Hill Sphere Calculator
Compute the Hill radius r_H ≈ a(m/(3M))^{1/3}.
Input Data
Input Semi-major axis a.
m
Input Satellite mass m.
kg
Input Primary mass M.
kg
Results
61,514,073.58m
r_H ≈ a (m/(3M))^{1/3} = 6.1514e+7 m
At a glance:Hill Sphere Calculator: enter parameters to compute results; complements related calculators.
Formula
r_H ≈ a (m / (3 M))^{1/3}
a: satellite's orbit semi-major axis about primary
How to Use
- Enter semi-major axis a, satellite mass m, primary mass M.
- Get Hill radius r_H.
Case Studies
Moon around Earth
a=3.844×10⁸, m=7.34×10²², M=5.97×10²⁴ → r_H≈6.1×10⁷ m.
FAQ
Is the real Moon inside?
The Moon's orbit radius ≈ a, far below r_H, so Earth stably holds the Moon.
Related Tools
References
Content review: Calculatorism Science Team. Formula and numeric tests verified; results for reference only.