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Whats is volume of mass at the centre of the sun

  1. May 19, 2012 #1
    Thank you
     
    Last edited: May 19, 2012
  2. jcsd
  3. May 19, 2012 #2

    Total solar radius:
    [tex]R_{\odot} = 6.955 \cdot 10^8 \; \text{m}[/tex]
    Inside 24% of the Sun's radius, 99% of the power has been generated, and by 30% of the radius, fusion has stopped nearly entirely.

    Active solar core fusion radius:
    [tex]r_f = 0.3 R_{\odot}[/tex]
    Average active fusion core volume:
    [tex]V_f = \frac{4 \pi r_f^3}{3} = 3.805 \cdot 10^{25} \; \text{m}^3[/tex]
    [tex]\boxed{V_f = 3.805 \cdot 10^{25} \; \text{m}^3}[/tex]
    The proton–proton chain occurs around 9.2×10^37 times each second in the core of the Sun. This reaction uses four free protons (hydrogen nuclei).

    Solar core fusion reaction rate:
    [tex]\frac{dn}{dt} = 9.2 \cdot 10^{37} \; \frac{\text{fusions}}{\text{s}}[/tex]
    Solar mass fusion reaction rate:
    [tex]\frac{dm}{dt} = 4 m_p \frac{dn}{dt} = 6.155 \cdot 10^{11} \; \frac{\text{kg}}{\text{s}}[/tex]
    [tex]m_p - \; \text{proton mass}[/tex]
    [tex]\boxed{\frac{dm}{dt} = 6.155 \cdot 10^{11} \; \frac{\text{kg}}{\text{s}}}[/tex]
    One-third the present volume of the Sun.

    Reference:
    Solar - core - Wikipedia
     

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    Last edited: May 19, 2012
  4. May 26, 2012 #3

    jimgraber

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    Gold Member

    Simple nitpick: one third radius = 1/27 volume, or .3 radius -> .027 volume.
    Still pretty large. I would have guessed much smaller.
    Best,
    Jim Graber
     
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