Hydrostatic equilibrium

hydrostatic balanceequilibriumhydrostaticcollapsedHydrostatic fluidrounded by its own gravityellipsoidalEquilibrium figureequilibrium formequilibrium shapes
In fluid mechanics, a fluid is said to be in hydrostatic equilibrium or hydrostatic balance when it is at rest, or when the flow velocity for each parcel of fluid is constant over time.wikipedia
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Dwarf planet

dwarf planetsList of dwarf planetsplanet
Hydrostatic equilibrium is the current distinguishing criterion between dwarf planets and small Solar System bodies, and has other roles in astrophysics and planetary geology.
That is, it is in direct orbit of its star and is massive enough to be plastic – for its gravity to maintain it in a hydrostatically equilibrious shape (usually a spheroid) – but has not cleared the neighborhood around its orbit of other material.

Fluid mechanics

fluid dynamicistfluidfluid physics
In fluid mechanics, a fluid is said to be in hydrostatic equilibrium or hydrostatic balance when it is at rest, or when the flow velocity for each parcel of fluid is constant over time.
It embraces the study of the conditions under which fluids are at rest in stable equilibrium; and is contrasted with fluid dynamics, the study of fluids in motion.

Solar System

outer Solar Systeminner Solar Systemouter planets
There are a dozen or so confirmed such objects (apart from the Sun), sometimes called planemos, in the Solar System, with others possible.
The temperature, reaction rate, pressure, and density increased until hydrostatic equilibrium was achieved: the thermal pressure equalled the force of gravity.

Hydrostatics

hydrostatic pressurehydrostaticfluid statics
The hydrostatic equilibrium pertains to hydrostatics and the principles of equilibrium of fluids.
It encompasses the study of the conditions under which fluids are at rest in stable equilibrium as opposed to fluid dynamics, the study of fluids in motion.

Pressure-gradient force

pressure gradient forcedifference in atmospheric pressurepressure gradient
This occurs when external forces such as gravity are balanced by a pressure-gradient force.
When a fluid is in an equilibrium state (i.e. there are no net forces, and no acceleration), the system is referred to as being in hydrostatic equilibrium.

Small Solar System body

small Solar System bodiessmall bodiesmacroscopic system
Hydrostatic equilibrium is the current distinguishing criterion between dwarf planets and small Solar System bodies, and has other roles in astrophysics and planetary geology.
Some of the larger small Solar System bodies may be reclassified in future as dwarf planets, pending further examination to determine whether or not they are in hydrostatic equilibrium.

Planet

planetsFormer classification of planetsplanemo
There are a dozen or so confirmed such objects (apart from the Sun), sometimes called planemos, in the Solar System, with others possible. Such a body will often have the differentiated interior and geology of a world (a planemo), though near-hydrostatic or formerly hydrostatic bodies such as the proto-planet 4 Vesta may also be differentiated and some hydrostatic bodies (notably Callisto) have not thoroughly differentiated since their formation.
A planet is an astronomical body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.

Star

starsstellarmassive star
In any given layer of a star, there is a hydrostatic equilibrium between the outward thermal pressure from below and the weight of the material above pressing inward.
When the protostellar cloud has approximately reached the stable condition of hydrostatic equilibrium, a protostar forms at the core.

Piriform

pyriformPiriform (disambiguation)
A star with an angular velocity above the critical angular velocity becomes a Jacobi (scalene) ellipsoid, and at still faster rotation it is no longer ellipsoidal but piriform or oviform, with yet other shapes beyond that, though shapes beyond scalene are not stable.

Definition of planet

definition of a planetCHXR 73 bdefine the term ''planet
According to the definition of planet adopted by the International Astronomical Union in 2006, one defining characteristic of planets and dwarf planets is that they are objects that have sufficient gravity to overcome their own rigidity and assume hydrostatic equilibrium.
This definition, which applies only to the Solar System, states that a planet is a body that orbits the Sun, is massive enough for its own gravity to make it round, and has "cleared its neighbourhood" of smaller objects around its orbit.

Ceres (dwarf planet)

Ceres1 CeresAtmosphere of Ceres
The smallest body confirmed to be in hydrostatic equilibrium is the dwarf planet Ceres, which is icy, at 945 km, whereas the largest body known to not be in hydrostatic equilibrium is the Moon, which is rocky, at 3,474 km.
Ceres is the only object in the asteroid belt known to be currently rounded by its own gravity, although detailed analysis was required to exclude Vesta.

