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Topic: Hydrostatic equilibrium

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	Stars
		During this phase, hydrostatic support is provided by the heat generated during contraction; after the main sequence, most of the nuclear fuel in the center has been used up.
		A consequence of hydrostatic balance is that the pressure on each shell from material outside it must be less than the pressure from material inside it.
		In the case of a star, the temperature of the gas determines the density structure via the hydrostatic equilibrium condition, so understanding the transport is important.
	imagine.gsfc.nasa.gov /docs/science/know_l2/stars.html (2263 words)

	Indian Institute of Astrophysics: Ask an Astronomer
		The term 'convective equilibrium' is used to describe those layers of a star where all the energy is transported by convective motions and in a constant manner, i.e., the convective energy flux is constant through the layers.
		Thus, convective equilibrium in the convection zone of a star is coupled to the hydrostatic equilibrium in the sense that violation of one lead to the violation of the other and eventually leading to the restoration of equlibria.
		Hydrostatic equilibrium refers to the force balance between the gas pressure and the gravitational force (the weight of the material) and is a consequence of one (momentum) of the three basic conservation laws, viz., the mass momentum and energy conservations.
	www.iiap.res.in /answers/stellar.html (3126 words)

	* Hydrostatic Equilibrium - (Astronomy): Definition
		Hydrostatic equilibrium 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,...
		hydrostatic equilibrium -- the condition in which pressure and gravitational forces in a star or planet are in balance.
		hydrostatic equilibrium 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.
	en.mimi.hu /astronomy/hydrostatic_equilibrium.html (318 words)

	Hydrostatic equilibrium: Definition and Links by Encyclopedian.com
		If a given layer is in hydrostatic equilibrium, the lithostatic pressure at a depth z is given by...are no longer in hydrostatic equilibrium.
		Hydrostatic equilibrium occurs when compression due to gravity is balanced by outward pressure.
		Hydrostatic equilibrium also explains why Earth's atmosphere does not collapse to a very thin layer on the ground and how the tires on your car or bicyle are able to support the weight of your vehicle.
	www.encyclopedian.com /hy/Hydrostatic-equilibrium.html (306 words)

	Hydrostatic equilibrium
		The Hydrostatic equilibrium pertains to hydrostatics and the principles of equilibrium of fluids.
		A Hydrostatic balance is a particular balance for weighing substances in water.
		In physics, Hydrostatic equilibrium also explains why Earth's atmosphere does not collapse to a very thin layer on the ground and how the tires on your car or bicyle are able to support the weight of your vehicle.
	www.xasa.com /wiki/en/wikipedia/h/hy/hydrostatic_equilibrium.html (195 words)

	The Sun and Stellar Structure
		Hydrostatic equilibrium also explains why the Earth's atmosphere does not collapse to a very thin layer on the ground and how the tires on your car or bicyle are able to support the weight of your vehicle.
		You have already seen in the previous section that hydrostatic equilibrium also provides a ``thermostatic control'' on the energy generation inside a star and keeps the star stable.
		The equation of state, hydrostatic equilibrium and the other physical principles are put together for each layer in a star.
	www.astronomynotes.com /starsun/s7.htm (1326 words)

	Isotropy of hydrostatic pressure
		Hydrostatic equilibrium represents that state of a fluid for which all of it sparts are macroscopically at rest relative to an externally applied, invariant field of force.
		In a fluid which is in a state of hydrostatic equilibrium the pressure is isotropic, that is, the normal stress
		That is, the hydrostatic pressure at a given point is independent of direction, and therefore isotropic.
	stommel.tamu.edu /~baum/reid/book1/book/node55.html (302 words)

	Astronomy Supplement - Life and Birth of Stars
		Hydrostatic Equilibrium: At any distance from the center of a star, if the weight of overlying layers is balanced by the upward pressure of hot gas in layers closer to the center, then the star is said to be in a state of hydrostatic equilibrium.
		Thermal equilibrium is self-regulating in that if more energy is released in a star's center than is radiated away at its surface, the temperature inside the star rises.
		The Sun is in a state of thermal equilibrium, with the temperature declining from some 15 million K at the center to about 6000 K in the photosphere.
	www.physics.gmu.edu /~jevans/astr103/CourseNotes/ECText/ch17_txt.htm (7266 words)

