Laplace Sphere Of Influence
Compute the Laplace sphere-of-influence scale a(m/M)^(2/5), not a Hill-stability radius.
Description
The Laplace sphere of influence is an approximate scale for changing a patched-conic reference body.
The Laplace sphere of influence is an approximate scale for changing a patched-conic reference body. It differs from the Hill radius and is not a sharp surface where only one body exerts gravity.1
Compute the Laplace sphere-of-influence scale a(m/M)^(2/5), not a Hill-stability radius.
When to use Laplace Sphere Of Influence
Use this tool to compute the Laplace sphere-of-influence scale a(m/M)^(2/5), not a Hill-stability radius.
Prepare the orbital state or model parameters in one reference frame. Confirm compatible distance/time units and the stated angular and gravitational-parameter conventions.
How to use Laplace Sphere Of Influence and understand its results
- Prepare the orbital state or model parameters in one reference frame. Confirm compatible distance/time units and the stated angular and gravitational-parameter conventions.
- Enter orbitalSemimajorAxis, secondaryMass, primaryMass using the field table and calculation rules, then run the tool.
- Read influenceRadius. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| orbitalSemimajorAxis | Orbital semimajor axis | number | Required |
| secondaryMass | Secondary mass | number | Required |
| primaryMass | Primary mass | number | Required |
Enter a positive orbital semimajor axis and positive common-unit masses, with secondary below primary. The tool applies the two-fifths mass-ratio power and returns a radius in the semimajor axis's unit.
influenceRadius = semimajorAxis × (secondaryMass/primaryMass)^0.4 Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| influenceRadius | Influence radius | number |
{
"input": {
"orbitalSemimajorAxis": 10,
"secondaryMass": 1,
"primaryMass": 100000
},
"output": {
"influenceRadius": 0.09999999999999998
}
}Limitations and assumptions
This is a small-secondary approximation without an ephemeris or force comparison. It does not select a hysteresis policy or establish Hill stability.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Mutual Hill Separation: Compute mutual-Hill separation and screen a supplied boundary; the conventional 2√3 criterion assumes small, circular, coplanar two-planet orbits. For a complementary task, use Soi Handoff Hysteresis: Apply caller-defined sphere-of-influence handoff hysteresis to a sampled trajectory; boundaries are not universal force-dominance limits.
References
-
Laplace Sphere Of Influence — tool.io
Similar or alternative tools
- Mutual Hill Separation
Compute mutual-Hill separation and screen a supplied boundary; the conventional 2√3 criterion assumes small, circular, coplanar two-planet orbits.
- Soi Handoff Hysteresis
Apply caller-defined sphere-of-influence handoff hysteresis to a sampled trajectory; boundaries are not universal force-dominance limits.