Can the moon be moved out of orbit by rockets?

Answer

There is no rocket powerful enough to do this. The reason is the gigantic mass of the moon compared to that of a rocket. A Space Shuttle has a final mass of about 20 tones, so 20000 kilograms when it enters orbit around the earth.
The moon has a mass of 7.4 10²² kilogram, so 3.7 billion billion times more. With a shiuttle you could see the moon a speed on the order of 10^-15 m/s can give. After one year, the moon would have moved a few hundred thousandths of a millimeter.
NASA did, of course, bring moonSTONES to Earth during the Apollo project. I thought the former USSR was once able to bring a moon rock to Earth via an unmanned probe. Maybe they meant moon rocks in that comic.