Hill sphere calculator.

What the Hill sphere is

The Hill sphere is the region around a planet where its own gravity, rather than its star's, dominates the motion of a small satellite. A common approximation is r ≈ a(1 − e) · ∛(m / 3(M + m)), where a is the semi-major axis, e the eccentricity, m the smaller mass and M the larger (Wikipedia, Hill sphere). The (1 − e) factor shrinks the sphere to its closest-approach size; the tool shows both that and the plain average-distance value.

Worked example, Earth. With the Sun's mass 1,988,400 × 10²⁴ kg, Earth's 5.9722 × 10²⁴ kg, a = 149.598 million km and e = 0.0167 (NASA fact sheets), the closest-approach radius is 1.4716 million km. Wikipedia's table lists 1.4714 million km and says the sphere extends to about 1.5 million km (0.01 AU).

Worked example, the Moon. Using Earth's and the Moon's masses with a = 384,400 km and e = 0.0549, the Moon's own Hill radius at closest approach is 57,910 km. Wikipedia lists 57,910 km at perigee.

The formula is an approximation. It assumes the smaller body is much lighter than the larger one and does not capture how long an orbit near the edge remains stable.