Hill Sphere Calculator

Hill Sphere

Calculate the Hill sphere radius of a body orbiting a more massive primary, defining the region where the body can gravitationally retain satellites.

Semi-Major Axis (km)

Orbiting Body Mass (kg)

Primary Body Mass (kg)

Orbital Eccentricity

Formula

Hill Radius = a x (1 - e) x (m / 3M)^(1/3); where a = semi-major axis, e = eccentricity, m = body mass, M = primary mass

Frequently Asked Questions

What is the Hill sphere?

The Hill sphere is the region around a body where its gravity dominates over the gravitational influence of the larger body it orbits. Moons must orbit within the Hill sphere of their planet to remain captured.

How large is the Hill sphere of Earth?

The Hill sphere of Earth extends about 1.5 million km from Earth, roughly four times the Earth-Moon distance. The Moon orbits well within this boundary.

Can objects orbit at the edge of the Hill sphere?

In practice, stable orbits require being well inside the Hill sphere. Orbits beyond roughly one-third to one-half of the Hill sphere radius tend to be unstable due to perturbations from the primary body.

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