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fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasma (physics), plasmas) and the forces on them. Originally applied to water (hydromechanics), it found applications in a wide range of discipl ...
, hydrostatic equilibrium, also called hydrostatic balance and hydrostasy, is the condition of a
fluid In physics, a fluid is a liquid, gas, or other material that may continuously motion, move and Deformation (physics), deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are M ...
or
plastic Plastics are a wide range of synthetic polymers, synthetic or Semisynthesis, semisynthetic materials composed primarily of Polymer, polymers. Their defining characteristic, Plasticity (physics), plasticity, allows them to be Injection moulding ...
solid at rest, which occurs when external forces, such as
gravity In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...
, are balanced by a pressure-gradient force. In the planetary physics of Earth, the pressure-gradient force prevents gravity from collapsing the
atmosphere of Earth The atmosphere of Earth is composed of a layer of gas mixture that surrounds the Earth's planetary surface (both lands and oceans), known collectively as air, with variable quantities of suspended aerosols and particulates (which create weather ...
into a thin, dense shell, whereas gravity prevents the pressure-gradient force from diffusing the atmosphere into outer space. In general, it is what causes objects in space to be spherical. Hydrostatic equilibrium is the distinguishing criterion between
dwarf planet A dwarf planet is a small planetary-mass object that is in direct orbit around the Sun, massive enough to be hydrostatic equilibrium, gravitationally rounded, but insufficient to achieve clearing the neighbourhood, orbital dominance like the ...
s and
small solar system bodies A small Solar System body (SSSB) is an object in the Solar System that is neither a planet, a dwarf planet, nor a natural satellite. The term was first IAU definition of planet, defined in 2006 by the International Astronomical Union (IAU) as fo ...
, and features in
astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline, James Keeler, said, astrophysics "seeks to ascertain the ...
and planetary geology. Said qualification of equilibrium indicates that the shape of the object is symmetrically rounded, mostly due to
rotation Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an ''axis of rotation''. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersect ...
, into an
ellipsoid An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional Scaling (geometry), scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface;  that is, a Surface (mathemat ...
, where any irregular surface features are consequent to a relatively thin solid crust. In addition to the Sun, there are a dozen or so equilibrium objects confirmed to exist in the
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Sola ...
.


Mathematical consideration

For a hydrostatic fluid on Earth: dP = - \rho(P) \, g(h) \, dh


Derivation from force summation

Newton's laws of motion Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body re ...
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. This means the sum of the forces in a given direction must be opposed by an equal sum of forces in the opposite direction. This force balance is called a hydrostatic equilibrium. The fluid can be split into a large number of
cuboid In geometry, a cuboid is a hexahedron with quadrilateral faces, meaning it is a polyhedron with six Face (geometry), faces; it has eight Vertex (geometry), vertices and twelve Edge (geometry), edges. A ''rectangular cuboid'' (sometimes also calle ...
volume elements; by considering a single element, the action of the fluid can be derived. There are three 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 Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
, F_\text = - P_\text A Similarly, the force on the volume element from the pressure of the fluid below pushing upwards is F_\text = P_\text A Finally, the
weight In science and engineering, the weight of an object is a quantity associated with the gravitational force exerted on the object by other objects in its environment, although there is some variation and debate as to the exact definition. Some sta ...
of the volume element causes a force downwards. If the
density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...
is ''ρ'', the volume is ''V'' and ''g'' the
standard gravity The standard acceleration of gravity or standard acceleration of free fall, often called simply standard gravity and denoted by or , is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is a constant ...
, then: F_\text = -\rho g V The volume of this cuboid is equal to the area of the top or bottom, times the height – the formula for finding the volume of a cube. F_\text = -\rho g A h By balancing these forces, the total force on the fluid is \sum F = F_\text + F_\text + F_\text = P_\text A - P_\text A - \rho g A h This sum equals zero if the fluid's velocity is constant. Dividing by A, 0 = P_\text - P_\text - \rho g h Or, P_\text - P_\text = - \rho g h ''P''top − ''P''bottom is a change in pressure, and ''h'' is the height of the volume element—a change in the distance above the ground. By saying these changes are
infinitesimal In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referred to the " ...
ly small, the equation can be written in differential form. dP = - \rho g \, dh Density changes with pressure, and gravity changes with height, so the equation would be: dP = - \rho(P) \, g(h) \, dh


Derivation from Navier–Stokes equations

Note finally that this last equation can be derived by solving the three-dimensional
Navier–Stokes equations The Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician Georg ...
for the equilibrium situation where u = v = \frac = \frac = 0 Then the only non-trivial equation is the z-equation, which now reads \frac + \rho g = 0 Thus, hydrostatic balance can be regarded as a particularly simple equilibrium solution of the Navier–Stokes equations.


