Mass of the core of the sun > mass of the sun?

[h1a8]

I tried calculating the mass of the core of the sun but keep coming up with a number that exceeds the entire mass of the sun. I used http://en.wikipedia.org/wiki/Sun" facts on the sun. It says the core of the sun extends from its center to .2 to .25 times it's radius. I used the number .225 as an average. So this would make the volume of the core to be (.225)^3 or .011 times the sun's total volume. The volume of the Sun is stated to be 1.412e18 km^3 or 1.412e27 m^3. Thus the volume of the core is .011 x 1.412e27 km^3 or 1.608e25 km^3.

Now http://en.wikipedia.org/wiki/Sun#Core" says the density of the core is about 150g/cm^3 or 1.5e5kg/m^3. So since mass = density x volume I get the mass of the core to be:

1.5e5 x 1.608e25 kg = 2.413e30 kg. This exceeds the state mass of the sun (1.9891e30 kg). What is wrong here?

 

[cjl]

That's probably the density at the actual center of the sun, not the average density of the core. Because of that, your mass is coming out too large.

 

[nasu]

In your second link it says that the density of the core varies from 150g/cm3 at the very center to 20 g/cm3 at the edge of the core.
So cjl is right. The average density of the core is significantly lower than 150.

 

[JeffKoch]

I didn't check your numbers, but yes, there isn't a single number for the density of "the core", the density varies with radius. You'd need to integrate over the radial density distribution, and I don't think that's an obvious function since temperature varies with radius too.

 

[pmacias]

I understand your confusion and concern about the calculations you have done for the mass of the core of the sun. However, it is important to note that the mass of the core of the sun is not a fixed value and can vary depending on the methods and assumptions used in calculations.

Firstly, the core of the sun is a highly dynamic and constantly changing region. Its temperature, density, and composition can vary significantly at different depths. Therefore, using a single value for the core's density may not accurately reflect its true mass.

Additionally, your calculation assumes that the entire core has a uniform density, which is not the case. The core is actually composed of different layers, with varying densities, temperatures, and pressures. This makes it difficult to accurately calculate the mass of the core.

Furthermore, the measurements and estimates of the sun's mass and volume are not precise and can have a margin of error. Therefore, your calculations may be affected by these uncertainties.

In conclusion, while your calculations may show a higher mass for the core of the sun compared to the total mass of the sun, it is important to consider the limitations and uncertainties in these calculations. The exact mass of the core of the sun is still a topic of ongoing research and cannot be accurately determined at this time.