The earth sits in a perfectly balanced belt around the sun at the perfect distance to support life as we know it, and if it were to move just a few miles off course as a result of the moon exploding we would end up freezing and getting extremely hot as the earth wobbled around in a much more unstable orbit. Basically there would be nothing we could I and we would all die.
the distance isn't that big of a deal...
and it wouldn't "wobble around" in relation to the orbit either
the tides would be greatly affected, which would cause a whole lot of problems. there wouldn't be the moon to reflect light at night anymore, which would also be a problem.
it would wobble though. just on its axis, not in its orbit around the sun. which would cause a lot more weather issues than any change in our distance from the sun that might happen