Derivation from general relativity

By plugging the energy–momentum tensor for a perfect fluid T^ = \left(\rho c^ + P\right) u^\mu u^\nu + P g^ into the
Einstein field equations In the General relativity, general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of Matter#In general relativity and cosmology, matter within it. ...
R_ = \frac \left(T_ - \frac g_ T\right) and using the conservation condition \nabla_\mu T^ = 0 one can derive the Tolman–Oppenheimer–Volkoff equation for the structure of a static, spherically symmetric relativistic star in isotropic coordinates: \frac = -\frac \left(1+\frac\right) \left(1+\frac\right) \left(1 - \frac\right)^ In practice, ''Ρ'' and ''ρ'' are related by an equation of state of the form ''f''(''Ρ'',''ρ'') = 0, with ''f'' specific to makeup of the star. ''M''(''r'') is a foliation of spheres weighted by the mass density ''ρ''(''r''), with the largest sphere having radius ''r'': M(r) = 4\pi \int_0^r dr' \, r'^2 \rho(r'). Per standard procedure in taking the nonrelativistic limit, we let , so that the factor \left(1+\frac\right) \left(1+\frac\right) \left(1-\frac \right)^ \rightarrow 1 Therefore, in the nonrelativistic limit the Tolman–Oppenheimer–Volkoff equation reduces to Newton's hydrostatic equilibrium: \frac = -\frac = -g(r)\,\rho(r)\longrightarrow dP = - \rho(h)\,g(h)\, dh (we have made the trivial notation change ''h'' = ''r'' and have used ''f''(''Ρ'',''ρ'') = 0 to express ''ρ'' in terms of ''P''). A similar equation can be computed for rotating, axially symmetric stars, which in its gauge independent form reads: \frac - \partial_i \ln u^t + u_t u^\varphi\partial_i\frac=0 Unlike the TOV equilibrium equation, these are two equations (for instance, if as usual when treating stars, one chooses spherical coordinates as basis coordinates (t,r,\theta,\varphi), the index ''i'' runs for the coordinates ''r'' and \theta).


Applications


Fluids

The hydrostatic equilibrium pertains to
hydrostatics Hydrostatics is the branch of fluid mechanics that studies fluids at hydrostatic equilibrium and "the pressure in a fluid or exerted by a fluid on an immersed body". The word "hydrostatics" is sometimes used to refer specifically to water and ...
and the principles of equilibrium of
fluids In physics, a fluid is a liquid, gas, or other material that may continuously move and deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot res ...
. A hydrostatic balance is a particular balance for weighing substances in water. Hydrostatic balance allows the
discovery Discovery may refer to: * Discovery (observation), observing or finding something unknown * Discovery (fiction), a character's learning something unknown * Discovery (law), a process in courts of law relating to evidence Discovery, The Discovery ...
of their specific gravities. This equilibrium is strictly applicable when an ideal fluid is in steady horizontal laminar flow, and when any fluid is at rest or in vertical motion at constant speed. It can also be a satisfactory approximation when flow speeds are low enough that acceleration is negligible.


