Calculatorism

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

  1. Enter semi-major axis a, satellite mass m, primary mass M.
  2. 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.

Found a problem with the results?

If this calculator's result is wrong, or you have any question about the calculation logic, please let us know. You are viewing:Hill Sphere Calculator/physics/hill-sphere)。