During the part when Picard is on the planet and the rocket is fired at the star, it appears as though just as the rocket disappears from sight, the star goes black. Now it takes eight minutes for light from the sun to reach the earth. Even assumming that the rocket had warp, which it probably didn't, it still should have taken a few minutes for the light to stop. If the planet was that close, it would have been too hot and the star would have appeared much bigger.
I'm not even going to get into the facts about stellar structure.