z This means the sum of the forces in a given direction must be opposed by an equal sum of forces in the opposite direction. Consequently, Vega is about 20% larger at the equator than at the poles. Hydrostatic-equilibrium definitions A state of balance by which the internal pressure of a gaseous body, such as a star, exactly balances its gravitational pressure.

r

: The integral is a measure of the total mass of the cluster, with [3] 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.

The baryonic density satisfies the above equation

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 body to have a noticeable deviation from hydrostatic equilibrium is Iapetus (moon) being made of mostly permeable ice and almost no rock [7]. ρ , the index i runs for the coordinates r and

(That is, the body as a whole can be considered to be in hydrostatic equilibrium even if the crust is not. −

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.

/ / B [4] A similar equation can be computed for rotating, axially symmetric stars, which in its gauge independent form reads: Unlike the TOV equilibrium equation, these are two equations (for instance, if as usual when treating stars, one chooses spherical coordinates as basis coordinates ( r A rotating star in hydrostatic equilibrium is an oblate spheroid up to a certain (critical) angular velocity. 0 ( ρ This occurs when external forces such as gravity are balanced by a pressure-gradient. Instead, it is rather in a strange walnut-like shape due to its unique equatorial ridge. 0 It flattens the surface of undisturbed liquids. ) {\displaystyle (t,r,\theta ,\phi )} 2 / {\displaystyle \theta }

{\displaystyle z} B are the temperature and density of the baryonic matter, and ρ D The hydrostatic equilibrium pertains to hydrostatics and the principles of equilibrium of fluids. B

k

-equation, which now reads. is Boltzmann's constant and

It can also be a satisfactory approximation when flow speeds are low enough that acceleration is negligible.

By balancing these forces, the total force on the fluid is. Strobel, Nick. of the dark matter, which is given by, The central density ratio

satisfies the non-linear differential equation, 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.

k

{\displaystyle \rho _{B}(0)/\rho _{M}(0)} For example, the massive base of the tallest mountain on Earth, Mauna Kea, has deformed and depressed the level of the surrounding crust, so that the overall distribution of mass approaches equilibrium. {\displaystyle k}

hydrostatic equilibrium (countable and uncountable, plural hydrostatic equilibria), The concept of hydrostatic equilibrium, frequently alluded to with non-technical approximations such as "rounded", is used in astronomy as part of the definitions of planet and dwarf planet, and sometimes of planetary object. Thus, hydrostatic balance can be regarded as a particularly simple equilibrium solution of the Navier–Stokes equations.

{\displaystyle {\mathcal {L}}_{X}=\Lambda (T_{B})\rho _{B}^{2}}

{\displaystyle \rho _{D}=\rho _{M}-\rho _{B}} = (May, 2001). If this were the case, … yields, If we make the assumption that cold dark matter particles have an isotropic velocity distribution, then the same derivation applies to these particles, and their density

r

: The integral is a measure of the total mass of the cluster, with [3] 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.

The baryonic density satisfies the above equation

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 body to have a noticeable deviation from hydrostatic equilibrium is Iapetus (moon) being made of mostly permeable ice and almost no rock [7]. ρ , the index i runs for the coordinates r and

(That is, the body as a whole can be considered to be in hydrostatic equilibrium even if the crust is not. −

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.

/ / B [4] A similar equation can be computed for rotating, axially symmetric stars, which in its gauge independent form reads: Unlike the TOV equilibrium equation, these are two equations (for instance, if as usual when treating stars, one chooses spherical coordinates as basis coordinates ( r A rotating star in hydrostatic equilibrium is an oblate spheroid up to a certain (critical) angular velocity. 0 ( ρ This occurs when external forces such as gravity are balanced by a pressure-gradient. Instead, it is rather in a strange walnut-like shape due to its unique equatorial ridge. 0 It flattens the surface of undisturbed liquids. ) {\displaystyle (t,r,\theta ,\phi )} 2 / {\displaystyle \theta }

{\displaystyle z} B are the temperature and density of the baryonic matter, and ρ D The hydrostatic equilibrium pertains to hydrostatics and the principles of equilibrium of fluids. B

k

-equation, which now reads. is Boltzmann's constant and

It can also be a satisfactory approximation when flow speeds are low enough that acceleration is negligible.

By balancing these forces, the total force on the fluid is. Strobel, Nick. of the dark matter, which is given by, The central density ratio

satisfies the non-linear differential equation, 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.

k

{\displaystyle \rho _{B}(0)/\rho _{M}(0)} For example, the massive base of the tallest mountain on Earth, Mauna Kea, has deformed and depressed the level of the surrounding crust, so that the overall distribution of mass approaches equilibrium. {\displaystyle k}

hydrostatic equilibrium (countable and uncountable, plural hydrostatic equilibria), The concept of hydrostatic equilibrium, frequently alluded to with non-technical approximations such as "rounded", is used in astronomy as part of the definitions of planet and dwarf planet, and sometimes of planetary object. Thus, hydrostatic balance can be regarded as a particularly simple equilibrium solution of the Navier–Stokes equations.

{\displaystyle {\mathcal {L}}_{X}=\Lambda (T_{B})\rho _{B}^{2}}

{\displaystyle \rho _{D}=\rho _{M}-\rho _{B}} = (May, 2001). If this were the case, … yields, If we make the assumption that cold dark matter particles have an isotropic velocity distribution, then the same derivation applies to these particles, and their density

.

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