In a technical sense, the temperature at the Earth’s core remains unmeasured and has never been directly assessed. The temperature(s) of Earth’s core are educated guesses based on seismic activity, magnetic activity, and the current theories on the Earth’s interior composition.
Scientists use seismic waves (shockwaves generated by earthquakes or artificial sources) to study the Earth’s interior. These waves travel through the Earth, and the way they behave provides information about the composition and temperature of the Earth’s layers.
Changes in the Earth’s magnetic field provide insights into the dynamics of the outer core, which is composed mainly of molten iron and nickel.
Scientists have been able to pinpoint with greater specificity the exact melting point of iron, which allows them to make educated guesses about the temperatures that must exist in Earth’s inner and outer cores.
I am not an expert in geology, so I will summarize my reading of these sources:
[Source 1](https://www.nature.com/articles/363534a0#:~:text=Thus%2C%20the%20most%20reliable%20means,of%20the%20inner%20core%20boundary.).
[Source 2](https://www.scientificamerican.com/article/why-is-the-earths-core-so/)
The Earth is like an apple with its three layers: the skin, the fruity flesh, and the core. The Earth’s skin is called the crust and it is a thin solid rocky layer that we live on, with tectonic plates and oceans and all that life stuff. The fleshy middle part of the Earth is called the mantle and is mostly hot solid rock with some liquid rock on the outer layers, also known as magma or lava when it comes out of the ground. The core of the Earth is also called the core, and it has an outer layer of liquid metal with a solid inner metal core.
How do we know what the inside of the Earth is made of?
**Wave Impedance**
Slap a wall and you can hear a thud. If you slap over the part with a stud behind it you hear a higher pitch thud. If you play a guitar and pluck the string it makes a sound, and if you tighten the string it makes a higher pitch sound. So sound travels through things differently depending on how stiff and dense they are.
**Density**
Rock and iron have different densities, a milk jug full of iron is a lot heavier than a milk jug of rock. The Earth is really big and is squeezing everything inside it to crazy high pressures, millions of atmospheres, so things are more dense. Iron in the middle of the Earth’s core is almost twice as dense as iron we work with on the surface.
**Refraction and Reflection**
When waves move from one thing to another sometimes they partially bounce off or reflect, and will also refract or change speed and direction slightly. Put one hand in water and one above it, you will notice that the hand in the water looks like it shrunk. This is because the light bends when it goes from air to water. This is how glasses work, they are shaped so that when light goes from air to glass to air the angles work out so that the light bends in the opposite way that your eye is mixed up, so things look normal. If you carefully measure how a wave is bent when it goes through a thing you can figure out what the thing is. Water and glass bend light different amounts, so if you can measure the amount the wave bent you can figure out if the thing is glass or water.
**Seismic Measurements**
Earthquakes are powerful and can shake the entire Earth. We are really good at measuring how much the ground is moving, and so can measure motions from Earthquakes on the other side of the Earth. When lots of different labs around the globe measure the motion of the Earthquake and compare notes after, they can figure out how long it took the shaking to get to the different labs. Putting all that together they can figure out what materials or layers of materials the shaking went through. From the series of reflections and refractions and when all those signals arrive, scientists have determined that the Earth is made of a bunch of layers of liquid and solid, and also the density of the layers.
**Results**
So we also know that the outer mantle layers are mostly made of rock, and the core is mostly made of iron. We know how thick these layers are, and where it changes from solid to liquid and from liquid to solid. We can measure how the density changes with depth, and by comparing that with measurements of how density changes with pressure that we can do in our labs, we can figure out what pressure the layers are under. At a certain pressure and temperature certain things will melt in iron in certain amounts, so by carefully measuring what stuff is melted into the layer of liquid metal core that is touching up against the solid metal core, we can figure out what the temperature is at that boundary. We can put all this together as a model of the pressure, density, and temperature of the Earth, and see if it makes sense with the other bits we know about the Earth, how we think it formed and what we see about how other planets formed.
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