Orbital mechanics · r_H ≈ a (m / 3M)^(1/3)

Hill Sphere Radius

The radius within which a body's gravity dominates over the larger body it orbits — the region where its moons can hold. Earth's Hill sphere reaches about 1.5 million kilometres.

Orbital distance (AU)Body mass (M⊕)Central mass (M☉)

Hill radius0.010003AU

Formula: r_H ≈ a (m / 3M)^(1/3)

Worked example

With the default inputs, hill sphere radius evaluates to 0.010003 AU — Earth → ~0.01 AU (1.5 million km). The validator recomputes this against the known value on every build, so the formula is checked, not asserted.

Highlights

›Earth: ~0.01 AU

The Hill Sphere

Knowledge connections

Associated withThe Hill Sphere

Sources

Facts on this topic will be cited from these primary and reference sources.

NASANational Aeronautics and Space Administration
Mission data, planetary science, space telescopes, and public-domain imagery.
Most NASA-produced imagery is in the public domain; individual items are checked for usage terms before publication.

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Hill Sphere Radius

Worked example

Highlights

The physics behind it

Knowledge connections

Sources

Hill Sphere Radius

Worked example

Highlights

The physics behind it

Knowledge connections

Sources