ρ ), Definition from Wiktionary, the free dictionary, https://en.wiktionary.org/w/index.php?title=hydrostatic_equilibrium&oldid=47577783, Creative Commons Attribution-ShareAlike License. Hydrostatic balance allows the discovery of their specific gravities. T An example of this is Beta Lyrae. m This force balance is called a hydrostatic equilibrium. = 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. B 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. B Consequently, Vega is about 20% larger at the equator than at the poles. Hydrostatic Equilibrium For the majority of the life of a star, the gravitational force (due to the mass of the star) and the gas pressure (due to energy generation in the core of the star) balance, and the star is said to be in ‘ hydrostatic equilibrium ’. {\displaystyle \theta } ρ M The hydrostatic equilibrium pertains to hydrostatics and the principles of equilibrium of fluids. 0 T By plugging the energy momentum tensor for a perfect fluid. r D / : The integral is a measure of the total mass of the cluster, with Λ If the star has a massive nearby companion object then tidal forces come into play as well, distorting the star into a scalene shape when rotation alone would make it a spheroid. {\displaystyle dP=-\rho gdr} An extreme example of this phenomenon is the star Vega, which has a rotation period of 12.5 hours. https://en.wikipedia.org/w/index.php?title=Hydrostatic_equilibrium&oldid=979865432, Articles needing additional references from May 2010, All articles needing additional references, Creative Commons Attribution-ShareAlike License, This page was last edited on 23 September 2020, at 06:54. Density changes with pressure, and gravity changes with height, so the equation would be: Note finally that this last equation can be derived by solving the three-dimensional Navier–Stokes equations for the equilibrium situation where, Then the only non-trivial equation is the {\displaystyle \theta } ( = Hydrostatic equilibrium is the distinguishing criterion between dwarf planets and small Solar System bodies, and has other roles in astrophysics and planetary geology.
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