How hot is the core of the Sun?



Warning: mathematics ahead





Hydrostatic Equilibrium is the balance between pressure pushing the star apart, and gravity pulling the star inwards.

Newton's first law: F=ma


change in force = mass * acceleration of gravity


change in pressure = mass * acceleration / area


change in pressure = mass * G * mass / radius4


pressure in center = G * mass2 / radius4


now we know that pressure = constant * density * temperature, so


temperature in center = pressure in center / (constant * density)


and we know that density = mass / volume, so


temperature in center = G * mass2 * radius3 / (constant * radius4 * mass)


temperature in center = G * mass / (constant * radius) = 20,000,000 K



The Sun's core is