Astrophysics (index)

Laplace Radius

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

A Laplace Radius (rL) is a limit on a radius of an orbit around a planet, below which the orbit is not made unstable by the star. Above this radius, the Kozai Mechanism is a factor.

rL5 = J2R2a3(1-e2)3/2M/MStar

Where:

  • J2 - J2 of the planet.
  • R - radius of the planet.
  • a - Semi-Major Axis (a) of the planet's orbit around the star.
  • e - Eccentricity (e) of the planet's orbit around the star.
  • M - mass of the planet.
  • MStar - the mass of the star.

(dynamics,secular,orbits,radius,limit)
http://arxiv.org/pdf/1212.0028.pdf

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