Hill Sphere Calculator

A hot Jupiter at 0.04 AU has a Hill sphere of only ~450,000 km. The stable prograde zone ends at ~225,000 km — smaller than the Moon's 384,400 km orbit around Earth. Any moon that existed was swept away during the planet's inward migration, and no new one could survive there. This is why no confirmed exomoon has ever been found around a hot Jupiter. The same geometry explains where space telescopes park: the Lagrange points L1 and L2 sit at almost exactly one Hill sphere radius from Earth (~1.5 million km). JWST orbits L2, which places it just inside Earth's gravitational boundary — far enough to escape atmospheric and thermal interference, close enough that Earth's gravity keeps it bound against solar perturbations. The Hill sphere is not just a theoretical limit; it is the address of our most powerful observatory.

A moon is caught in a tug-of-war: its planet pulls it close while the far more massive Sun tries to pry it loose. The Hill sphere marks where the planet wins — inside it orbits can be stable, while outside a satellite drifts off onto its own path around the Sun. The radius grows only with the cube root of the mass ratio, so it changes slowly. As a rule of thumb, a moon on a normal prograde orbit stays safe only out to about half the Hill radius, which is why real moons huddle well inside the boundary.

Counterintuitively, a moon circling its planet the wrong way — retrograde, opposite the planet's motion — stays stable out to roughly 0.7 of the Hill radius, while a prograde moon breaks free past about 0.5. The reversed motion softens the Sun's repeated tug over each orbit. This is no curiosity: nearly all of Jupiter's and Saturn's distant outer moons orbit retrograde, precisely because those are the only wide orbits that last.