I hope the question is suitable for this forum....

Watching Star Trek: The Next Generation, I have found at least a couple cases where a navigation malfunction on a shuttle makes it fall towards the nearby planet in cuestion of minutes (note that the ship is just passing by, not getting out of the planet).

I'm not an expert physicist, but judging by the way we move our probes through the solar system and that even asteroids just pass near earth without blinking I understand that you have to spiral around the planet for some time before entering it and crashing on its surface... even the Tiangong-1 chinese station took a long time to fall.

I know the situation is created in the sake of drama but I wonder about the possibilities for a shuttle to get captured by a planet's gravity and be forced to crash almost instantly, making useless every rescue effort.

Any of you could enlighten me?