Why didn’t the Death Star just jump in a position where it could immediately fire at Yavin 4, instead of circling the planet for half an hour?
Because it was clearly tracking/following the Millennium Falcon. The film shows the Falcon, having come out of hyperspace, arriving at a big red planet and flying under (around) it to a little blue planet. It makes sense that the DS would follow suit and assess things from there.
Wouldn’t the tracking device show them where exactly the Falcon is in relation to the planet?
My own explanation is that there are certain hyperspace routes, which are safe to travel. Outside of these routes, you can only go under light speed. The DS could only enter Yavin’s orbit at this specific point.
The same thing applies to TLJ. Once the Resistance ships were fleeing, the nearest hyperspace access point was behind them, so the FO couldn’t simply jump ahead.
Those are great theories. In the case of the DS in ep.4 I think we’re overthinking it. It seems to me that the visuals were very deliberate in this instance, because George and co. needed that particular sense of tension for the film’s climax - hence the scenes showing the Falcon approaching Yavin and then going beyond to the moon (I think the idea of Yavin itself being a gas giant was deliberate too ie you probably can’t blow up a gas giant). Then we see the DS approaching Yavin and Tarkin gets the “moon with the base is on the far side” call. The DS has clearly followed the Falcon’s path precisely. It makes sense for the DS to come out of hyperspace right where the Falcon did and follow from there. Since Han had already established that hyperspace jumps were a precise business, it makes sense that you wouldn’t risk simply warping to the end point of a tracking exercise (the DS might collide with a planet or accidentally occupy the same space as the Yavin moon). It makes more sense to come out of warp at the edge of the system (where the Falcon did) and mark their progress from there.
By the way I had no problem with the space-chase in TLJ at all. I thought it was a really cool idea and didn’t entertain the notion of FO ships warping ahead and cutting them off. That actually sounds too complicated to me (can ships warp such tiny distances? I guess I’m agreeing with your ‘hyperspace access points’ theory in a way) and I love the sadism of Hux deciding to simply flow with it all and keep the pressure up.
In fact whatever my niggling beefs with this movie, the idea of starting the film immediately after its predecessor, and having that chase be the whole body of the movie is genius as far as I’m concerned. We’re so used to gaps of 1 to 10 years between these films, so this was a real breath of fresh air.