Consider a cylindrical region (length **dr**,
end area **dA**) at a distance **r**
from the center of the sun:

And the cylinder has properties

Now, define the quantity

so that we have

What balances this gravitational force? **Pressure**.
So let's calculate the pressure acting on the cylinder. *(remember
Pressure = Force/Area)*

The cylinder feels the pressure
from the stuff above it pushing ** down**, plus the pressure from
the stuff below pressing

and the force associated with this pressure is

OK. ** These
forces must balance** for the sun to
be in equilibrium:

For an ideal gas