Fluid Roche Limit

Estimate a fluid Roche limit from caller densities and structural coefficient; rigid and strength-supported bodies require different models.

Description

A fluid Roche estimate expresses the tidal-disruption distance using primary radius and a density ratio.

A fluid Roche estimate expresses the tidal-disruption distance using primary radius and a density ratio. A caller-supplied structural coefficient makes the assumed fluid model explicit.^[1]

Estimate a fluid Roche limit from caller densities and structural coefficient; rigid and strength-supported bodies require different models.

When to use Fluid Roche Limit

Use this tool to estimate a fluid Roche limit from caller densities and structural coefficient; rigid and strength-supported bodies require different models.

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 Fluid Roche Limit 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 primaryRadius, primaryDensity, satelliteDensity, fluidCoefficient using the field table and calculation rules, then run the tool.
Read rocheDistance. 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
primaryRadius	Primary radius	number	Required
primaryDensity	Primary density	number	Required
satelliteDensity	Satellite density	number	Required
fluidCoefficient	Fluid coefficient	number	Required

Enter positive primary radius, positive densities in matching units and a positive fluid coefficient. The tool evaluates the cube-root scaling and returns distance in the radius's unit. Equal densities leave the coefficient-times-radius value.

rocheDistance = coefficient × primaryRadius × (primaryDensity/satelliteDensity)^(1/3)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
rocheDistance	Roche distance	number

json

{
  "input": {
    "primaryRadius": 10,
    "primaryDensity": 8,
    "satelliteDensity": 1,
    "fluidCoefficient": 2.44
  },
  "output": {
    "rocheDistance": 48.8
  }
}

Limitations and assumptions

Rigid or strength-supported bodies need different assumptions. Rotation, shape, eccentricity and a detailed disruption outcome are not calculated; no coefficient is chosen automatically.

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 Stellar Tidal Disruption Radius: Estimate the Newtonian stellar tidal radius using a point central mass; relativistic capture and stellar structure are not modeled.

References

Fluid Roche Limit — 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.
Stellar Tidal Disruption Radius
Estimate the Newtonian stellar tidal radius using a point central mass; relativistic capture and stellar structure are not modeled.