How to use the hill sphere radius calculator
Estimate the region where a planet's gravity dominates. Enter orbital distance, planet mass, star mass in the fields above; the hill radius is computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “moon stability”, “hill sphere of earth”, “satellite capture”, “calculate hill sphere radius”, “find hill radius”.
Formula
Variables
- a — Orbital distance (AU)
- m — Planet mass (Earth masses)
- M — Star mass (solar masses)
Worked example
With orbital distance = 1 AU, planet mass = 1 Earth masses, star mass = 1 solar masses, the calculator gives hill radius ≈ 1.496546 million km.
Frequently asked questions
What is the hill sphere radius calculator used for?
Estimate the region where a planet's gravity dominates. It helps with questions such as “moon stability”, “hill sphere of earth”, “satellite capture”.
What is the formula for the hill sphere radius calculation?
Hill radius (million km) = a × AU × cbrt(m × MEARTH / (3 × M × MSUN)) / 1e9. Here a is orbital distance (AU), m is planet mass (Earth masses), M is star mass (solar masses).
What inputs do I need for the hill sphere radius calculator?
You need orbital distance in AU, planet mass in Earth masses, star mass in solar masses. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the hill sphere radius calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the hill sphere radius result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.