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
- HOT -> Temperature = 15,000,000 K
- DENSE -> Density = 150 g/cm3 (water=1)
- SMALL -> Radius = 200,000 km (much bigger than Earth)