Find Hill sphere size for planets, moons, and satellites. Check orbital reach, compare stability zones, and export useful physics results fast.
| System | Orbiting Mass | Central Mass | Semi-Major Axis | Eccentricity | Axis Unit |
|---|---|---|---|---|---|
| Earth around Sun | 5.972e24 | 1.989e30 | 1 | 0.0167 | AU |
| Moon around Earth | 7.342e22 | 5.972e24 | 384400 | 0.0549 | km |
| Jupiter around Sun | 1.898e27 | 1.989e30 | 5.2044 | 0.0489 | AU |
| Mars around Sun | 6.417e23 | 1.989e30 | 1.5237 | 0.0934 | AU |
These sample entries help you test the calculator with well-known orbital systems.
The classical Hill sphere radius estimates the region where a smaller orbiting body dominates the gravity felt by nearby objects. It is commonly used for planets, moons, and spacecraft studies.
Formula: rH = a(1 - e) × (m / 3M)1/3
Where:
The calculator also reports approximate stable satellite zones. A practical prograde limit is often near 0.49 of the Hill radius. A wider retrograde stability limit can extend near 0.93 of the Hill radius.
The Hill sphere marks the area around an orbiting body where its gravity can hold satellites against the stronger pull of a central object. In celestial mechanics, this boundary helps estimate whether moons, rings, dust, or artificial satellites can remain gravitationally bound. It does not guarantee perfect long-term stability, but it gives a strong first estimate.
Three factors dominate the result. The first is orbital distance. A body farther from the central mass usually gets a larger Hill sphere. The second is the mass ratio. A more massive orbiting body controls a larger surrounding region. The third is eccentricity. Higher orbital eccentricity reduces the effective Hill radius because the tightest gravitational competition often appears near periapsis.
Astronomers use Hill sphere calculations when studying exoplanets, moon formation, ring systems, Trojan companions, and capture scenarios. Mission planners also use it when evaluating temporary orbital zones and spacecraft operations near smaller bodies. The value is especially useful during early design work because it gives fast physical insight from a compact formula.
The Hill sphere is an approximation. Real systems include perturbations, resonances, radiation pressure, non-spherical bodies, and long-term dynamical effects. That is why this calculator also shows conservative prograde and wider retrograde stability estimates. Use the output for screening, education, and comparison, then follow with detailed numerical simulations for mission-critical problems.
A Hill sphere is the region around an orbiting body where its gravity dominates over the central body's tidal pull for nearby satellites.
Higher eccentricity brings the body closer to the central mass at periapsis. That stronger tidal influence reduces the effective gravitational control region.
Not always. Long-term stable orbits usually occupy only a fraction of the full Hill radius, especially for prograde motion.
Retrograde satellites can remain stable farther out than prograde satellites. Reporting both gives a more practical planning range.
Use the unit that best matches your data. The calculator accepts both and converts AU to kilometers internally.
Yes. It is widely used for first-pass exoplanet analysis, though detailed stability studies still need numerical integrations.
No. The Hill sphere concerns external gravitational dominance, while the Roche limit concerns tidal disruption of a nearby body.
Yes, for early estimates and comparisons. Final trajectory and stability studies should use higher-fidelity dynamical models.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.