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=5.67036713E−8
!radiantion constant in J / K
kbolzmann=1.3806485279E−23
!gravity constant
GRAVITY=6.67408E−11
! 1 mol
mol=6.02214085774E23
! 1 u (atomic mass )in kg
u=1.66053904020E−27
! mass of 1 electron in kg
me=9.1093835611E−31
!hydrogen mass
mh=1.00782503223∗u
!neutron mass
mn=1.00866491585∗u
! speed of light, in m / s
c=299792458
! plank constant h in kg * m^2 / s
hp=6.62607004081E−34
! reduced plank constant hr in kg * m^2 / s
hpr=frachp(PI∗2)
amount=79378857878009573048911997815206
! iron with 26 protons 30 neutrons
element=26Fe56
elementmass=55.934936
atoms=amount
neutrons=(56−26)∗amount
electrons=26∗amount
particlecount=atoms+electrons
!4.4400513610370694E30 kg, about 2.3 Mass of the sun
Mass=elementmass∗amount
Radius=2228588
Temperature=9.45179584120983E−7
fgravitation=fracGRAVITY∗(Mass2)Radius
volume=((frac4.03.0)∗PI∗(Radius3))
!density in particles / m^3
particledensity=fracparticlecountvolume
a=4.0∗fracsbolzmannc
!radiation pressure in J / m^3
rpressure=frac1.03.0∗a∗(Temperature4)
!gas pressure in J / m^3
gpressure=particledensity∗kbolzmann∗Temperature
!electron degeneracy pressure
epressure=(frac(PI3)∗(hpr2)(15∗me))∗((frac3∗electrons(volume∗PI))(frac5.03.0))
! electron degeneracy pressure formula 2
epressure2=frac((PI2)∗(hpr2))(5∗me∗(mh(frac5.03.0)))∗((frac3.0PI)(frac2.03.0))∗((frac(fracMassvolume)1)(frac5.03.0))
!neutron degeneracy pressure
npressure=frac(PI3)∗(hpr2)(15∗me))∗((frac3∗neutrons(volume∗PI))(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=totalpressure∗volume
!if factor = 1 then the body is in equilibrium
factor=fractotalpressureforcefgravitation
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