That is a very good question!! As you know, photons travel at the speed of light: 300,000 km/s, so you would think that it would take them a miniscule amount of time to reach the surface of the sun and escape. However, in reality, a photon inside of the sun can only travel less than a centimeter before it is deflected in another direction by a charged particle (such as a proton). This means that to reach the surface of the sun, the photon is deflected many many times in random directions. Think about it as a path through a labyrinth, where you can't just go straight, but you have to keep taking many turns before you get to the end. So, based on how dense the interior of the sun is (how many charged particles the photon will collide with), scientists can estimate how many turns the photon will have to take, and how long of a path it can travel at each turn. Knowing the speed of the photon (speed of light) scientists calculate how long each of these steps will take. Then, adding up the time it takes for all of these steps, we estimate how long it will take the photon to reach the surface of the sun. The answer is usually around 170,000 years. Of course, no one can directly measure how long this process takes inside of the sun. But, as you can see, if we know some simple facts about the sun from physics - such as how dense it is (how many particles the photon will collide with), as well as how big the sun is, we can calculate the number we need. Here is a nice website from NASA that gives an explanation in even more detail: http://sunearthday.nasa.g...ons/ttt_sunlight.php