Estimating The Sun's Central Pressure and Temperature
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
(how did he do this?)
So that he derives
We know these
numbers, so we can calculate the pressure:
Being Homer, he was only a factor
of 100 too low. To do it right we need to actually integrate
the equation of hydrostatic equilibrium:
But we don't know M(r) and rho(r) explicitly, so this is
hard. But it can be done through models, and we get the better value of
What about the central temperature?
Use the equation of state (the ideal
gas law) to estimate the central temperature:
and we get
which, actually isn't too bad. The actual "best" value
is more like 15 million K.