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

It’s kind of like in trigonometry where if you know at least two angles or side lengths or even one of each you can calculate the rest of the angles and side lengths. Except for the angles and side lengths that we know are actually the periodic table of elements. We just keep coming up with new tools of measurement and mathematics that increase our precision when it comes to measuring things that are far away.

We know how hot the sun’s core is within a shrinking margin of error because we know what the sun is made of and how much there is and we can calculate pretty precisely exactly what happens when you put that quantity of that specific stuff in that specific amount of space in a vacuum.