Eli5: how does for over 4.5b years the earths core still hasn’t cooled off?
That’s gravity and radiation times mass.
Earth’s gravity heats itself. Radioactive decay also creates heat. Earth’s crust is a great insulator.
There are a lot of radioactive elements down there and their decays generate heat. The only way that can escape is to reach the surface and radiate sway. That takes a long time and heat is still bring generated, and will be for a long time to come
There are several things that act together to keep it hot.
First, there was a (literally) “astronomical” amount of energy involved in the first place, and the upper mantle and crust are relatively insulative over many miles of thickness, like a wool blanket over a hot water bottle. So, it just takes a very, very long time to get rid of that heat, no matter what.
Then, there is radioactive decay happening in the core. Elements like Uranium keep breaking down and adding energy. It’s like there were millions – probably more like billions – of nuclear reactors in the core doing nothing but heating it up.
There are also tidal forces at work, which are mainly from the pull of the moon and the sun. Those forces rob energy from the moon and Earth’s orbits, and that energy is converted to heat. Imagine all that core metarial being pulled around in a circle, about once a day, for billions of years – it will generate some heat.
Finally, we think of space as “cold”, but a vacuum isn’t actually “cold” – it doesn’t transfer any heat at all. So, all the energy that leaves the earth has to pass through the crust, the atmosphere including clouds, and then radiate away without being reflected (rather than being conducted away as if it were in cold air).