Gravitational binding energy of the sun?

[Researcher X]

Could anyone give me a figure (in joules/kilo joules) for this?

Wikipedia says (on it's gravitational binding energy page) that the gravitational binding energy of a star is equal to about two times it's internal thermal energy.

I looked for "internal thermal energy" and could not find anything on it at all. I found figures for Earth's gravitational binding energy, but not for the sun.

There's a formula you can do to work it out, but my knowledge of maths is the layman's type, not the type with the "weird symbols" so I would have to have them explained to me.

 

[PeterDonis]

Wikipedia says (on it's gravitational binding energy page) that the gravitational binding energy of a star is equal to about two times it's internal thermal energy.

The Wikipedia article in question is here:

https://en.wikipedia.org/wiki/Gravitational_binding_energy

From the article, the formula for gravitational binding energy for a sphere of uniform density is

$$
U = - \frac{3 G M^2}{5 R}
$$

Note that the Sun, like any star, is not actually a sphere of uniform density, so this formula is not exact for the Sun (or indeed for any actual astronomical object, since none of them have uniform density). But it is a fairly good order of magnitude approximation. If we use the above formula for the Sun, we have $G = 6.67 \times 10^{-11}$, $M = 1.989 \times 10^{30}$, and $R = 6.957 \times 10^8$, which gives $U = - 2.28 \times 10^{41}$ Joules.

The statement about gravitational binding energy being twice the internal thermal energy is a consequence of the virial theorem, and only applies to stars in hydrostatic equilibrium. The internal thermal energy is the kinetic energy, in the star's rest frame, of the particles in the star.