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Laplace radius

(rL)
(a radius for a stable orbit of a satellite around a planet)

A Laplace radius (rL) is a limit on the radius of an object's (moon's) orbit around a planet, above which the 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:

It is a calculated radius above which orbit instability is best analyzed using the plane of the planet's orbit around the star, to deal with perturbations by the star, and below which it is better to use the planet's equatorial plane, to deal with perturbations 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.


(dynamics,secular,orbits,radius,limit)
Further reading:
https://en.wikipedia.org/wiki/Laplace_plane
https://ui.adsabs.harvard.edu/abs/2013AJ....145...54T/abstract
https://books.google.com/books?id=CX8XDQAAQBAJ&lpg=PA54&ots=zn4kmiRuv3&dq=%22laplace%20radius%22%20goldreich&pg=PA54#v=onepage&q=%22laplace%20radius%22%20goldreich&f=false
https://ui.adsabs.harvard.edu/abs/2009AJ....137.3706T/abstract
http://commercialspace.pbworks.com/w/file/fetch/88916768/Rosengren,%20Scheeres%202014.pdf

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