Elementary physics tells us that we actually can move the planets. Launching a rocket into space pushes the Earth a bit in the opposite direction, like the recoil from a gun.
Science-fiction author and trained physicist Stanley Schmidt exploited this fact in his novel The Sins of the Fathers, in which aliens built giant rocket engines at the South Pole to move the Earth. (Read about other sci-fi novels and films that have tackled the problem of moving worlds.)
In real life, however, the Earth is so massive that a rocket would have little effect on its motion. Launching a billion 10-tonne rockets in exactly the same direction would change the Earth’s velocity by just 20 nanometres per second – peanuts compared to the planet’s current speed of 30 kilometres per second.
A few astronomers have tackled the problem of moving planets, but not for dealing with emergencies on human time scales. They’re actually devising thought experiments to understand the dynamics of planetary systems, says Greg Laughlin of the University of California, Santa Cruz. So processes that occur on geologic time scales work perfectly well.
Read more about moving the planet on New Scientist.