Orbital Mechanics
Hill Sphere
Region around a planet where its gravity dominates over its star — defines moon stability
The Hill sphere is the region around a planet where its gravitational influence dominates over its host star. Within Hill sphere, planet can hold moons stably; beyond, moons would be stripped by stellar tides. Earth's Hill sphere: ~1.5 million km radius (Moon at 384,000 km is well within). Sun's Hill sphere: ~125,000 AU (~2 light-years) — extends to nearby star limits. Concept by George Hill (1878). Important: defines stable orbital regions, satellite stability, planet formation.
- Earth's Hill radius~1.5 million km
- Sun's Hill radius~125,000 AU (~2 ly)
- Formular_H ≈ a × (m / 3M)^(1/3) (m: planet, M: star, a: semi-major axis)
- Moon's stabilityWell within Earth's Hill sphere
- DiscoveredGeorge Hill, 1878
- ApplicationStability of moons; planet formation
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Why Hill sphere matters
- Moon stability. Sets bounds for stable orbits.
- Planet formation. Region where planets can grow.
- Moon capture. Within Hill sphere required.
- Solar system boundary. Sun's Hill ~125,000 AU.
- Exomoon habitability. Limits possible exomoon orbits.
- Trojan asteroids. Stable accumulation regions.
- Galactic tides. Forces beyond Hill sphere.
Common misconceptions
- Hill sphere is hard boundary. Approximate; gradual transition.
- All planets have same Hill sphere. Mass and distance dependent.
- Hill sphere is small. 1.5 million km for Earth (vs Moon at 384,000 km).
- Beyond Hill sphere unstable. Generally; specific orbits may be possible.
- Hill sphere = atmosphere. Different concepts.
- Hill sphere fixed. Changes with planet's orbit (eccentricity).
Frequently asked questions
What's the Hill sphere?
Volume around an orbiting body where its gravity is dominant over the central body. For planet around star: distance r_H = a × (m_p / 3M_s)^(1/3), where a is semi-major axis, m_p is planet mass, M_s is star mass. Inside r_H, planet's gravity wins; outside, star's tidal force dominates.
How big is Earth's Hill sphere?
1.5 million km. Moon orbits at 384,000 km — well inside (about 25% of Hill radius). Stable indefinitely. Hypothetical satellite at 1.5 million km would be unstable. Apollo and other lunar missions stayed within.
What about other planets?
Larger planets and farther from Sun → bigger Hill sphere. Jupiter: 53 million km. Saturn: 65 million km. Neptune: 116 million km. Mass and distance both important. Hill sphere shapes planet formation in disks.
Why is it called "Hill sphere"?
Discovered by American astronomer George William Hill (1878). Working on three-body problem. Found region where third body (small) is gravitationally bound to second body (intermediate). Named after him posthumously.
How is this used in solar system?
(1) Defines region where moons are stable. (2) Constrains satellite captures (Jupiter, Saturn captured many irregular moons within Hill sphere). (3) Relevant for Trojan asteroids in Lagrange points (within shared Hill region). (4) Sets stability boundary for hypothetical moons.
What about the Sun's Hill sphere?
Boundary where Sun's gravity dominates over galactic gravitational field. ~125,000 AU (~2 light-years). Oort Cloud's outer edge approximately matches this. Comets at edge are weakly bound. Beyond: galactic tides may strip them.
How does it apply to exoplanets?
Stability of exomoons. Habitable exomoons must orbit within planet's Hill sphere. Hot Jupiters: small Hill spheres (close to star). Cold Jupiters: large Hill spheres. Earth-mass HZ exoplanets: Hill spheres similar to Earth's. Important for hypothetical exomoon habitability.