That’s 2.3 seconds (432,000/186,000) at the speed of light in a vacuum (supposedly) A photon prob. takes less that 10 seconds to reach the sun’s surface if that’s true!
The Random Walk
Imagine there’s a guy so drunk that he needs to hold on to a light post to stand up. He wants to get to the next light post, just 10 steps away, but he’s so drunk that he can’t walk in a straight line. Heck, he’s so drunk that after he takes one step his next step could be in any other direction. That’s what physicists and mathematicians call a “drunkard’s walk” or “random walk” problem. The question is, how long will it take that guy to get from one lamppost to the next? The answer is that if his starting point and ending point are separated by 10 steps, it will take him — on average — 100 steps to get there — that’s 10 squared. That’s the same situation a gamma ray faces in the core of the sun.
Assumptions
When you’re trying to solve a random-walk problem, the most important thing you need to know is how big the steps are. There are two problems with figuring that out for a gamma ray photon in the sun. First, conditions are not the same all throughout the sun, so the distance between gamma ray “crashes” with other particles changes. Second, no one has ever visited the center of the sun, so some assumptions need to be made, anyway. There are all sorts of reasonable assumptions, varying from one-tenth of a millimeter to about a centimeter. The choice of this distance has a big impact on the time calculation.
How Long it Takes
The radius of the sun is 700,000 kilometers, which is 7 trillion “steps” if each step is a tenth of a millimeter, and 70 billion steps if each step is 1 centimeter. From the drunkard’s-walk problem, you know that the average number of steps it takes to get a certain distance is equal to the square of the number of steps it would take to go in a straight line. So it would take 49 trillion trillion steps of 0.1 millimeter and 490 billion trillion steps of 1 centimeter each. The time it takes to travel those steps is the total distance divided by the speed of light. So, if you think photons only travel 0.1 millimeters between crashes, it will take more than half a million years for the photon to escape the sun. If you think it’s about a centimeter, then it will take about 5,000 years for the photon to get outside the sun.