As the effective radius tends to get nullified at the center of gravity equation so there must be huge gravity force acting on the matter nearby.what happens with them? Is the process is similar to that of a black hole? If yes then in how many years a planet like earth will turn into black hole?
As you easily read from the internet the pressure at the center of Earth is arround 360 GPa. There seems to be no way for Earth to turn into a black hole.
You seem to be misled by misunderstanding a concept of an effective radius (which I don't even know). It is a widespread misunderstanding that the gravity force in a massive sphere has to be kind of singular at the center. Actually it vasnishes there. Nevertheless gravitation creates a pressure (or stress if we are in the solid state) there which is proportional to the mass of the body.
It means that it is the pressure that cause the formation of black holes not the gravity directly.......
did i get it right?
Since the pressure is a direct consequence of gravitation also the consequences of the pressure can be considered direct consequences of gravitation. The chains of notions and their dependencies are artifacts of human thinking and not given by Nature.
Think of air filled under pressure into a steel bottle. Come the forces from the steel since it confines the air? Or, are they caused by the air molecules hitting the steel?
I would like to spell out the reason for the surprising fact that a spherical massive body may create a huge pressure near its center and nevertheless create only a quite small force field there (that even vanishes at the center).
To understand this it is sufficient to consider the gravitational potential of a thin spherical shell of material of constant density. As it comes out easily by searching the spherically symmetric solutions of Poisson's equation and very tediously by integrating over the forces from the mass elements of the shell that the gravitational potential is constant in the space sourrounded by the shell. Outside the shell it is given as the gravitational potential of a point mass which concentrates the mass of the shell in its center.
If we now consider a spherically symmetric mass agglomeration and a point with distance r from the center, all gravitational forces at that point are created by the sphere of radius r arround the center. For r=0 this force is 0.
It is tricky but i got the answer.
But somehow i can not explain it to others.
@Vikash
to be able to explain it to others comes close to being the definition of having understood something.
Ulrich Mutze sir,
The moment I can explain this I will first remember you.
A black hole forms if a mass is contained within its Schwarzschild radius. For a rocky body like the Earth, the density varies slightly but the mass contained within any radius depends on the cube of the radius. Since the Schwarzschild radius is proportional to the mass contained, the situation for a small volume near the centre is less like a black hole than the total mass contained within the surface of the body.
Dear Thierry,
my forth contribution to the present discussion explained this already!
Thierry,
also a floating submarine is weightless but ignoring the pressure would not be wise.
Thierry,
The nett gravitational attraction at the centre of a solid sphere is indeed zero, but the pressure cannot be zero unless we have a perfectly rigid material to make up this ball.
Drop a pressure sensor into an incompressible ball of fluid. At a radius, r, there is a ball of fluid below the sensor - the mass of which falls as the sensor descends. That column has a weight. As the fluid is incompressible, the weight is opposed by pressure.
I believe that Iain Banks made use of this notion in one of his works: The Algebraist, IIRC.
Perhaps the Pascal's barrel (see https://en.wikipedia.org/wiki/Blaise_Pascal ) is a convincing explanation of some doubts expressed in this thread?
Thierry De Mees
You wrote, " Do mines collapse if they are arched? Do caves exist? "
They do, close to the surface.
But when the compressive pressure exceeds the strength of the material, they cannot.
> it is possible to imagine that successive shells are self-supporting,
Yes, it's possible. That's why I specified a strengthless fluid. But I think that few geophysicists would hold with the notion of a 'self-supporting' material at the core of, say, the Earth.
Ah, I read on: you now think that the pressure at the centre of a planet is generally not zero?
Thierry,
even if matter may not be a fluid near the center of planets there is mechanical stress there (if one could create a small cave there it would immediately collapse). Calling these elastic stresses pressure may not always be technically correct but using pressure in a wider sense that includes the strained states in solids your dictum 'No weight, no pressure' is fundamentally wrong.
Dear Thierry De Mees
I was satisfied with the explanations of Ulrich Mutze andI am thankful to you that you asked something that leads to further discussion on the topic. However, I would like to say that even air and water are fluids theirs shearing strength are not same (viscosity) and thus they shear with applied load similar to rock but with lower resistance to deformation (even metals start flowing at extreme pressure). This is also applicable for earthy mass which transfers shearing to the centre of the earth by conduction through neighbouring material and mass.
Dear Vikash,
the core of earth is a plasma, there are ions of Nichel and Iron which lost most of their electrons due to the fact that electronic orbitals cannot withstand the pressure..
. The coulomb repulsion between very positive ions is the one which resists the huge presssure in the Earth core. Nuclei of Nichel and IRON , are the most stable in the periodic table, survive there with no problem. At variance with what occurs in Jupiter, composed mostly of lighter element, even increasing dramatically its mass of trillion times, earth would not ingnite any termonuclear reaction since Iron and Nichel cannot provide energy out of fusion but suck energy producing heavier Nuclei.
Before becoming a BH there would be the transition to a Neutron star, but there is absolutely nothing which make anyone thing that it will happen.
What is not known is the possibility of the Core to break down the much heavier nuclei (atomic weight over 200) which arrive there due to their heavier weight and produce lighter nuclei, neutrons and a lot of radioactivity. Radioactivity is in fact the main reason of production of heat in the core of Earth and such activity has been found through the detection of earth neutrinos.
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