Rigid body Roche limit calculator

Enter the primary radius, the primary mean density, and the satellite mean density in consistent units. The calculation applies the conventional rigid-satellite coefficient of about 1.26, returns the distance in the same unit as the radius, and rejects zero or negative densities instead of producing a physically meaningless result.

Enter radius and densities in consistent units

Start with the mean radius of the primary body and choose any convenient length unit, such as kilometres, metres, or miles. The returned Roche limit will use that same unit, so no fixed length conversion is hidden in the calculation. Next, enter the primary and satellite mean densities using the same density unit for both values. Kilograms per cubic metre and grams per cubic centimetre are both acceptable choices, but they must not be mixed because the formula uses their ratio. Each density must be strictly greater than zero. A zero or negative density has no physical meaning here and is rejected as invalid input. The primary radius must also be positive and finite. Use representative mean densities rather than a surface value or a density measured for one small region. If an object is strongly layered, porous, or irregular, remember that this compact estimate describes an idealized body. Keeping a note of your chosen units and source values makes the result easier to reproduce and compare with published orbital distances. This input discipline is especially important when copying figures from tables that use different unit systems.

Understand the rigid-satellite formula

The calculator evaluates d = 1.26 × R × (primary density / satellite density)^(1/3). Here, R is the primary radius and d is the centre-to-centre Roche-limit distance. The density quotient is dimensionless because both densities use the same unit. Taking its cube root makes the result respond moderately rather than linearly to density changes: multiplying the density ratio by eight doubles its cube-root contribution. The coefficient 1.26 is the standard approximate factor for the idealized rigid-body case. The response also reports the density ratio and the distance measured in primary radii, which is useful for checking the arithmetic or comparing systems of very different sizes. A denser primary raises the limit, while a denser satellite lowers it because the satellite resists tidal disruption more strongly. The calculation is deterministic and does not use object-name presets, external catalogues, random values, or live astronomical data. Values are rounded to stable significant precision in the JSON response so repeated calls with the same input produce the same practical representation across the API and browser calculator.

Interpret the estimate and its boundaries

Treat the computed distance as a classical approximation, not as a prediction of the exact moment when every real moon, ring particle, spacecraft, or rubble pile will break apart. The rigid model assumes the satellite retains structural integrity and uses a simplified balance between tidal effects and self-gravity. It does not model tensile strength explicitly, rotation, orbital eccentricity, resonances, thermal stress, internal layering, an atmosphere, or deformation over time. A fluid satellite uses a different and substantially larger conventional coefficient, so do not substitute this result when the object behaves like a strengthless fluid. The Roche limit is reported from the centre of the primary, not as altitude above its surface. To obtain an approximate surface altitude for comparison, subtract the primary radius yourself while preserving the same length unit. If the reported distance lies inside the primary body, the simplified disruption boundary has no directly accessible external orbit in that scenario. For research, mission safety, or unusual material structures, use this value as a screening calculation and follow it with a model that represents the relevant mechanics and uncertainties. For education and quick comparisons, it provides a clear, reproducible rigid-body baseline.