Description
Estimate degree-two tidal gravity from supplied body geometry and Love numbers, retaining the gravity/correction sign distinction.
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.
Estimate degree-two tidal gravity from supplied body geometry and Love numbers, retaining the gravity/correction sign distinction.
When to use this tool
Use this tool when you need to estimate degree-two tidal gravity from supplied body geometry and Love numbers, retaining the gravity/correction sign distinction.
How to use the tool and how it works
- Enter bodyGm, bodyDistanceMeters, bodyZenithDegrees, earthRadiusMeters, loveH2, loveK2 using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.gravimetricFactor, result.tidalDownGravityChangeMicrogal, result.correctionToObservedMicrogal, using the stated boundary, ordering, sign and absence conventions.
For each supplied body, accumulate outward degree-two acceleration GM×R/r³×(3cos²(zenith)−1). Multiply by 1+h2−1.5k2, negate for down-positive gravity change, and convert m/s² to microgal by 10⁸. Return the opposite sign as the correction to observed gravity.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| bodyGm | One to eight positive body gravitational parameters GM in m³/s², each at most 2×10²⁰. | Dense list of at most 128 finite numbers, under the stated integer/range rules. |
| bodyDistanceMeters | Body-center distances in meters, aligned to bodyGm, each from 10 Earth radii through 10¹³. | Dense list of at most 128 finite numbers, under the stated integer/range rules. |
| bodyZenithDegrees | Body zenith angles in degrees, zero through 180, aligned to bodyGm. | Dense list of at most 128 finite numbers, under the stated integer/range rules. |
| earthRadiusMeters | Explicit spherical reference radius in meters, 10⁶–10⁷. | Finite numeric value satisfying the stated comparisons. |
| loveH2 | Dimensionless degree-two displacement Love number h2, zero through one. | Finite numeric value satisfying the stated comparisons. |
| loveK2 | Dimensionless degree-two potential Love number k2, zero through 0.5. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.gravimetricFactor | Dimensionless 1+h2−1.5k2 applied to the supplied degree-two body contributions. |
| result.tidalDownGravityChangeMicrogal | Modeled down-positive gravity change in microgal. |
| result.correctionToObservedMicrogal | Opposite-signed correction to remove the modeled gravity change, in microgal. |
{
"input": {
"bodyGm": [
100000000000000
],
"bodyDistanceMeters": [
100000000
],
"bodyZenithDegrees": [
0
],
"earthRadiusMeters": 1000000,
"loveH2": 0.6,
"loveK2": 0.3
},
"output": {
"result": {
"gravimetricFactor": 1.1500000000000001,
"tidalDownGravityChangeMicrogal": -23000.000000000004,
"correctionToObservedMicrogal": 23000.000000000004
}
}
}Limitations and assumptions
- One to eight bodies use GM in m³/s², distance at least 10 Earth radii and at most 10¹³ m, and zenith in [0,180] degrees. Love numbers h2∈[0,1], k2∈[0,0.5] must yield a positive factor. No ephemerides, ocean loading or full tidal spectrum are included.
- 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
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