Hill Sphere
The Region of Gravitational Dominance
The planet's Hill sphere (green) is where its gravity dominates over the star's. Inside, the moon orbits stably. The moon's own (much smaller) Hill sphere defines the region it dominates. Particles inside are captured; outside, they drift back to the star.
r_H ≈ a · (m / 3M)^(1/3)
Where a is the body's semi-major axis around its parent, m is the body's mass, and M is the parent's mass.
The Hill radius is approximately the distance to the L1 and L2 Lagrange points of the body-parent system. Anything orbiting within that radius is gravitationally bound to the body; outside it, the parent dominates.
Earth's Moon orbits at ~26% of Earth's Hill radius — comfortably stable.
The Hill sphere explains a lot of what you see in the system map. Close-in planets have tiny Hill radii — they can't hold large moons against the star's tides.
Outer gas giants have enormous Hill spheres → huge moon collections (Jupiter has 95+, Saturn 100+). ED reflects this — gas giants in cold orbits often host the densest moon systems.
Tightly-bound stellar binaries share Hill spheres with each other. A planet around one star in a close binary lives in a small effective Hill region — explaining why S-type planets in tight binaries are rare.
| Body | Distance from Sun | Hill Radius | Largest Moon Inside | Note |
|---|---|---|---|---|
| Mercury | 0.39 AU | 0.0012 AU (175,000 km) | Tiny / none stable | Sun's tides destabilise even close moons |
| Venus | 0.72 AU | 0.0067 AU (1.0 M km) | None observed | Captured moons would be unstable on long timescales |
| Earth | 1.0 AU | 0.010 AU (1.5 M km) | Moon at 384,400 km | Moon orbits at ~26% of Hill radius |
| Mars | 1.52 AU | 0.0066 AU (985,000 km) | Phobos & Deimos (very close) | Both moons well inside Hill radius |
| Jupiter | 5.2 AU | 0.355 AU (53 M km) | Callisto at 1.88 M km | Hosts 95+ moons, mostly captured asteroids |
| Saturn | 9.5 AU | 0.435 AU (65 M km) | Iapetus at 3.56 M km | Wide Hill sphere → hundreds of small moons |
| Neptune | 30 AU | 0.77 AU (115 M km) | Triton (retrograde capture) | Far from Sun → enormous Hill sphere |