Hill Sphere Calculator

About this calculator

The Hill sphere (or Roche sphere) is the region around a celestial body — a planet orbiting a star, or a moon orbiting a planet — within which its own gravity dominates over the pull of the larger body it orbits, so that it can hold onto satellites. It's approximated by r ≈ a·(m / 3M)^(1/3), where a is the orbital distance between the smaller body (mass m) and the larger one (mass M).

Astronomers use the Hill sphere to determine whether a planet's candidate moon can remain gravitationally bound, to set the outer stability limit for exoplanet moons ("exomoons") in habitability studies, and to explain why moons far from a planet (like an outer irregular satellite) are more easily stripped away by the Sun's gravity. Earth's Hill sphere, for comparison, extends to about 1.5 million km — well beyond the Moon's orbit, which is why the Moon remains stably bound to Earth rather than the Sun.