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As far as I am aware, we can calculate GBE using the formula U = (3*G*M^2)/(5*r), but it seems like this formula gives results that are different than what some sources say the Sun's GBE is. Upfront, plugging in the values we know of the Sun into the formula, U = 2.277164x10^41 seems to be the answer. However, in these sources the Sun's GBE is cited to be 3.8x10^41. Still in the same ballpark, but not the same, and different from what is calculated. For the Stellar Structure source, scroll down to page 5.

Another user pointed out that stars have far more dense cores than outer layers, and thus the GBE formula lowballs their true GBE. However I question this, as attempting to calculate the Earth's GBE using the aforementioned formula still gives a result very close to a well-sourced number, despite the Earth also being more centrally dense due to our iron core. He then pointed to this source (page 101, equation 90), saying that

*n*needs to be added to the formula to compensate for non-uniform density. However it seems like this is in reference to Omega, which was previously used as Gravitational Potential Energy.

Is GPE the same as GBE?

So my big question is this: Does average density account for the increased core density when using the aforementioned GBE formula, or does it not compensate enough? If the formula does not account for non-uniform density enough and an additional variable is needed, and that variable is

*n*of the formula listed on page 101, how do we find

*n*for other stars?

As it stands stars such as UY Scuti are less durable than our own Sun, given the formula, which doesn't seem to make sense, since large stars have more dense cores with higher thermal energy than our Sun, or so I have been told by the aforementioned user. In fact, according to the information on radius and mass on many stars, smaller stars seem to be more durable than larger stars, and vice versa. This seems to be very unusual, as I would assume that a star measuring several AU in radius would be higher in GBE than a star smaller than our own Sun.

Here is the full thread for those interested (and dedicated). I really appreciate any help I can get, as it seems like for every answer I find I come out with another question. Thanks for your time!

http:// https://www.astro.umd.edu/~jph/A320_Stellar_Structure.pdf