How do we know the temperature of the Sun’s core, if we can’t even go near it?

Question

I’ve read a lot of astronomy, and it’s always been emphasized how hot the Sun’s core is, 15 million C.

But HOW did we get to that number? Why specifically 15 million and not scientists ballparking it as ‘more than a million’?

I’ve studied transport phenomena in university, so I guessed that maybe they constructed an equation of temperature as a function of radius, and substituted r=0 to get 15 million. But it can’t possibly be that simple, as the Sun has different layers of unknown size (and if known, how do we know?) that we aren’t even about the properties.

If possible, explain this to me as simple as possible, while still describing simply the math that caused the scientist to arrive at the 15 million number

In: Planetary Science

Answer 1

We certainly can’t put a thermometer there, but we can directly measure lots of things about the sun, such as the power density of radiation it produces, the color temperature and size. From this and other variables we can be fairly certain of its mass and composition, then we can model the fusion reaction powering the sun, how much energy is dissipated, density, etc. There’s lots of complex modeling but that’s the eli5.