Description
Calculate spherical satellite elevation and straight-line range from geocentric radii and separation.
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 spherical satellite elevation and straight-line range from geocentric radii and separation.
When to use this tool
Use this tool when you need to calculate spherical satellite elevation and straight-line range from geocentric radii and separation.
How to use the tool and how it works
- Enter stationRadiusMeters, satelliteRadiusMeters, geocentricSeparationDegrees using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.elevationDegrees, result.slantRangeMeters, using the stated boundary, ordering, sign and absence conventions.
Resolve the satellite vector into local up=rSat cos(angle)−rStation and horizontal=rSat sin(angle). Return atan2(up,horizontal) in degrees and hypot(up,horizontal) in meters.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| stationRadiusMeters | Positive geocentric station radius in meters, at most 10⁸. | Finite numeric value satisfying the stated comparisons. |
| satelliteRadiusMeters | Geocentric satellite radius in meters, greater than station radius and at most 10⁹. | Finite numeric value satisfying the stated comparisons. |
| geocentricSeparationDegrees | Station-to-satellite radial angular separation in degrees, zero through 180. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.elevationDegrees | Signed spherical satellite elevation above local horizontal in degrees. |
| result.slantRangeMeters | Station-to-satellite straight-line range in meters. |
{
"input": {
"stationRadiusMeters": 10,
"satelliteRadiusMeters": 20,
"geocentricSeparationDegrees": 0
},
"output": {
"result": {
"elevationDegrees": 90,
"slantRangeMeters": 10
}
}
}Limitations and assumptions
- Positive station radius is at most 10⁸ m, satellite radius must be larger and at most 10⁹ m, and separation is 0–180°. This is spherical geometry without an orbit, ellipsoidal normal, refraction or obstruction model; negative elevation is retained.
- 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
- Horizon Dip Angle from Eye Height Calculator
Calculate geometric spherical horizon dip from eye height and radius, excluding refraction.
- ENU Local Tangent Plane Component Converter
Rotate an ECEF displacement into local east, north and up at a supplied origin direction.