Calculating the Moment of Inertia of the Sun for Determining Rotational Energy

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To calculate the rotational energy of the Sun, the moment of inertia (I) is crucial, with the formula Erot=1/2*I*ω². Using the sphere's moment of inertia formula, I=2/5*m*r², yields an incorrect value for the Sun due to its non-uniform density. The Sun's core, which contains about half its mass, occupies only 1.5% of its volume, making a uniform density model inadequate. An empirical value for I/MR² for the Sun is 0.059, significantly lower than the 0.4 expected for a uniform sphere. Accurate calculations for the Sun's rotational energy require this empirical approach rather than a simplistic model.
AndersLau
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I want to find the rotational energy of the sun.
Erot=1/2*I*ω2

m=1.9891*10^30 kg
r=6.955*10^5 km


When I am using the formula for a sphere's moment of inertia: I=2/5*m*r2
I'm getting 3.848671797*1047 km*m2

Can i find the moment of inertia in another way? the moment of inertia needs to be in *1046 , to get the rotational energy right.

Thank you.
 
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A uniform density sphere is a fairly bad model even for the earth, which is more or less solid. For a gas it is an incredibly lousy model. The sun's core contains about half of the total mass of the sun but only 1.5% of its total volume.

Unless you want to get into astrophysics, you are going to need an empirical value. From http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html, I/MR2 for the sun is 0.059. Compare that for a uniform density sphere, where I/MR2=2/5 or 0.4.
 
Thank you very much for the answer, that sorts it out. Much appreciated.
I'm waiting with the astrophysics :)
 
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