Roche Limit Calculator

The Roche limit is the minimum orbital distance at which a self-gravitating body (held together by its own gravity) can orbit a more massive primary without being torn apart by tidal forces. Inside this distance, the primary's tidal acceleration across the satellite exceeds the satellite's self-gravity, and the satellite is disrupted. It was derived by the French astronomer Edouard Roche in 1849. Material inside the Roche limit cannot coalesce into a moon and instead forms rings, as in the case of Saturn's ring system.

The fluid body Roche limit is d = 2.44 x R_M x (rho_M / rho_m)^(1/3), where R_M is the primary's radius, rho_M is the primary's mean density, and rho_m is the satellite's mean density. The rigid body Roche limit is d = 1.26 x R_M x (rho_M / rho_m)^(1/3). The ratio 2.44/1.26 = 1.937 means the fluid limit is about 94% larger than the rigid limit.

The fluid Roche limit (coefficient 2.44) applies to a satellite held together only by self-gravity with no material tensile strength, such as a loosely-bound rubble pile, a comet nucleus, or a liquid body. The rigid body Roche limit (coefficient 1.26) applies to a solid object with significant internal strength (rocks, ice). Real bodies fall somewhere between these limits depending on their composition and internal cohesion.

Yes. Saturn's main rings (A, B, and C rings) lie between about 1.1 and 2.4 Saturn radii from Saturn's center. The fluid Roche limit for ice (density 917 kg/m³) around Saturn (density 687 kg/m³) is about 2.22 R_Saturn (129,000 km). The outer A ring extends to about 2.35 R_Saturn, right at the Roche limit. This is why Saturn's ring particles have never accreted into moons: they are inside the disruption zone.

Yes. Phobos orbits at 9,376 km from Mars's center. The fluid Roche limit for Phobos (density approximately 1876 kg/m³) around Mars (density 3934 kg/m³) is approximately 10,586 km. Phobos is inside this fluid limit but outside the rigid body limit (approximately 5,466 km), meaning it is held together by its material strength but is slowly being torn apart by tidal forces. Phobos will either disintegrate into a ring or collide with Mars in roughly 50 million years.

The Roche limit scales as (rho_M / rho_m)^(1/3). If the primary is denser than the satellite, the Roche limit is larger (the satellite is easier to disrupt). If the satellite is denser than the primary (rho_m greater than rho_M), the Roche limit shrinks below the primary's radius, meaning the body can orbit safely at any external distance. For Earth and the Moon: rho_Earth = 5515 kg/m³ greater than rho_Moon = 3346 kg/m³, so the ratio is 1.65 and the cube root is 1.18.

Yes. Comet Shoemaker-Levy 9 broke apart in 1992 when it passed within Jupiter's Roche limit at about 1.3 Jupiter radii. Its density was roughly 500 to 600 kg/m³ and Jupiter's is 1326 kg/m³. The fluid Roche limit for that density ratio is about 2.88 R_J, so the comet was well within the disruption zone. It broke into 21 fragments that collided with Jupiter in July 1994, providing spectacular impact observations.

For the Earth-Moon system, using rho_Earth = 5515 kg/m³, R_Earth = 6371 km, and rho_Moon = 3346 kg/m³: the fluid Roche limit is 2.44 x 6371 x (5515/3346)^(1/3) = 18,365 km. The rigid body limit is 1.26 x 6371 x 1.181 = 9,483 km. The Moon currently orbits at 384,400 km, far outside both limits. However, if a future process brought the Moon inside 18,365 km, tidal forces would begin to overwhelm its self-gravity.

Yes. Hot Jupiters (gas giants orbiting very close to their host stars) can approach their stellar Roche limits. For a Jupiter-density planet around a Sun-density star, the Roche limit is about 2.44 x R_Sun x (1410/1326)^(1/3) = 2.52 R_Sun = 1.75 million km = 0.012 AU. Some ultra-short-period planets orbit at only 2-3 stellar radii and may be slowly losing mass through Roche overflow.

A neutron star has rho approximately 5 x 10^17 kg/m³ and radius about 12 km. The Roche limit for a human body (rho approximately 1000 kg/m³) is d = 2.44 x 12 x (5e17/1000)^(1/3) = 2.44 x 12 x 794 = 23,300 km. This is much larger than the neutron star radius, meaning a human body approaching a neutron star would be tidally disrupted tens of thousands of kilometres above the surface.

The fluid body formula d = 2.44 R_M (rho_M/rho_m)^(1/3) is an approximation assuming the satellite is much less massive than the primary (so the primary's gravity dominates) and the orbit is circular. For non-circular orbits, the effective Roche limit varies around the orbit. The 2.44 coefficient is for an incompressible fluid body in synchronous rotation; other body shapes and rotation states give slightly different values.

At exactly the Roche limit, the primary's tidal force just equals the satellite's surface gravity on the sub-primary hemisphere. Inside the Roche limit, material near the sub-primary point begins to flow toward the primary (for fluid bodies) or experience net tensile stress (for solid bodies). In practice, disruption is gradual: fluid bodies begin losing mass via Roche overflow before complete disruption, while rigid bodies may survive intact until well inside the fluid limit if their material strength is sufficient.