### 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 particular body orbiting it
can approach before breaking up due to tidal forces.
A moon orbiting a planet within their 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 (including the masses
of both objects), 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.

The term **Roche sphere** is generally used as a synonym for
**Hill sphere**, which applies to the influence of the host's
gravity as if tidal forces were not a factor: the Roche/Hill sphere's
radius is *not* this Roche radius, but is termed the **Hill radius**.

The term **Roche lobe** is more related to the Hill radius than the
Roche limit, (the Roche lobe is not defined by tidal force): it
indicates the actual elongated (non-spherical) regions of orbiting
body's gravitational influence that meet at their L1 Lagrangian point.

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

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

**Referenced by pages:**

atmospheric escape

contact binary

hydrodynamic escape

Roche lobe

Index