Astrophysics and planetary science

From the time of
Isaac Newton Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...
much work has been done on the subject of the equilibrium attained when a fluid rotates in space. This has application to both stars and objects like planets, which may have been fluid in the past or in which the solid material deforms like a fluid when subjected to very high stresses. In any given layer of a star, there is a hydrostatic equilibrium between the outward-pushing pressure gradient and the weight of the material above pressing inward. One can also study planets under the assumption of hydrostatic equilibrium. A rotating star or planet in hydrostatic equilibrium is usually an oblate spheroid, an
ellipsoid An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional Scaling (geometry), scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface;  that is, a Surface (mathemat ...
in which two of the principal axes are equal and longer than the third. An example of this phenomenon is the star Vega, which has a rotation period of 12.5 hours. Consequently, Vega is about 20% larger at the equator than from pole to pole. In his 1687 ''
Philosophiæ Naturalis Principia Mathematica (English: ''The Mathematical Principles of Natural Philosophy''), often referred to as simply the (), is a book by Isaac Newton that expounds Newton's laws of motion and his law of universal gravitation. The ''Principia'' is written in Lati ...
'' Newton correctly stated that a rotating fluid of uniform density under the influence of gravity would take the form of a spheroid and that the gravity (including the effect of
centrifugal force Centrifugal force is a fictitious force in Newtonian mechanics (also called an "inertial" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It appears to be directed radially away from the axi ...
) would be weaker at the equator than at the poles by an amount equal (at least asymptotically) to five fourths the centrifugal force at the equator. In 1742,
Colin Maclaurin Colin Maclaurin (; ; February 1698 – 14 June 1746) was a Scottish mathematician who made important contributions to geometry and algebra. He is also known for being a child prodigy and holding the record for being the youngest professor. ...
published his treatise on fluxions in which he showed that the spheroid was an exact solution. If we designate the equatorial radius by r_e, the polar radius by r_p, and the
eccentricity Eccentricity or eccentric may refer to: * Eccentricity (behavior), odd behavior on the part of a person, as opposed to being "normal" Mathematics, science and technology Mathematics * Off-Centre (geometry), center, in geometry * Eccentricity (g ...
by \epsilon, with : \epsilon=\sqrt, he found that the gravity at the poles is : \begin g_p & =4\pi\frac\fracG\rho \\ &=3\fracGM \\ \end where G is the gravitational constant, \rho is the (uniform) density, and M is the total mass. The ratio of this to g_0, the gravity if the fluid is not rotating, is asymptotic to : g_p/g_0\sim 1+\frac 1\epsilon^2\sim 1+\frac 2 f as \epsilon goes to zero, where f is the flattening: : f=\frac. The gravitational attraction on the equator (not including centrifugal force) is : \begin g_e &=\frac 32\left(\frac 1-\frac\right)GM\\ & =\frac 32\frac GM \\ \end Asymptotically, we have: : g_e/g_0\sim 1-\frac 1\epsilon^2\sim 1-\frac 1 f Maclaurin showed (still in the case of uniform density) that the component of gravity toward the axis of rotation depended only on the distance from the axis and was proportional to that distance, and the component in the direction toward the plane of the equator depended only on the distance from that plane and was proportional to that distance. Newton had already pointed out that the gravity felt on the equator (including the lightening due to centrifugal force) has to be \fracg_p in order to have the same pressure at the bottom of channels from the pole or from the equator to the centre, so the centrifugal force at the equator must be : g_e-\fracg_p\sim \frac 25\epsilon^2g_e\sim\frac 45fg_e. Defining the latitude to be the angle between a tangent to the meridian and axis of rotation, the total gravity felt at latitude \phi (including the effect of centrifugal force) is : g(\phi)=\frac. This spheroid solution is stable up to a certain (critical)
angular momentum Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of Momentum, linear momentum. It is an important physical quantity because it is a Conservation law, conserved quantity – the total ang ...
(normalized by M\sqrt), but in 1834, Carl Jacobi showed that it becomes unstable once the eccentricity reaches 0.81267 (or f reaches 0.3302). Above the critical value, the solution becomes a Jacobi, or scalene, ellipsoid (one with all three axes different).
Henri Poincaré Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philosophy of science, philosopher of science. He is often described as a polymath, and in mathemati ...
in 1885 found that at still higher angular momentum it will no longer be ellipsoidal but piriform or oviform. The symmetry drops from the 8-fold D
point group In geometry, a point group is a group (mathematics), mathematical group of symmetry operations (isometry, isometries in a Euclidean space) that have a Fixed point (mathematics), fixed point in common. The Origin (mathematics), coordinate origin o ...
