What would happen to the moon?
On a more realistic note, this sort of thing does actually happen, but not between a planet and its moon. A runaway star can come about when a partner star in a binary system goes supernova. The runaway keeps going at its orbital speed, but due to the sudden drop in mass of the parent within the orbital radius the star just heads off out of the orbit. Basically only the mass inside the orbital radius will keep the object orbiting. If the mass drops too much the partner will disappear off. You can calculate how much mass must be blown off for this to happen relatively simply.
I think it depends on the exact cause of Earth’s destruction and how it happens. Notice that the moon orbits the Sun on its own accord, besides orbiting Earth, so if Earth simply disappeared there would be a good chance of the moon keeping a similar solar orbit. An explosion with sufficient magnitude to cause what you describe will generate a debris impact wave that will certainly intersect the moon’s orbit and send it travelling to some direction. At this point Earth’s gravity has ceased to have any significant effect. From then, it may be captured by another planet gravity field (Mars or Venus), enter a stable orbit on its own or collapse into the Sun. If some alien kid just slices the Earth gently with her dimensional scissors, then I don’t know what happens. Maybe the moon joins the new belt, since it is already orbiting the sun now, but ceases to orbit what was the Earth.
Something like this already happened once in the Solar System’s past, it is thought by planetary astrophysicists. It’s how the Earth-Moon system got here. The leading hypothesis is that the Moon (which is very much made of the same stuff as the Earth’s crust) was formed when a then-smaller Earth was impacted by a smaller planetesimal some 4 billion+ years ago. The collision completely destroyed the planetesimal, and ripped off huge portions of the Earth’s crust (which at the time was mostly liquid). A huge could of molten rock and such ringed the Earth for awhile, which eventually coalesced into what we call the Moon. The Earth picked up some extra mass from the planetesimal. The majority of the mass involved in the impact ended up staying a part of the Earth-Moon system. So, assuming the Earth was not destroyed by some really outlandish means, something like that would just happen again. The Moon would not go careening of out of the Solar System, nor would it fall into the Sun. It wou
The Moon orbits the earth in the same direction as the Earth orbits the Sun; therefore while it is inside Earth’s orbit it is orbiting the Sun both closer to and slower than Earth. But closer orbits have greater orbital speeds. So I think that if the Earth’s mass were dispersed outside the Moon’s orbit while the Moon was waning crescent or new, it would fall into the Sun. Conversely, if the Moon had been waxing gibbous or full it would be moving faster than orbital speed and would fall away from the sun. Here, this might help. If the Moon were waxing crescent or waning gibbous, though, it might have enough momentum to be thrown across Earth’s old orbit into (or past) an orbit appropriate to its speed.
Well, I for one wouldn’t assume the mass of the Earth would go anywhere but simply create a belt around the orbit that the Earth used to have. Additionally, I don’t know/think this mass would ever form another planet again even if it was to collect into one large mass. As for the moon. If the mass of the Earth spread out, either in a belt or by flying off in some other direction, to such a degree that the gravitational pull on the moon was lessened, the moon would fly off in whatever direction it happened to be going at that moment. The only think keeping the moon in orbit is that it is constantly falling toward the Earth due to gravity. An object in motion, tends to stay in motion, and without the gravity keeping it from going in a straight line, it would just do that: go in a straight line. As for where it would go, well that would depend on the time of the month and the time of the year this event happened…
