Well, we'd need to apply 40 km/s of delta-v. The moon weighs 1/80th as much as the Earth. By the rocket equation, we'd have to throw the material of the Moon

Well, we'd need to apply 40 km/s of delta-v. The moon weighs 1/80th as much as the Earth. By the rocket equation, we'd have to throw the material of the Moon away from Earth at 3219 km/s or 1/100 of the speed of light in order to accelerate Earth enough.