Advanced Roche Limit Calculator

Calculator Input

This layout stays single-column overall, while the input grid uses 3 columns on large screens, 2 on medium screens, and 1 on mobile.

Primary Radius

Primary Radius Unit

Primary Density (kg/m³)

Density Input Mode

Satellite Density (kg/m³)

Primary Mass

Primary Mass Unit

Current Orbit Distance

Orbit Distance Unit

Satellite Mass

Satellite Mass Unit

Satellite Radius

Satellite Radius Unit

Output Unit

Plotly Graph

The graph compares the primary radius, rigid Roche limit, fluid Roche limit, and the current orbital distance in your selected output unit.

Example Data Table

Case	Primary Radius	Primary Density	Satellite Density	Orbit Distance	Typical Use
Earth–Moon style input	6371 km	5514 kg/m³	3340 kg/m³	384400 km	Rocky moon around rocky planet
Ring system check	58232 km	687 kg/m³	900 kg/m³	140000 km	Icy fragments near giant planet
Dense exoplanet case	1.2 Earth radii	6500 kg/m³	3200 kg/m³	3.5 Earth radii	Tidal stability screening

Formula Used

Fluid satellite Rigid satellite Density ratio Orbital period

Fluid Roche limit: d = 2.44 × R_p × (ρ_p / ρ_s)^1/3

Rigid Roche limit: d = 1.26 × R_p × (ρ_p / ρ_s)^1/3

Density ratio: ρ_p / ρ_s

Orbital period at a given radius: T = 2π × √(a³ / GM)

Here, d is the Roche limit distance, R_p is primary radius, ρ_p is primary density, ρ_s is satellite density, a is orbital radius, G is the gravitational constant, and M is primary mass.

How to Use This Calculator

Enter the primary body radius and density.
Enter the primary mass to estimate orbital periods.
Choose whether satellite density is entered directly or derived from mass and radius.
Add the current orbital distance for a stability comparison.
Select the output unit you prefer.
Press Calculate Roche Limit to show the result above the form.
Use the CSV or PDF buttons to export the computed values.
Review the graph and interpretation to judge tidal breakup risk.

Frequently Asked Questions

1) What is the Roche limit?

The Roche limit is the minimum distance at which a satellite can orbit without being torn apart by tidal forces from the primary body.

2) Why are there fluid and rigid Roche limits?

A fluid body deforms more easily, so it breaks apart farther away. A rigid body can resist tidal stress better and survive somewhat closer in.

3) Why do densities matter so much?

The key ratio is primary density divided by satellite density. Denser primaries and less dense satellites increase the Roche limit distance.

4) Can this calculator help explain planetary rings?

Yes. Ring systems often exist near or inside Roche-limit regions where larger weak bodies cannot remain intact and may break into debris.

5) Does being outside the Roche limit guarantee stability?

No. It only reduces tidal breakup risk. Other factors like eccentricity, internal strength, spin, heating, and collisions still matter.

6) Why does the calculator ask for primary mass?

Mass is used to estimate orbital periods at the Roche limits and at the current orbit. The limit distance formulas themselves mainly use radius and density.

7) Should I use direct or derived satellite density?

Use direct density when you already know it. Use derived mode when you know satellite mass and radius but not density.

8) What units work best for astronomy cases?

Kilometers are intuitive for moons and planets. Astronomical units help with large stellar cases. Earth and Jupiter radii are useful for quick comparisons.