	Hydrostatic equilibrium
		The principle of hydrostatic equilibrium is that the pressure at any point in a fluid at rest (whence, “hydrostatic”) is just due to the weight of the overlying fluid.
		Hydrostatic equilibrium is a little more complicated to apply to air, because air is very compressible.
		But, even though we can't integrate the hydrostatic equation until some additional information (such as the run of T with height, or the dependence of P on ρ) is available, we can still evaluate the height of the homogeneous atmosphere.
	mintaka.sdsu.edu /GF/explain/thermal/hydrostatic.html (1097 words)

	Axisymmetric Objects
		An extra term due to rotation is introduced into the equation governing hydrostatic equilibrium (in the form of the centrifugal force), breaking the spherical symmetry of the problem.
		Hence, as a rule, the equilibrium properties of rotating, self-gravitating configurations are not describable in terms of analytical functions.
		All equilibrium axisymmetric figures must be in steady-state as viewed by an observer in the inertial reference frame.
	www.phys.lsu.edu /astro/H_Book.current/Applications/Structure/Axisymmetric/Axisym.intro.text.shtml (866 words)

	SUN
		Equilibrium is re-established when the sound waves have adjusted the pressures throughout the star and have been dissipated by viscosity.
		Evaluate this integral by a "one-step" integration of the equation of hydrostatic equilibrium, replacing M(r) by M, r and dr by R/2 (since most of the star's mass resides inside R/2), etc. Derive the equation for p(center) as function of M and R. Evaluate for the Sun.
		Within the steady gaseous Sun, the equation of hydrostatic equilibrium specifies that each layer of the star is supported by a pressure gradient to balance the force of gravity.
	www.columbia.edu /~ah297/unesa/astrophysics/astro-chapter5.html (6199 words)

	Numerical Simulation of a Hydrostatic Equation
		The rest were gravitationally ejected from the central cluster before they gathered enough mass to trigger thermonuclear fusion, the fusing of hydrogen into helium that powers a real star.
		Here we examine the step by step process of nebula cloud condensation and the hydrostatic relationship between the reduction radius, increase of pressure within the spherical nebula cloud and does gravitational acceleration factor in to provide an equilibrium.
		The conclusion here is that a hydrogen- helium nebula cloud could not collapse due to its own self contained mass due the factor 10 problem of the hydrostatic equation.
	www.grantchronicles.com /numericalsimulation.htm (833 words)

	Geology 150 - Climate Changes
		Hydrostatic equilibrium: expresses the balance between the Gravitational Force and the vertical Pressure Gradient Force.
		Hydrostatic equilibrium states that the pressure fall with height is proportional to density.
		From the hydrostatic approximation, we know that pressure will decrease more rapidly in a dense column of air than in a less dense column of air.
	earth.usc.edu /~geol150/weather/winds.html (739 words)

	Hydrostatic equilibrium of the atmosphere
		Let us, first of all, consider the hydrostatic equilibrium of the atmosphere.
		In equilibrium, this upward force must be balanced by the downward force due to the weight of the slice: this is
		This is called the equation of hydrostatic equilibrium for the atmosphere.
	physics.ship.edu /~mrc/thermo/ut_thermo/node53.html (195 words)

	The hydrostatic equation
		Hereafter, hydrostatic eqilibrium will be understood to imply hydrostatic equilibrium of a fluid in the presence of a field of gravity of the earth (i.e., geo-hydrostatic equilibrium).
		which is the scalar form of the differential equation for hydrostatic equilibrium.
		are identical under hydrostatic conditions and would form approximately spheroidal surfaces on the earth under this condition.
	stommel.tamu.edu /~baum/reid/book1/book/node57.html (551 words)

	Cosmic Evolution - Epoch 3 - Stellar Evolution
		Hydrostatic equilibrium—as in a “compressible fluid,”; which is the way stars are modeled—tends to stabilize a star at every point within the star, to keep it from collapsing or exploding, in either case catastrophically.
		Note also, to make another clarification, that even in hydrostatic equilibrium, a star like the Sun continues to change its luminosity—that is, its rate of energy flow—ever so slightly over the course of its lifetime.
		This small expansive adjustment of the core halts the gravitational contraction of the star, reestablishing an equilibrium of sorts—in this case, a balance occurring at the quantum level among the densely packed electrons whose tiny point-like spheres are essentially touching one another, thereby physically holding up the aged star against gravity.
	www.tufts.edu /as/wright_center/cosmic_evolution/docs/text/text_stel_4.html (5502 words)

