Holding On to Moons

The Hill sphere

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Hill radius $r_H \approx a\,(m/3M)^{1/3}$: where the planet beats the Sun’s tidal pull.
• It grows with distance from the Sun and the cube root of the planet’s mass.
• Stable moons orbit well inside it (the Moon is at about a quarter).

Steps

1. A tug of war with the Sun
2. Jupiter’s Hill sphere
3. A heavier Earth
4. Moonless Mercury
5. Where the Moon sits
6. Moving out