MarkB
Legend
Yes, they know this. Book's ship has a dilithium recrystalliser built in, he mentions in the first episode that it's malfunctioning and he needs to get it fixed.Do the writers of Disco know this? There's been a whole lot of hand-wavium and traveling and transporting vaster distances than other shows have demonstrated. I'm sure the people involved love star trek, but this series doesn't abide limits.
And in the third episode it's a significant plot point that the trip to Earth would have been unfeasible for Book without being able to tag along with Discovery's spore drive jump.
If you want something to pick at, it is an awfully convenient coincidence that Book's ship is just perfectly sized and shaped to slot neatly into Discovery's hangar bay.