Then sun is quite massive. Energy produced in the center, which is quite large, will be constantly absorbed by other bits of sun, and re-emitted in an arbitrary direction. It sort of “wanders” without aim.
Energy emitted from the surface, however, is all EM waves, light. The light isn’t hitting a whole lot along the way to earth, so it travels at more or less C, the speed of light, and so it arrives quite fast.
When two hydrogen atoms fuse into helium, they release energy in the form of gamma rays. Because the atoms in the sun are so tightly packed together, that energy is re-absorbed by other atoms, only to be re-emitted later. Each jump is very small (on the scale of millimeters or even micrometers) until the energy reaches the outer layers of the sun, at which point it is emitted a final time and escapes the lattice of atoms.
The sun is made up of a number of particles that is impossible for a person to perceive. Whatever number you’re thinking of, it’s probably bigger. These particles are very small and are very easily influenced as far as direction goes. They’re all like little pool balls and each one will bounce around until they 1. Run out of energy (they dont) or 2. Reach the “pocket” (surface).
How long this takes is entirely dependent on how many particles it hits on the way. It’s very unlikely but a particles can shoot right from the core to the surface. It has to not hit any of the 10^24 particles present every cubic centimeter, but it can.
Now compare that huge amount of particles in a cubic centimeter of the sun to the roughly 5.9 particles present in a cubic *meter* of space. That’s basically nothing. That’s like shooting a pool ball down an airport runway in a random direction and seeing if it hits another ball before it gets to the end. These particles will cover that distance essentially undisturbed. Whatever direction they were going once they hit the surface is the direction they’ll go until they hit something, which may not happen for thousands of years.
Imagine a huge crowd of people, all gathered in a big empty field. Each person is walking at a reasonable pace but when they bump into someone else they have to change direction. If the crowd is big enough you can imagine that someone near the center might take hours to reach the edge. Once they do they can walk in a straight line because they aren’t bumping into anyone.
The people that escape the crowd can just walk right to you now. The people in the crowd might be stuck there for a long time.
There is of course a lot more going on inside the sun, but this is the basic idea.
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