	Dr
		Hydrostatic Equilibrium: An example of hydrostatic equilibrium is when a molecular cloud in space (it is a gas--hence the 'hydro') is unable to further collapse inward ('static').
		The collapse, which is caused by the gravity of the particles, is halted because the pressure within the cloud is balanced with the force of gravity ('equilibrium').
		Accretion will relate to the discussion of angular momentum and how it relates to bipolar outflows, the word tenuous will be used in describing the stellar wind that is involved in the formation of bipolar outflows, and hydrostatic equilibrium will be used in speaking about the molecular cloud that a star forms from.
	staff.imsa.edu /~brazzle/IMSAastro/Archive/2004 (1069 words)

	Hydrostatic Equilibrium - Bad Astronomy and Universe Today Forum
		But in general objects don't need to be spherical to be in hydrostatic equilibrium: they can also come in a variety of (smooth!) ellipsoidal shapes according to their state of rotation or tidal forces.
		Some measure of deviation from the best fit hydrostatic ellipsoid (for years, the gravity depression near India was infamous, but lately geophysicists have been using the hydrostatic ellipsoid, and the depression is not so severe), but I got the impression that that was what baric was angling for anyway.
		Some measure of deviation from the best fit hydrostatic ellipsoid (for years, the gravity depression near India was infamous, but lately geophysicists have been using the hydrostatic ellipsoid, and the depression is not so severe)...
	www.bautforum.com /showthread.php?t=46253 (1343 words)

	Hydrostatic equilibrium - Definition, explanation
		Hydrostatic balance allow the discovery of their specific gravities.
		In astrophysics, in any given layer of a star, there is a balance between the thermal pressure (outward) and the weight of the material above pressing downward (inward).
		In physics, Hydrostatic equilibrium also explains why Earth's atmosphere does not collapse to a very thin layer on the ground and how the tires on your car or bicycle are able to support the weight of your vehicle.
	www.calsky.com /lexikon/en/txt/h/hy/hydrostatic_equilibrium.php (242 words)

	ESA Science & Technology: Stellar Radiation & Stellar Types
		The star is now in equilibrium: the energy generated by nuclear fusion in the stellar core radiates outwards, balancing the force of gravity pulling the star inward.
		At any point within a star in hydrostatic equilibrium the underlying pressure supports the weight from the overlying material.
		The equation for hydrostatic equilibrium is shown below.
	sci.esa.int /science-e/www/object/index.cfm?fobjectid=35774&fbodylongid=1693 (166 words)

	SparkNotes: The Sun: The Sun's Interior
		The structure of Sun's interior is the result of the hydrostatic equilibrium between gravity and the pressure of the gas.
		In a situation of equilibrium, gravity exactly balances this 'pressure gradient,' and the gas can be considered as approximately sta tic.
		From the laws of thermodynamics and the hydrostatic equilibrium we can, using a computer, reconstruct the density, the pressure and the temperature inside the Sun, as a function of the distance from its center.
	www.sparknotes.com /astronomy/sun/section4.rhtml (1473 words)

	The Sun and Stellar Structure
		Hydrostatic equilibrium is the balance between the thermal pressures from the heat source pushing outwards and gravity trying to make the star collapse to the very center.
		I will discuss hydrostatic equilibrium in more depth (no pun intended) in a later section.
		Once the hydrogen fuel in the core has been used up, hydrostatic equilibrium can no longer stabilize the star.
	www.astronomynotes.com /starsun/s3.htm (2069 words)

	Geotimes - August 2002 - Antarctic Melting
		Grounded ice is blue, floating ice is red, the transition from grounded to floating ice is blue, to light green, to yellow and red as the ice adjusts to hydrostatic equilibrium.
		The ocean water is 2 to 3 degrees above freezing and, due to its saline composition, is able to melt the ice.
		Although the authors suggest that melt rates maintain the equilibrium of the Antarctic ice sheet, they estimate that a 0.1 degree Celsius increase in ocean temperatures will lead to melt increases of a meter per year.
	www.agiweb.org /geotimes/aug02/NN_antarctic.html (355 words)

	Introduction and FAQ
		A "planet" is 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 hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit.
		A "dwarf planet" is 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 hydrostatic equilibrium (nearly round) shape2, (c) has not cleared the neighbourhood around its orbit, and (d) is not a satellite.
		All other objects3 except satellites orbiting the Sun shall be referred to collectively as "Small Solar-System Bodies".
	www.nineplanets.org /intro.html (2366 words)

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