Questions tagged [hydrostatic-equilibrium]
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Deriving Faber-Jackson Relation from Milgrom's Law
I am reading Famaey & McGaugh 2011, a review paper on Modified Newtonian Dynamics. My question concerns bullet 3 in Sec 5.2, where the authors try to explain how Faber-Jackson Relation can be ...
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Where can I find the $\mu$ value in galaxy clusters for ideal gas law?
I am studying hydrostatic equilibrium in galaxy clusters and encountered the following expression:
$P=(kT/\mu m_p)\rho$
The interpretation of this formula is obvious. It is just the ideal gas law ...
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How to show that $P_c=(9GM^2)/(14\pi R^4)$ from equation of hydrostatic equilibrium
I need to show that $$P_c=\frac {9GM^2}{14\pi R^4}$$
from the equation of hydrostatic equilibrium: $\frac {dP}{dr}=-\frac{GM\rho}{r^2}$
in the exercise before, we show that $\rho_c=\frac {6M}{5 \pi R^...
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Virial theorem, contraction, and stars getting hotter
So, for a homogeneous sphere made of ideal gas the virial theorem applies:
$$E_{int}=-\frac{1}{2}E_{grav}$$
I have read that this implies that a star must get hotter when it contracts.
I don't quite ...
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What does it mean for cold clouds to be in pressure equilibrium with a diffuse hot medium?
I often read about cold objects (namely cold clouds in the Galactic halo or cold filaments accreting into high-redshift galaxies) being in pressure equilibrium with the diffuse hot ambient gas. What ...
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Aren't denser bodies more likely to collapse into hydrostatic equilibrium?
It is said that at small sizes, icy planets are more likely to be in hydrostatic equilibrium than terrestrial rocky ones. But why, as a matter of fact? Shouldn't denser bodies be more likely to ...
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Why red giants have cooler surface than MS stars?
I know that with increasing age and depletion of hydrogen in the core the radiation inside a main sequence (MS) star increases pushing the envelope/surface of the star outwards. What I don't ...
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What is the mass for a celestial body to definitely achieve hydrostatic equilibrium?
While these posts (attempt to) answer what the minimum mass is to be able to achieve an ellipsoidal shape, my question asks for the mass at which a body definitely collapses into an ellipsoid. Meaning,...
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Using a differential force in the derivation of hydrostatic equilibrium in a star
I've been banging my head against this particular derivation of hydrostatic equilibrium in a star for the last few days, from Carroll and Ostlie's Introduction to Modern Astrophysics (2nd ed. p. 286):
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Is the Moon not in hydrostatic equilibrium?
Given the recently-announced observations from VLT/SPHERE that 10 Hygiea may be sufficiently round to qualify as the second main-belt dwarf planet, I found myself perusing Wikipedia's Hydrostatic ...
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Virial Shock Heating
In the review paper on protoclusters, Roderik Overzier (pg 25) mentions the concept of virial shock heating which seems to be a process involved with galaxy cluster formation.
I'm not fully certain ...
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Why 225088 Gonggong is not a dwarf Planet yet?
Per definition 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 ...
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Are larger stars rounder?
The Earth is a very smooth sphere, and the Sun even more so, with only minor fluctuations. I am wondering: are larger stars even rounder? Intuitively, that seems self evident, but I am not so sure. ...
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Formulae for gravitatitional equilibrium
I am trying to calculate at which point gravitational equilibrium sets in for various bodies (planets stars neutron stars etc.) assuming they are perfect spheres. However, the radius I get is not ...
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How to calculate the mean molecular weight of the Sun
I have a homework question in which I need to estimate a parameter known as $\beta_{P}$ and also the core temperature, both for the Sun.
However, prior to doing this I need to know the mean molecular ...
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Is there a mechanism that makes small moons more rounded than comets?
67P/Churyumov–Gerasimenko has a highly irregular dumbbell shape. But the sample of comet shapes observed is very small, so I wonder if irregular shape is the norm for comets and for small moons. Many ...
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What happens to the Gas Pressure when working out the Eddington Luminosity?
I am looking at how the Eddington Luminosity is derived and I do no understand why we only care about $P_{rad}$?
When working out $L_{Edd}$ you take the ratio between $dP_{rad}/dr$ and $dP_{...
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Can objects enter hydrostatic equillibrium through processes other than the influence of gravity?
Wouldn't a droplet of liquid (say water) floating around in space become spherical and "in hydrostatic equilibrium" due to surface tension but not gravity?
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How can astronomers determine the difference between "hydrostatic equilibrium" and "just happens to be spherical"?
This is relevant for the definition of a dwarf planet.
I presume the answer will be, well, if we can tell the mass of the body and guess the material. I don't find this very satisfactory because (1)...
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What's an order-of-magnitude main sequence star look like?
I'm looking for a very rough, order-of-magnitude approach to the main sequence.
What I mean is, I have a spherically-symmetric hydrogen distribution. I'm looking to get a rough approximation for ...
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What is the time/size/rigidity ratio for a space object to become mostly round?
In the answer here multiple comets are identified that do not form a single round body.
A drop of water will form a round shape in the time it takes to free fall a couple of feet.
All of the ...