What is a sphere of influence?

The sphere of influence (Hill sphere) is the roughly spherical region around a body where its own gravity is the dominant force controlling the motion of nearby objects, rather than the gravity of a more massive parent body. Objects within this sphere can form stable orbits around the smaller body.

What is the formula used?

This calculator uses the Hill sphere formula: r = a × (m / 3M)^(1/3), where r is the Hill sphere radius, a is the semi-major axis of the orbiting body around the parent, m is the mass of the orbiting body, and M is the mass of the parent body.

What units should I use?

You can enter masses in kilograms (kg) or solar masses, and distances in meters, kilometers, or astronomical units (AU). The calculator accepts any consistent unit combination and converts results automatically.

Does the Hill sphere represent a hard boundary?

No. The Hill sphere is an approximation. Objects near its edge may be unstable due to tidal perturbations. In practice, stable long-term orbits typically stay within about one-third to one-half of the Hill sphere radius.

What is Earth's Hill sphere radius?

Earth's Hill sphere radius is approximately 1.5 million km (about 0.01 AU). The Moon orbits at ~384,000 km — well within this boundary, which is why it remains in stable orbit around Earth.

Sphere of Influence Calculator

Name: Sphere of Influence Calculator
Availability: InStock
Author: Nham Vu

Enter the masses of two bodies and their orbital distance to calculate the Hill sphere (gravitational sphere of influence) radius.

Input Parameters

Parent Body Mass (M)

Mass of the central / dominant body (e.g. the Sun)

Orbiting Body Mass (m)

Mass of the smaller body whose sphere is being calculated

Semi-major Axis (a)

Average distance between the two bodies (orbital semi-major axis)

Quick Presets

Enter the parameters and click Calculate

or choose a preset above

Summary

Enter the masses of two bodies and their orbital distance to calculate the Hill sphere (gravitational sphere of influence) radius.

How it works

Enter the mass of the parent body (e.g. the Sun) in kilograms.
Enter the mass of the orbiting body (e.g. a planet) in kilograms.
Enter the semi-major axis (average orbital distance) in meters or astronomical units.
Click Calculate to compute the Hill sphere radius.
The result is shown in meters, kilometers, and astronomical units for easy comparison.

Use cases

Determine whether a moon can remain in stable orbit around a planet.
Check the maximum distance at which an asteroid can hold a captured companion.
Compare the Hill spheres of Solar System planets.
Estimate stable satellite orbit limits for exoplanet systems.
Educational exercises in orbital mechanics and celestial dynamics.
Mission design for interplanetary probes near gravitational boundaries.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu