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

AI Thread Summary
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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