ONE FORMULA, ONE ANSWER
Hill Sphere Radius Calculator
Estimate the Hill radius of a low-mass body on a circular orbit around a primary. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
Approximate Hill radius r_H
Enter values and select Calculate.
r_H = a (m/(3M))^(1/3)
Assumptions
Required: positive inputs, a circular restricted three-body setting, m/M≤0.01 and r_s(M)/a≤0.01. The orbit must be external and nonintersecting; a test satellite has negligible mass. The Hill region is not an exact sphere, and being within this radius does not guarantee long-term orbital stability. Excluded: eccentricity, additional perturbations and satellite mass.
Displayed values are floating-point approximations. Design safety factors and unprovided error contributions are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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