Sphere of Influence Calculator
Enter the masses of two bodies and their orbital distance to calculate the Hill sphere (gravitational sphere of influence) radius.
Use the Sphere of Influence Calculator
Input Parameters
Mass of the central / dominant body (e.g. the Sun)
Mass of the smaller body whose sphere is being calculated
Average distance between the two bodies (orbital semi-major axis)
Quick Presets
Enter the parameters and click Calculate
or choose a preset above
Result in Different Units
Practical Stable Orbit Limit
Objects typically remain in long-term stable orbits within ~1/3 of the Hill sphere radius (tidal truncation limit).
Calculation Summary
r = a × (m / 3M)1/3
Summary
This calculator computes the Hill sphere radius using r_H = a × (m / 3M)^(1/3), where a is semi-major axis, m is the smaller body's mass, and M is the parent mass. Although “sphere of influence” is sometimes used informally for the Hill region, this is not the Laplace sphere of influence r_SOI = a × (m/M)^(2/5) used in patched-conic mission analysis.
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.