List of gravitationally rounded objects of the Solar System

Gravitationally rounded objectaverage distance19 moons
There are a dozen or so confirmed such objects (apart from the Sun), sometimes called planemos, in the Solar System, with others possible.
This is a list of gravitationally rounded objects of the Solar System, which are objects that have a rounded, ellipsoidal shape due to their own gravity (current or past hydrostatic equilibrium).

Mimas (moon)

MimasPangea Chasma
The smallest object that appears to have an equilibrium shape is the icy moon Mimas at 397 km, whereas the largest object known to have an obviously non-equilibrium shape is the rocky asteroid Vesta at 525 km (573 × 557 × 446 km).
However, Mimas is not actually in hydrostatic equilibrium for its current rotation.

Intracluster medium

intracluster gasgasICM
Hydrostatic equilibrium is also important for the intracluster medium, where it restricts the amount of fluid that can be present in the core of a cluster of galaxies.
Measurements of the temperature and density profiles in galaxy clusters allow for a determination of the mass distribution profile of the ICM through hydrostatic equilibrium modeling.

4 Vesta

Vesta(4) VestaAsteroidal Gravity Optical and Radar Analysis
The smallest object that appears to have an equilibrium shape is the icy moon Mimas at 397 km, whereas the largest object known to have an obviously non-equilibrium shape is the rocky asteroid Vesta at 525 km (573 × 557 × 446 km). Such a body will often have the differentiated interior and geology of a world (a planemo), though near-hydrostatic or formerly hydrostatic bodies such as the proto-planet 4 Vesta may also be differentiated and some hydrostatic bodies (notably Callisto) have not thoroughly differentiated since their formation.
A 2012 analysis of Vesta's shape and gravity field using data gathered by the Dawn spacecraft has shown that Vesta is currently not in hydrostatic equilibrium.

Ellipsoid

ellipsoidalellipsoidstriaxial
This qualification means that the object is symmetrically rounded into a ellipsoid shape, where any irregular surface features are due to a relatively thin solid crust.
A spinning body of homogeneous self-gravitating fluid will assume the form of either a Maclaurin spheroid (oblate spheroid) or Jacobi ellipsoid (scalene ellipsoid) when in hydrostatic equilibrium, and for moderate rates of rotation.

Fluid

fluidsanalysis of fluidsenergy fluids
In fluid mechanics, a fluid is said to be in hydrostatic equilibrium or hydrostatic balance when it is at rest, or when the flow velocity for each parcel of fluid is constant over time. The hydrostatic equilibrium pertains to hydrostatics and the principles of equilibrium of fluids.

Gravity

gravitationgravitationalgravitational force
This occurs when external forces such as gravity are balanced by a pressure-gradient force.

Atmosphere of Earth

airEarth's atmosphereatmosphere
For instance, the pressure-gradient force prevents gravity from collapsing Earth's atmosphere into a thin, dense shell, whereas gravity prevents the pressure gradient force from diffusing the atmosphere into space.

Astrophysics

astrophysicistastrophysicaltheoretical astrophysics
Hydrostatic equilibrium is the current distinguishing criterion between dwarf planets and small Solar System bodies, and has other roles in astrophysics and planetary geology.

Planetary geology

astrogeologyplanetary geologistregio
Hydrostatic equilibrium is the current distinguishing criterion between dwarf planets and small Solar System bodies, and has other roles in astrophysics and planetary geology.

Crust (geology)

crustEarth's crustcrustal
This qualification means that the object is symmetrically rounded into a ellipsoid shape, where any irregular surface features are due to a relatively thin solid crust.

Newton's laws of motion

Newton's second lawNewton's third lawNewton's second law of motion
Newton's laws of motion state that a volume of a fluid that is not in motion or that is in a state of constant velocity must have zero net force on it.

Cuboid

rectangular cuboidsquare prismrectangular prism
The fluid can be split into a large number of cuboid volume elements; by considering a single element, the action of the fluid can be derived.

Pressure

water pressurenegative pressurefluid pressure
There are 3 forces: the force downwards onto the top of the cuboid from the pressure, P, of the fluid above it is, from the definition of pressure,