Saturday, 14 February 2015

star - Formulas for gravitatitional equilibrium

I am trying to calculate at which point gravitational equilibrium sets in for various bodys (planets stars neutron stars etc.) assuming they are perfect spheres. However the radius i get is not equal to what it should be according to wikipedia (i tried for the sun a planet and a neutron star, all of them were off by quite a bit)



below is the example of the neutron star radius i m trying to get



my result (factor) is 1 at:
Radius : 2228588 m
Density: 1.2768744892680034E11 kg / m^3



the wikipedia article about neutron stars says radius of a neutron star is about 12 km and the density about 10 times higher than mine but my result is 2228km which is quite a bit off, so i got a 2 part question:
a) am i calculating all forces i need?
and
b) are the formulas i am using correct?



i took them from wikipedia and / or university slides and i found multiple variations of almost all of them(most of which i actually didnt list below), so i m quite confused as to what is correct



i know that i m using iron as element and i should split it up and convert the protons to neutrons but that would only increase the degegeneracy pressure further resulting in an even bigger radius if i m not mistaken.
heres how i calculated it (everything behind a "!" is a comment that describes what it is):



!radiantion constant  in Wm^-2K-4


sbolzmann=5.67036713E8



!radiantion constant  in J / K


kbolzmann=1.3806485279E23



!gravity constant


GRAVITY=6.67408E11



! 1 mol


mol=6.02214085774E23



! 1 u (atomic mass )in kg


u=1.66053904020E27



! mass of 1 electron in kg


me=9.1093835611E31



!hydrogen mass


mh=1.00782503223u



!neutron mass


mn=1.00866491585u



! speed of light, in m / s 


c=299792458



! plank constant h in kg  *  m^2 / s    


hp=6.62607004081E34



! reduced plank constant hr in kg  *  m^2 / s   


hpr=frachp(PI2)



amount=79378857878009573048911997815206



! iron with 26 protons 30 neutrons


element=26Fe56



elementmass=55.934936



atoms=amount



neutrons=(5626)amount



electrons=26amount



particlecount=atoms+electrons



!4.4400513610370694E30 kg, about 2.3 Mass of the sun


Mass=elementmassamount



Radius=2228588



Temperature=9.45179584120983E7



fgravitation=fracGRAVITY(Mass2)Radius



volume=((frac4.03.0)PI(Radius3))



    !density in particles / m^3


particledensity=fracparticlecountvolume



a=4.0fracsbolzmannc



    !radiation pressure in  J / m^3


rpressure=frac1.03.0a(Temperature4)



    !gas pressure in J / m^3


gpressure=particledensitykbolzmannTemperature



    !electron degeneracy pressure 


epressure=(frac(PI3)(hpr2)(15me))((frac3electrons(volumePI))(frac5.03.0))



    ! electron degeneracy pressure formula 2


epressure2=frac((PI2)(hpr2))(5me(mh(frac5.03.0)))((frac3.0PI)(frac2.03.0))((frac(fracMassvolume)1)(frac5.03.0))



    !neutron degeneracy pressure


npressure=frac(PI3)(hpr2)(15me))((frac3neutrons(volumePI))(5.0/3.0))



    !neutron degeneracy pressure formula 2


npressure2=frac((3(frac10.03.0))(hpr2))(15(PI(frac1.03.0))(mn(frac8.03.0))(radius5))((fracMass4)(frac5.03.0))



totalpressure=gpressure+rpressure+npressure+epressure



totalpressureforce=totalpressurevolume



!if factor = 1 then the body is in equilibrium


factor=fractotalpressureforcefgravitation

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