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.

Yes, roughly 53 million km in radius, allowing it to hold many moons.

Estimate the Hill sphere radius within which a body's gravity dominates: r_H = a * (m / (3M))^(1/3).

Orbital Distance (a)

Orbiting Body Mass

Primary Body Mass

Hill Sphere Radius

1,496,396,438 m

Hill Radius (km)1,496,396 km

Hill Sphere Radius vs Orbital Distance (a)

The Hill sphere approximates the region around a body where its gravity dominates over tidal forces from a larger primary.

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).

Find Earth's Hill sphere radius with respect to the Sun.