### hydrostatic equilibrium

**(hydrostatic balance)**
(state of a fluid body when forces are such that the fluid is at rest)

**Hydrostatic equilibrium** (**hydrostatic balance**) in
a body of fluid (e.g., gas) is the state
such that forces cancel and the fluid remains still.
A calm lake is at hydrostatic equilibrium. In astrophysics, a gas
ball (e.g., star) or a planetary atmosphere is at hydrostatic
equilibrium if at each level, gravity (toward the center)
matches the upward pressure, i.e., for a spherical symmetric
star:

dP M_{r}ρ
—— = -G ———
dr r²

- r - radial spherical coordinate, 0 at center of the star.
- P - pressure (dependent on r).
- ρ - density (dependent on r).
- M
_{r} - mass within the spherical volume of radius r.
- G - gravitational constant.

Other forces (inertia, if the body
is spinning, magnetic force, a nearby object's gravity)
can be additional factors.
A protoplanetary disk can take a
flared torus shape in hydrostatic equilibrium due to the star's
heating and radiation pressure.

An example of something not at hydrostatic equilibrium could
be a gas cloud in the midst of collapse or expansion.

For many purposes, such as modeling stars,
the state of a volume of material can be sufficiently close to
hydrostatic equilibrium that it can be assumed for simplicity's sake.
In other words, movement is trivially slow compared to the
aspects under consideration.

A **differentiated object** is an astronomical object that
has settled so that inner material is not uniform. A sufficiently
massive object in hydrostatic equilibrium often forms layers
(concentric shells) based upon density of the material.
By some definitions, the distinction between planet and
planetesimal is that the former is a *differentiated object*
and the latter is not. A solid (rocky) planet may
be described as in *hydrostatic equilibrium* if it approximately
matches the concept, presumably falling into such a state during a
previous time when the planet was more liquid-like and/or through
a long-term rearrangement of the solids over geologic time.

(*physics,statics,fluid mechanics,hydrostatics*)
**Further reading:**

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

**Referenced by pages:**

baryon acoustic oscillations (BAO)

Eddington luminosity

gravitational collapse

gravity anomaly

Hayashi limit

hydrodynamic equations

isostasy

J_{2}

Lane-Emden equation

partial ionization zone

planet

pulsating star

stellar structure

Tolman-Oppenheimer-Volkoff limit (TOV)

turbulent pressure

Vogt-Russell theorem (VR theorem)

Index