1 {scene: Death Star control room}
1 Imperial Officer: Orbiting the planet at maximum velocity. The moon with the Rebel base will be in range in thirty minutes.
2 Vader: We can move this thing across the galaxy faster than light and we have to wait to orbit a planet?
3 Imperial Officer: To increase speed we'd need to drop our orbital altitude below the Roche limit and the Death Star will be torn to pieces by tidal forces.
4 Vader: Since when did physics become important in the Empire?!

If you assume the Death Star does indeed have to orbit Yavin (rather than just scooting around under its own power, as it obviously is capable of doing), then the Imperial officer has a point. To orbit faster without flying off into interplanetary space, you have to orbit lower. And below a certain altitude, called the Roche limit, tidal forces generated by the primary object (Yavin in this case) will tend to rip the orbiting body apart.

And yes, the structural strength of the Death Star means it can orbit a bit below the idealised Roche limit without flying apart, but the officer has already stated that they are orbiting at maximum velocity, which implies that they are right at the actual limit below which the Death Star would be threatened.

---

2013-06-12 Rerun commentary: It's good to have a stormtrooper in the background, just... guarding.

The stormtrooper guns are actually just a LEGO megaphone reversed, with an orange piece on the end. I can just imagine some poor trooper accidentally picking up the wrong piece of equipment and getting blasted in his own face with a wave of amplified sound.