Nothing. Nothing happens when you fly into a planet, moon, or sun in Starfield. Your spaceship will get stuck 9990 meters above the surface of the planet and you will keep flying infinitely into an invisible barrier. The screen will look pixelated because you are so close to the planet and the game was designed for viewing them from afar.
You can’t land on planets or moons by flying into them.
As for suns, for one they are too far away to fly there, and the same thing happens where you just keep flying infinitely and never actually reach the surface of the sun.
So unfortunately, it’s quite anticlimatic and just a waste of time to try. If you still want to try it, the quickest method would be going to Sol > Luna (moon of earth). Since moons are smaller you spawn closer to them. Get a fast ship, like the one you obtain from completing the Freestar Ranger’s questline. And then just keep flying straight towards the moon. By activating the scanner it will show the distance to the surface. It will still take like half an hour but the distance from where you spawn to the moon’s surface is much shorter than when you try it with bigger planets.