# the sun - relationship between gravity and temperature

In the sun's core, we know it's very hot.

I was curious to research why it was exactly and I think 99% of answers are not fully correct. They say that it's because of nuclear fusions.

I'd not agree as it first should be hot to even allow nuclear fusion to happen.

The only assumption why it's that hot is in my opinion: There's huge, huge gravity of hydrogens and the biggest gravity are in the center as every element tries to get to the center. Hence, this means it's much dense in the core that anywhere else in the sun. Due to huge density, we got high pressure there. Density + Pressure must be causing the elements to have very high kinetic energy which is why the temperature is very high.

I might be wrong, but would be great if you could shed some lights on it.

• Fusion contributes to the energy, and therefore temperature. So, in a way, fusion does make the core hotter, but you are also correct that fusion requires high density and temperature to begin with. What I can't answer is how much hotter the core of the sun is as a result of fusion, compared to the same mass and density before fusion started. I'll leave that to the folks here who know the real math. May 1 at 0:35
• @GregBurghardt it's completely the other way around. May 13 at 9:56

Density and pressure, don't produce heat in themselves. It is possible to have something extremely dense and under great pressure that is cold. Gravity also doesn't heat things. It is possible to have something under very extreme gravity, but cold.

However if you increase the pressure on a gas, and hence decrease its volume you must do work on it and this work is converted to heat, causing the temperature of the gas to rise. This is called adiabatic heating.

When a cloud of gas starts to collapse under gravity, the work done to increase the pressure causes an increase in temperature in the core. This mechanism for heating was worked out in the nineteenth century and is called the Kelvin Helmholtz mechanism.

The source of the energy for this heat is the gravitational potential energy in the gas.

This mechanism can heat the core of a star to temperatures at which fusion starts. Fusion releases more energy, and prevents further gravitational collapse and so prevents the core from getting any hotter.

The cores of young proto-stars are unstable, they shine by the Kelvin Helmholtz mechanism, the pressure and density in the core must be increasing. The energy comes from the gravitational potential energy in their gas. The sun is currently stable. Effectively all the energy produced comes from fusion.

The core of the Sun is not hot because of nuclear fusion. The core would be hotter if there were no nuclear fusion.

When a sphere of gas is created, it requires a pressure gradient to support it. This means it will adjust its structure so that it is dense and hot in the middle, supplying this pressure gradient. The gas gets hot because it is squeezed (by gravity) into a smaller volume until it achieves an equilibrium.

However, it cannot maintain that equilibrium because it is losing heat from its surface. This means it continues to shrink and the centre gets even hotter and denser.

This process is interrupted (for 10 billion years or so in the case of the Sun) by nuclear fusion. This can supply the heat that is being lost from the surface and stabilises the star. If you turned fusion off, the contraction would resume and the centre of the Sun would become hotter.