### Roche limit

**(Roche radius)**
(nearest a body can orbit another and survive)

The **Roche limit** (or **Roche radius**) is the nearest to an astronomical
body that a body orbiting it can approach before breaking up.
A moon within its planet's Roche limit
is being pulled apart by the planet's gravity more than
its own gravity is holding it together. Thus at this limit,
moons (or in the case of stars, its planets) tend to break
up into rings (like Saturn's) or circumstellar disks.
The exact formula depends upon a few factors, but
a basic formula is:

d = R_{m}(2 M_{M}/M_{m})^{1/3}

- d - the Roche limit: a distance from the primary body.
- M
_{M} - mass of the primary body.
- M
_{m} - mass of the secondary body.
- R
_{m} - radius of the secondary body.

This formula is derived by determining the distance at which the
gravitational force and tidal force balance.
At longer distances, the secondary body's gravity dominates,
holding it together, and at shorter distances, the tidal
force from the larger body overcomes its gravity and pulls it
apart.

**Roche lobe** means roughly the same thing as *Roche limit*,
but likely refers to the region within the limit,
which has a teardrop shape.
**Roche lobe overflow** (**RLOF**) refers to a body exceeds its
Roche lobe and material is pulled off, such as an interacting
binary star.

(*dynamics,limit,orbits,gravity,tidal*)
**Further reading:**

http://en.wikipedia.org/wiki/Roche_limit

**Referenced by pages:**

atmospheric escape

hydrodynamic escape

Index