Orbit changing is something we would likely only consider as a desperate last choice.
If our astronomers discover that earth is going to collide with a moon sized piece of space rock, we might want to accelerate the earth's speed to create a larger orbit, or decelerate to make a smaller orbit. By doing so, we might dodge the collision.
I don't give much chance to Hollywood's best efforts. Deep Impact and Armageddon are two recent films to deal with the subject. In one film, earth is saved by exploding an atom bomb on the asteroid. (I don’t know how earth was expected to miss the atomic clouds that might result, but luckily, in the movies you don’t have to deal with that.) In the other film, they can’t solve the problem and presumably human beings face extinction.
I don't think I would want those to be our only options. I personally would like the option of gently nudging earth out of the way of the threatening rock, and this would mean thrusters powerful enough to move the entire earth either higher, lower, faster or slower in its orbit around the Sun.
I suggest this would be our last resort because of the difficulties it would create. If we waited until the last minute and gave a mighty blast of our thrusters, we would likely lose our moon, and instantly rob ourselves of the wonders that all those satellites we've sent up do for us. In one burst, we would lose virtually all of the modern communications tools. We would lose television cable. Without GPS (Global Positioning Satellites) our ships would lose their way. I believe I read that the American navy has stopped teaching its navigators how to read their position from the stars.
It would be really ugly if we lost our moon. First of all, we would sling it off into who knows where, as we exited our position. Think of what it would do to love and romance to have no moonlight in the evening. And, getting back to even more real loss, think of all the undersea life that depends on the rising and falling of the tides. Think of the rinsing and cleaning process that occurs in harbors everywhere as the tides come in and sweep out.
If a moon-sized piece of space debris is on a collision course with earth, and we have to get out of the way, hopefully we'll have a number of years to get ready. If we have a lot of time, we wouldn't need to give a great burst of thrust to avoid the collision. If we used continuous thrusts with very gentle pushes, we might move slowly enough that we could keep our moon with us, (albeit in a less than circular orbit.) We might also be able to keep many of our satellites with us, but I think we would be wise to prepare backup satellites ready to launch if we have to take this course.
Notice one more thing as you think of a giant thrust big enough to effect earth's orbit. It's hard to imagine anyone crazy enough to take such an action. But, suppose a rogue state, with third world disadvantages, decided to rid the west of it's military and economic advantages. I can't think of a simpler way than building a thruster strong enough to make earth exit its orbit. In one effort, the Western Military would be blinded, deafened, and unable to communicate. The Western economies would be crippled by the loss of the computer networking, and the satellite communications and television capabilities. One assumes the major energies of those nations with evolved economies would make their first priority the readjustment of the orbit to contain the damage such a ill conceived orbit shift might have on earth's climate. In other words, all the work would have to focus on repair of the damage, and reconstruction of the lost capabilities.
This is one of many reasons that we must make all possible efforts to avoid thruster wars.
To learn more about our present orbit: