Calculateur de Sphère de Hill
Calculez le rayon de la sphère de Hill d'un corps céleste.
Hill Sphere Radius
1,496,396,438 m
Hill Sphere Radius vs Orbital Distance (a)
Formule
## The Hill Sphere The Hill sphere approximates the region around a body where its gravity dominates over tidal forces from a larger primary. ### Formula **r_H = a (m / 3M)^(1/3)** Moons must orbit well within the Hill sphere for long-term stability (typically within about one-third of r_H).
Exemple Résolu
Find Earth's Hill sphere radius with respect to the Sun.
- 01r_H = a (m / 3M)^(1/3)
- 02m / (3M) = 5.972e24 / (3 × 1.989e30) = 1.001e-6
- 03(1.001e-6)^(1/3) = 0.01000
- 04r_H = 1.496e11 × 0.01000 ≈ 1.5 million km
Questions Fréquentes
Can a moon orbit at the edge of the Hill sphere?
In practice no. Prograde moons are stable only within about r_H/2, and retrograde moons within about r_H.
How does the Hill sphere relate to the Roche limit?
The Hill sphere is where an orbiter can exist; the Roche limit is how close it can approach before tidal forces tear it apart.
Does Jupiter have a large Hill sphere?
Yes, roughly 53 million km in radius, allowing it to hold many moons.