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Hydrostatic Equilibrium

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Hydrostatic equilibrium is one of the most important fundamental principles in atmospheric physics and astrophysics.


Hydrostatic equilibrium: gravity compression is balanced by pressure outward.
Greater gravity compresses the gas, making it denser and hotter, so the outward pressure increases.

Hydrostatic Equilibrium
The simple model of any main sequence star is of a dense gas/fluid in a state of hydrostatic equilibrium. The inward acting force, gravity, is balanced by outward acting forces of gas pressure and the radiation pressure.

Hydrostatic equilibrium
A planet's defining physical characteristic is that it is large enough for the force of its own gravity to dominate over the electromagnetic forces binding its physical structure, leading to a state of hydrostatic equilibrium.

hydrostatic equilibrium
A balance between the weight of a layer in a star and the pressure that supports it.
hyperbolic
See hyperbolic space.

~
The balance between weight of the material pressing downward on a layer in a star and the pressure in that layer.
I ...

~ - Balance between gravity and gas pressure. In the case of a star, gravity originates in mutual gravitational attraction of the entire mass of the star. Gas pressure is produced by nuclear reactions that heat the star's gas.

~ - This is the balance between weight (gravity) and pressure (air pressure or gas pressure). This is like how the old dome on the UNI-Dome worked (and how the Metrodome in Minneapolis works).

~ - The balance between the inward directed gravitational force and the outward directed pressure force within a celestial body
Hyperbola - A curved path that does not close on itself. A body moving with a speed greater than escape velocity follows a hyperbola ...

~
The balance maintained within a star between the explosive pressure of the core caused by heat and the gravitational attraction of the mass of the star itself.

~ occurs when compression due to gravity is balanced by a pressure gradient which creates a pressure gradient force in the opposite direction....
, the boundary that separates objects from planethood.

~
A balance between the gravitational force inward and the gas and radiation forces outward in a star.
Hyperbolic Space ...

~
~ is a stable condition in a star in which the fluid matter within the star is at an equilibrium with respect to all forces, including the inward-pulling force of gravity, the out-ward pulling buoyancy due to pressure differentials, ...

~ :
gravity inwards = pressure outwards
stability : stellar thermostat
Chapter 12: Stellar Evolution ...

~ gives no net flow in the z-direction:
at density r. For a thin disk, this approaches -GMz/r³ so the disk thickness will be H ~ r/M.
The mass flow rate (accretion rate in a steady state) must by mass conservation be constant with radius ...

~
A state that occurs when compression due to gravity is balanced by a pressure gradient which creates a pressure gradient force in the opposite direction. Hydrostatic equillibrium is responsible for keeping stars from imploding and for giving planets their spherical shape.

Roundness - ~ due to mass - not size as I thought I'd made clear before. If it has enough mass to be round its a planet, if not, then not Pluto is round, Ceres is round, Vesta is not quite.

In addition to ~, the interior of a stable star will also maintain an energy balance of thermal equilibrium. There is a radial temperature gradient throughout the interior that results in a flux of energy flowing toward the exterior.

See magnetohydrodynamics. [H76]
~
A balance between the gravitational force inward and the gas and radiation forces outward in a star. [H76]
Hyperbolic Space ...

~ Balance between pressure forces and gravitational forces in a star's layers. hyperbola Open-ended curve of a conic section formed by the intersection of a plane with a right-circular cone at any angle between the axis of the cone and its slant edge.

~ 1. The state of a fluid whose surfaces of constant pressure and constant mass (or density) coincide and are horizontal throughout. Complete balance exists between the force of gravity and the pressure force. See hydrostatic equation. 2.

dwarf planet A celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a ~ (nearly round) shape2 , (c) has not cleared the neighbourhood around its orbit, and (d) is not a satellite.

The identity of g* and g is implied by the assumption of ~.

This balance is called ~. Now pressure is a force per unit area; you exert pressure on a wall if you put your hand on it and push. That pressure force is exerted only over the surface area covered by your hand.

This ~ condition usually also applies to changes of density inside the object, so that the density at a place inside the object will depend only on how far it is from the object's center. If this is so, the object is called spherically symmetric.

is in orbit around the Sun,
has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a ~ (nearly round) shape, and
has cleared the neighbourhood around its orbit
(official IAU definition dated 24 August 2006) plutoid a celestial body that ...

horizontal branch Region of the H-R diagram where post-main sequence stars again reach ~. At this point, the star is burning helium in its core, and hydrogen in a shell surrounding the core.

Scientifically, stars are defined as self-gravitating spheres of plasma in ~, which generate their own energy through the process of nuclear fusion.

horizontal branch Region of the Hertzsprung-Russell diagram where post-main sequence stars again reach ~. At this point, the star is burning helium in its core, and hydrogen in a shell surrounding the core.

where, most importantly P=pressure and T=Temperature. The outward pressure nearly balances the inward gravitational pull, a condition called ~.

Age: 1--3 yrs
R ~ 50 Rsun
Tcore = 150,000K
Tsurface = 3500K
Energy Source: Gravity
...

This whole process acts to maintain ~. As the core then contracts, the energy generation increases, causing the sun to become more luminous. A little-known fact is that the sun is approximately 140% as luminous now as it was when it was born.

Instead, as the hydrogen is used up by fusion, the star loses the balance of ~ and simply contracts and heats up due to gravity. At this point, it is no longer a main-sequence star (since it is no longer fusing hydrogen), but becomes a "white dwarf.

charged particles, such as free protons, alpha particles and beta particles, as well as a steady stream of neutrinos. It is the internal pressure of this nuclear fusion process that prevents the Sun from collapsing further under its own gravity (known as a state of ~).

See also: See also: What is the meaning of Astro, Solar, Sun, Earth, Planet?

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