Let's use the equation of hydrostatic
equilibrium to ** (very crudely!) **estimate the central pressure in the sun.

Remember we have

Homer estimates dP/dr to be

So that he derives

Use the equation of state (the ideal
gas law) to estimate the central temperature:

Make assumptions:

- constant density

- 100% hydrogen gas

which, actually isn't too bad. The actual "best" value
is more like 15 million K.