Spherical geometry distinguishes central angle, surface arc and straight chord. They coincide only in a small-angle limit, and a sphere-radius sensitivity differs from a geodesic calculation on an ellipsoid.
Rescale a spherical arc distance for a new radius at fixed central angle.
When to use this tool
Use Geodesic Radius Relative Distance Scale when checking a stated spherical arc, chord or radius relationship.
How to use the tool and how it works
- Enter distance, oldRadius, newRadius. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read distance, ratio. Use the output convention below.
Rescale a spherical arc distance for a new radius at fixed central angle. Require nonnegative distance and positive oldRadius/newRadius; ratio = newRadius/oldRadius and output distance multiplies that ratio.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| distance | Distance | Required. Finite number; minimum 0. |
| oldRadius | Old Radius | Required. Finite number; strictly above 0. |
| newRadius | New Radius | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| distance | Distance | Required. Finite number. |
| ratio | Ratio | Required. Finite number. |
{
"input": {
"distance": 20,
"oldRadius": 5,
"newRadius": 6
},
"output": {
"distance": 24,
"ratio": 1.2
}
}Limitations and assumptions
- This assumes the angular separation stays fixed and is not ellipsoidal geodesy.
- 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 endpoint coordinates and an appropriate spherical or ellipsoidal geodesic model for real geographic distance.
References
Similar or alternative tools
- Geodesic Chord Small Angle Error Term
Return the leading cubic arc-minus-chord error term.
- Fixed Radius Angular Gap Halfwidth
Return a fixed-radius arc-length envelope.