## Would the delay cause the box to move?

Well that is why the box is there so any movement of the sun causes the earth to move with it and vice versa. Since you couldn't make sun move away since that would cause the earth to move aswell, you just turn off the sun or blow it up, just as long as it is no longer there gravitationly. Also the sun and the earth are fixed in place inside the box.

 Quote by nemesiswes Well that is why the box is there so any movement of the sun causes the earth to move with it and vice versa. Since you couldn't make sun move away since that would cause the earth to move aswell, you just turn off the sun or blow it up, just as long as it is no longer there gravitationly. Also the sun and the earth are fixed in place inside the box.
Okay, is the box closed? If so, then it is a closed system. The mass of the sun remains in the box. The box may shift, but will come to rest again with the centre of mass still inside the box (though not necessarily at the same place inside the box.)

 Maybe another way to phrase the question would be that there is a space probe stationary 1 AU from the Sun firing its thrusters towards the Sun to stop it from falling towards it. All of a sudden the Sun disappears from the area (rapidly accelerates elsewhere or an anti-Sun annihilates with it and its mass-energy is quickly dispersed as photons) and around this time the space probe runs out of fuel (not sure if relativity of simultaneity will affect this). For the next ~8 minutes, will the probe accelerate towards where the sun once was until the "gravitational wave" meets it?
 Well the box is closed in the sense that the sun and the earth stay in inside but it is open in that the gravity can extend past the box, just not interact with the box. To make it easier, it is just floating out in space far way from other objects. Also in response to Waterfox, I think the anwser is yes. It makes sense that it would be yes at-least