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A Laplace radius (rL) is a limit on the radius of an object's (moon's) orbit around a planet, above which the host star has a greater likelihood of making the orbit unstable. It takes more factors into account than does the simpler Hill radius.
rL5 = J2R2a3(1-e2)3/2M/MStar
Where:
Above this a calculated radius, orbit instability is best analyzed using the plane of the planet's orbit around the star so as to deal with perturbations caused by the star. Below this radius, orbital instability is better analyzed using the planet's equatorial plane so as to deal with perturbations caused by the planet's oblateness.
The Laplace plane (or Laplace surface) for an orbit of a particular size is the orbital plane on which the perturbations due to the star and those due to the planet's oblateness are balanced, resulting in a more stable orbit. A small orbit has a Laplace plane that is close the planet's equatorial plane (e.g., the moons orbiting close to Jupiter) and a large orbit has one close to the planet's orbital plane (e.g., the Moon). At the Laplace radius, it is between the two.