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**astronomy-particle density/interior temp of sun**

## Homework Statement

The goal is to estimate the interior temperature of the Sun from its mass and particle density.

**a)**What is the average number density of particles within the Sun, given that the average mass per particle is about 10

^{-24}gram?

**b)**What is the approximate temperature necessary for gas pressure to balance gravity within the Sun, given the average particle density from a)?

**c)**How does your estimate compare with the internal core temperature of the Sun?

## Homework Equations

It has a reference to a "Mathematical Insight" problem that uses the equation: M

_{balance}= 18M

_{sun}[tex]\sqrt{\frac{T^{3}}{n}}[/tex] .... M

_{balance}being the minimum mass required to balance the force between pressure and gravity in star formation, and n being particles per unit area.

## The Attempt at a Solution

**a)**

V = [tex]\frac{4}{3}[/tex] * [tex]\pi[/tex] * R

^{3}= [tex]\frac{4}{3}[/tex] * [tex]\pi[/tex] * (6.95*10

^{8})

^{3}= 1.406 * 10

^{27}m

^{3}

density = mass / volume = (10

^{-24}g) / (1.406 * 10

^{27}m

^{3}) = 7.1 * 10

^{-52}g/m

^{3}

Did I do that the right way?

*I have a weird feeling about the mass*.. was I supposed to just use the mass/particle they gave me? So then my volume is the density of one particle per m

^{3}? I'm really confused on that, I'd appreciate any clearance.

**b)**

Well, I'm assuming this is the part they want us to use that mathemtical equation on.. but if I solve the equation for T, what is my M

_{balance}? Is it just what I got for volume times what I got for density? ... That would then be 9.98E-25 g - way too tiny!

**c)**

Not here yet.

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