### Laplace radius

**(r**_{L})
(a radius for a stable orbit of a satellite around a planet)

A **Laplace radius** (r_{L})
is a limit on a radius of an orbit around a planet,
above which the star can make the orbit unstable due to
the Kozai mechanism.

r_{L}^{5} = J_{2}R^{2}a^{3}(1-e^{2})^{3/2}M/M_{Star}

Where:

- J
_{2} - J_{2} of the planet.
- R - radius of the planet.
- a - semi-major axis of the planet's orbit around the star.
- e - eccentricity of the planet's orbit around the star.
- M - mass of the planet.
- M
_{Star} - the mass of the star.

(*dynamics,secular,orbits,radius,limit*)
**Further reading:**

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

Index