Hill Sphere Radius Calculator

Hill Sphere Radius Calculator computes the radius of the region around a celestial body where its gravity dominates, allowing stable satellite orbits. Enter the semi-major axis, mass of the secondary body, and mass of the primary body to calculate the Hill sphere radius using the equation r_H ≈ a (m / (3M))^1/3.

Enter Orbital Data

Semi-Major Axis (a, m)

Secondary Mass (m, kg)

Primary Mass (M, kg)

How to Use Hill Sphere Radius Calculator:

Enter the semi-major axis (a), mass of the secondary body (m), and mass of the primary body (M) using the keypad or direct input; use “Next” to switch fields.
Select appropriate units for distance (m, AU, km) and masses (kg, Earth masses, solar masses).
Click “Calculate” to see step-by-step results for the Hill sphere radius.
Use “Share Result” to get shareable text or “Copy Result” to copy to clipboard.

Formula:

Hill Sphere Radius:

            rH ≈ a (m / (3M))1/3
        

Where: a = semi-major axis (m), m = secondary mass (kg), M = primary mass (kg), r_H = Hill sphere radius (m)

Important Notes:

Inputs for semi-major axis and masses must be positive numbers.
The formula assumes the secondary’s mass is much smaller than the primary’s (m ≪ M) and a circular orbit (eccentricity ≈ 0).
Results are rounded to four decimal places in the selected unit for the semi-major axis.
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