Hill Sphere Stability Radius for Moons Calculator
Pericenter approximate Hill radius times independently chosen moon-orbit fraction; restricted three-body approximation, not guaranteed long-term stability.
Description
Hill Sphere Stability Radius for Moons Calculator: return conditional moon limit au.
The Hill scale estimates where a smaller body's gravity competes with the primary's. A moon-stability allowance is a fraction of that geometric scale.
This tool returns conditional moon limit au. Use the stated units and model convention when interpreting these fields.
When to use this tool
Use this tool when the supplied inputs match the specific operation described above and you need a repeatable result under its stated convention.
- Check the supported input and output contract against an existing calculation or observation.
- Use the complete example to confirm units, selector spelling and result interpretation.
How to use the tool and how it works
- Enter every field in the input table using the stated units and the exact supported selector spelling where applicable.
- Run the tool. Correct input errors before interpreting an output.
- Read the result fields below; use accompanying flags and the stated sign, boundary or model convention when interpreting a number.
Calculate semimajor axis times (1-e), times the cube root of planet mass divided by three primary masses, times callerStableFraction.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| semimajorAxisAu | Semimajor axis au. Astronomical units. | Finite number; greater than zero |
| eccentricity | Eccentricity. | Finite number |
| planetMassKg | Planet mass kg. Kilograms. | Finite number; greater than zero |
| primaryMassKg | Primary mass kg. Kilograms. | Finite number; greater than zero |
| callerStableFraction | Caller stable fraction. Fractional units; 0.2 means 20%. | Finite number; from zero to one inclusive |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.conditionalMoonLimitAu | Conditional moon limit au; use the stated units and sign convention. |
{
"input": {
"semimajorAxisAu": 1,
"eccentricity": 0,
"planetMassKg": 3,
"primaryMassKg": 1000,
"callerStableFraction": 0.5
},
"output": {
"result": {
"conditionalMoonLimitAu": 0.05
}
}
}Limitations and assumptions
- The planet must be lighter than the primary. The selected fraction is not a simulated stability boundary.
- Every declared field is required and unexpected fields are rejected. Numeric inputs must be finite; input errors are distinct from a valid false result or an explicitly qualified output.
- Extremely large inputs and nonfinite or excessively large outputs are rejected. List positions reported by the tool use zero-based indices unless stated otherwise.
Alternative or Complementary methods
Check the underlying observations, units and conventions independently before using the result in a larger workflow. The tools listed below address nearby tasks; compare their inputs and scope before substituting one for this operation.
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