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Old Jan 29th 2017, 03:21 AM   #1
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How to calculate the density of a star's core

For school I have to calculate certain aspects of a star but now I am stuck at the density.

My teacher gave me a formula but I got an unrealistic answer from it. (I know that the formula is very basic)

The formula is: P=Md*P(core pressure)/kT

Md=average mass of a particle:1,03E-27 Kg
Pressure=4,68E8 Pa
k=1,38E-23 J/K
T=5,87E5 K

Inserting these numbers in the formula gives 0,06kg/m3

If somebody has an idea of what I'm doing wrong it would be much appreciated.

Last edited by Migroh; Jan 29th 2017 at 03:23 AM.
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Old Jan 29th 2017, 07:36 AM   #2
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Your math is correct. I think the reason you are getting such a low number for a result is that the values for P (pressure) and T are way off. For our sun you would use values of P = 26.5x10^12 Pa, and T = 1.5 x 10^7 K. Try using those values and see what you get.
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Old Jan 29th 2017, 08:42 AM   #3
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Good to know that the calculation is correct, that the values for T and P are off must have something to do with my previous calculations(I'm not using the sun as reference)
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Old Jan 30th 2017, 03:10 PM   #4
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Are you sure the pressure is in Pascals?
Might it be in KPa?

You are obviously looking at a smaller and cooler star than our Sun,
but I would not expect the pressure to be over 5000 times less.

KPa gives a core pressure that is a more believable 5 times less,
although a density of 60kg/m still seems a bit low.

On Further Investigation:
I plugged the numbers ChipB gives into the equation and got about 130kg/m
However this Wikipedia article <Core of the Sun> gives the density as 150g/cm
which equates to 150000kg/m
and a pressure of 26.5 petapascals or 2.65e15 Pa

So I think the pressure from ChipB should be in KPa and your pressure should be in MPa!
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Last edited by Woody; Jan 30th 2017 at 03:13 PM.
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Old Jan 31st 2017, 09:56 AM   #5
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Originally Posted by Woody View Post
On Further Investigation:
I plugged the numbers ChipB gives into the equation and got about 130kg/m
However this Wikipedia article <Core of the Sun> gives the density as 150g/cm
which equates to 150000kg/m
and a pressure of 26.5 petapascals or 2.65e15 Pa

So I think the pressure from ChipB should be in KPa and your pressure should be in MPa!
You are correct - good catch! My source for pressure at the center of the sun was Wikipedia, which said "26.5 petapascals." But I'm afraid I converted to Pa by multiplying by E+12, whereas I should have multiplied that by E+15. So my calculation is low by a factor of 1000.

Originally Posted by Migroh View Post
the values for T and P are off must have something to do with my previous calculations(I'm not using the sun as reference)
Just for reference the pressure you are using of 4.68E+8 Pa is significantly less than the pressure at the center of the Earth, which is is about 3.6E+11 Pa. I doubt that there is any star that could sustain fusion at such low pressures.

Last edited by ChipB; Jan 31st 2017 at 10:05 AM.
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