Numerical Simulation
of a Hydrostatic Equation
Collapsing Nebula Cloud
In this^{ }numerical simulation we examine the same nebula cloud with the mass of 50 Suns and a diameter of 1 light year that is examined in a brief of an article below and compare results.
Reprinted from Source:
http://www.space.com/scienceastronomy/astronomy/stellar_chaos_020424.html
The findings are the result of computer simulations led by Matthew Bate of the University of Exeter and which were presented in early April at the UK National Astronomy Meeting.
The simulation followed the collapse of an interstellar gas cloud more than 1 lightyear in diameter and containing a mass of gas and dust equal to 50 Suns. The end result, after 266,000 years, was the formation of a cluster of stars typical to our galaxy.
Yet of the 50 objects that were formed, only about half became stars. 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.
The ostracized failures are considered brown dwarfs.
Link to total article:
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.
Formulas:
Gravitational Acceleration = G *M/ R^{2}
standard formulas for Volume of a sphere & pressure
A spherical homogenous body in hydrostatic
equilibrium satisfies the hydrostatic equation, so


where p
is the density and dP is the pressure change over a distance dr.
But the gravitational acceleration is given by


where G is the gravitational constant and
the mass interior to radius r by

Constants:
G = 6.67e11
M = 50*1.989e30
Breaking the equation down to a simplified set of steps where the radius is
reduced by a factor of 10 from the initial 1 light year diameter, a pattern
emerges. Pressure within the cloud has a mean increase at a factor of 1000 times
the initial, but the initial stellar mass (50 times that of our Sun) now
compressed into a cloud with a radius .1 of original. This generates
gravitational acceleration at a factor of 100 times the initial, thus the
factor 10 problem surfaces. For any nebula cloud and its set initial pressure, a
reduction of its radius by a factor of
Radius
in Light Years 
Increase
in Pressure P
= Initial 
Gravitational
Acceleration m/sec^{2} 



.5 
P 
2.96e10 
.05 
1e3 P 
2.96e8 
.005 
1e6 P 
2.96e6 
.0005 
1e9 P 
2.96e4 
.00005 
1e12 P 
2.96e2 
.000005 
1e15 P 
2.96 
How can we equate the force of Pressure to the basic formula P= M/V when this is related to density?
Ideal Gas Law PV = nRT is the true formula for gas in a nebula cloud, but how would this equation affect total results?
The relationship between shrinkage of the of the spherical cloud and a reduction of its radius to .1 of its original size to an increase the variable of P by a factor of 1000 is not dependent upon the constant R or number of moles, which is related to mass and moles/gram in the Ideal Gas Law. Mankind must realize that the fault with theories related to the collapsing nebula cloud, which constitutes the basis for stellar formation and planetary formation has a fault, the factor 10. Independent of initial pressures and gravitational acceleration due to total mass of the cloud, the ratio of factor 10 between gravitational acceleration and pressure remains the same for all random combinations of nebula clouds for each transition step. If on was to take the derivative of and equation where the ratio was x2 :: x3 with a constant, would not the constant go to 0 and the ratio be reduced to a factor 10? It is time to consider alternate to theory pertaining to the birth of stellar objects.
In the
equation below
P = nRT/V
where V is a sphere if the radius is reduced to .1r, then P
in this equation no matter what value it has, is a 1000 times greater so for all
values of nRT the defined ratio of P to P_{int}
is 1000P = nRT/V when the r subcomponent of V is reduced to .1r.
^{
}
Spherical Shape for the nebula cloud
Density variable but total mass always equals 50 Suns for given volume
Temperature near 0^{0} Kelvin thus a constant (If Temperature becomes a factor it increases the pressure negating a percentage of gravitational acceleration)
Mean P = 50*1.989e30 kg./ initial V
I would truly like to thank God for bestowing this knowledge
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