to the 4-fold C, with its axis perpendicular to the axis of rotation. Other shapes satisfy the equations beyond that, but are not stable, at least not near the point of bifurcation. Poincaré was unsure what would happen at higher angular momentum but concluded that eventually the blob would split into two. The assumption of uniform density may apply more or less to a molten planet or a rocky planet but does not apply to a star or to a planet like the earth which has a dense metallic core. In 1737,
Alexis Clairaut Alexis Claude Clairaut (; ; 13 May 1713 – 17 May 1765) was a French mathematician, astronomer, and geophysicist. He was a prominent Newtonian whose work helped to establish the validity of the principles and results that Isaac Newton, Sir Isaa ...
studied the case of density varying with depth. Clairaut's theorem states that the variation of the gravity (including centrifugal force) is proportional to the square of the sine of the latitude, with the proportionality depending linearly on the flattening (f) and the ratio at the equator of centrifugal force to gravitational attraction. (Compare with the exact relation above for the case of uniform density.) Clairaut's theorem is a special case for an oblate spheroid of a connexion found later by
Pierre-Simon Laplace Pierre-Simon, Marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French polymath, a scholar whose work has been instrumental in the fields of physics, astronomy, mathematics, engineering, statistics, and philosophy. He summariz ...
between the shape and the variation of gravity. If the star has a massive nearby companion object,
tidal forces The tidal force or tide-generating force is the difference in gravitational attraction between different points in a gravitational field, causing bodies to be pulled unevenly and as a result are being stretched towards the attraction. It is the d ...
come into play as well, which distort the star into a scalene shape if rotation alone would make it a spheroid. An example of this is
Beta Lyrae Beta Lyrae (β Lyrae, abbreviated Beta Lyr, β Lyr) officially named Sheliak (Arabic: الشلياق, Romanization: ash-Shiliyāq) ( IPA: ), the traditional name of the system, is a multiple star system in the constellation of Lyra. Base ...
. 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 A galaxy cluster, or a cluster of galaxies, is a structure that consists of anywhere from hundreds to thousands of galaxy, galaxies that are bound together by gravity, with typical masses ranging from 1014 to 1015 solar masses. Clusters consist o ...
. We can also use the principle of hydrostatic equilibrium to estimate the
velocity dispersion In astronomy, the velocity dispersion (''σ'') is the statistical dispersion of velocities about the mean velocity for a group of astronomical objects, such as an open cluster, globular cluster, galaxy, galaxy cluster, or supercluster. By measu ...
of
dark matter In astronomy, dark matter is an invisible and hypothetical form of matter that does not interact with light or other electromagnetic radiation. Dark matter is implied by gravity, gravitational effects that cannot be explained by general relat ...
in clusters of galaxies. Only baryonic matter (or, rather, the collisions thereof) emits
X-ray An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...
radiation. The absolute X-ray
luminosity Luminosity is an absolute measure of radiated electromagnetic radiation, electromagnetic energy per unit time, and is synonymous with the radiant power emitted by a light-emitting object. In astronomy, luminosity is the total amount of electroma ...
per unit volume takes the form \mathcal_X=\Lambda(T_B)\rho_B^2 where T_B and \rho_B are the temperature and density of the baryonic matter, and \Lambda(T) is some function of temperature and fundamental constants. The baryonic density satisfies the above equation p_B(r+dr)-p_B(r)=-dr\frac\int_0^r 4\pi r^2\,\rho_M(r)\, dr. The integral is a measure of the total mass of the cluster, with r being the proper distance to the center of the cluster. Using the
ideal gas law The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stat ...
p_B=kT_B\rho_B/m_B (k is the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative thermal energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the ...
and m_B is a characteristic mass of the baryonic gas particles) and rearranging, we arrive at \frac\left(\frac\right)=-\frac\int_0^r 4\pi r^2\,\rho_M(r)\, dr. Multiplying by r^2/\rho_B(r) and differentiating with respect to r yields \frac\left frac\frac\left(\frac\right)\right-4\pi Gr^2\rho_M(r). If we make the assumption that cold dark matter particles have an isotropic velocity distribution, the same derivation applies to these particles, and their density \rho_D=\rho_M-\rho_B satisfies the non-linear differential equation \frac\left frac\frac\left(\frac\right)\right-4\pi Gr^2\rho_M(r). With perfect X-ray and distance data, we could calculate the baryon density at each point in the cluster and thus the dark matter density. We could then calculate the velocity dispersion \sigma^2_D of the dark matter, which is given by \sigma^2_D=\frac. The central density ratio \rho_B(0)/\rho_M(0) is dependent on the
redshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and increase in frequency and e ...
z of the cluster and is given by \rho_B(0)/\rho_M(0)\propto (1+z)^2\left(\frac\right)^ where \theta is the angular width of the cluster and s the proper distance to the cluster. Values for the ratio range from 0.11 to 0.14 for various surveys.


Planetary geology

The concept of hydrostatic equilibrium has also become important in determining whether an astronomical object is a
planet A planet is a large, Hydrostatic equilibrium, rounded Astronomical object, astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself. The Solar System has eight planets b ...
,
dwarf planet A dwarf planet is a small planetary-mass object that is in direct orbit around the Sun, massive enough to be hydrostatic equilibrium, gravitationally rounded, but insufficient to achieve clearing the neighbourhood, orbital dominance like the ...
, or small Solar System body. According to the definition of planet that was adopted by the
International Astronomical Union The International Astronomical Union (IAU; , UAI) is an international non-governmental organization (INGO) with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreach, education, and developmen ...
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. Such a body often has the differentiated interior and geology of a world (a planemo), but near-hydrostatic or formerly hydrostatic bodies such as the proto-planet
4 Vesta Vesta (minor-planet designation: 4 Vesta) is one of the largest objects in the asteroid belt, with a mean diameter of . It was discovered by the German astronomer Heinrich Wilhelm Matthias Olbers on 29 March 1807 and is named after Vesta (mytho ...
may also be differentiated and some hydrostatic bodies (notably Callisto) have not thoroughly differentiated since their formation. Often, the equilibrium shape is an oblate spheroid, as is the case with Earth. However, in the cases of moons in synchronous orbit, nearly unidirectional tidal forces create a
scalene ellipsoid An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional Scaling (geometry), scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface;  that is, a Surface (mathemat ...
. Also, the purported dwarf planet is scalene because of its rapid rotation though it may not currently be in equilibrium. Icy objects were previously believed to need less mass to attain hydrostatic equilibrium than rocky objects. The smallest object that appears to have an equilibrium shape is the icy moon Mimas at 396 km, but the largest icy object known to have an obviously non-equilibrium shape is the icy moon
Proteus In Greek mythology, Proteus ( ; ) is an early prophetic sea god or god of rivers and oceanic bodies of water, one of several deities whom Homer calls the "Old Man of the Sea" (''hálios gérôn''). Some who ascribe a specific domain to Prote ...
at 420 km, and the largest rocky bodies in an obviously non-equilibrium shape are the asteroids Pallas and Vesta at about 520 km. However, Mimas is not actually in hydrostatic equilibrium for its current rotation. The smallest body confirmed to be in hydrostatic equilibrium is the dwarf planet Ceres, which is icy, at 945 km, and the largest known body to have a noticeable deviation from hydrostatic equilibrium is Iapetus being made of mostly permeable ice and almost no rock. At 1,469 km Iapetus is neither spherical nor ellipsoid. Instead, it is rather in a strange walnut-like shape due to its unique equatorial ridge. Some icy bodies may be in equilibrium at least partly due to a subsurface ocean, which is not the definition of equilibrium used by the IAU (gravity overcoming internal rigid-body forces). Even larger bodies deviate from hydrostatic equilibrium, although they are ellipsoidal: examples are Earth's
Moon The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...
at 3,474 km (mostly rock), and the planet Mercury at 4,880 km (mostly metal).Sean Solomon, Larry Nittler & Brian Anderson, eds. (2018) ''Mercury: The View after MESSENGER''. Cambridge Planetary Science series no. 21, Cambridge University Press, pp. 72–73. In 2024, Kiss et al. found that has an ellipsoidal shape incompatible with hydrostatic equilibrium for its current spin. They hypothesised that Quaoar originally had a rapid rotation and was in hydrostatic equilibrium but that its shape became "frozen in" and did not change as it spun down because of tidal forces from its moon Weywot. If so, this would resemble the situation of Iapetus, which is too oblate for its current spin.Cowen, R. (2007). Idiosyncratic Iapetus, ''Science News'' vol. 172, pp. 104–106
references
Iapetus is generally still considered a planetary-mass moon nonethelessEmily Lakdawalla et al.
What Is A Planet?
The Planetary Society, 21 April 2020
though not always. Solid bodies have irregular surfaces, but local irregularities may be consistent with global equilibrium. For example, the massive base of the tallest mountain on Earth,
Mauna Kea Mauna Kea (, ; abbreviation for ''Mauna a Wākea''); is a dormant Shield volcano, shield volcano on the Hawaii (island), island of Hawaii. Its peak is above sea level, making it the List of U.S. states by elevation, highest point in Hawaii a ...
, has deformed and depressed the level of the surrounding crust and so the overall distribution of mass approaches equilibrium.


Atmospheric modeling

In the atmosphere, the pressure of the air decreases with increasing altitude. This pressure difference causes an upward force called the pressure-gradient force. The force of gravity balances this out, keeps the atmosphere bound to Earth and maintains pressure differences with altitude.


See also

*
List of gravitationally rounded objects of the Solar System This is a list of most likely gravitationally rounded objects (GRO) of the Solar System, which are objects that have a rounded, ellipsoidal shape due to their own gravity (but are not necessarily in hydrostatic equilibrium). Apart from the Sun i ...
; a list of objects that have a rounded, ellipsoidal shape due to their own gravity (but are not necessarily in hydrostatic equilibrium) *
Statics Statics is the branch of classical mechanics that is concerned with the analysis of force and torque acting on a physical system that does not experience an acceleration, but rather is in mechanical equilibrium, equilibrium with its environment ...
* Two-balloon experiment


References


External links


Strobel, Nick. (May, 2001). Nick Strobel's Astronomy Notes.
* by Richard Pogge, Ohio State University, Department of Astronomy {{Portal bar, Physics, Astronomy, Stars, Outer space Concepts in astrophysics Concepts in astronomy Definition of planet Fluid mechanics Hydrostatics