[Anotheroneagain]

Yes, I guess you're right, you aren't going from orbit to orbit, you only try to crash something (and actually want to keep the difference to create an impact).

Still, your logic doesn't apply, and hitting something in a higher orbit shouldn't be that much harder. You also only need to nudge it to hit something UP. (though it does get harder with a lesser impact with increasing distances)

I fact there might not be that much of an effect at all when you consider that both Earth and the Oort cloud are in the Sun orbits - you would have to hit something pretty hard in the Oort cloud to create a massive impact on Earth, there would at best be a bit of leverage, which I guess wouldn't outweight the protective effect of Earth's atmosphere, unless you try to send something monumental, at which point you probably can just come down and hit Earth. Consider also the timescales involved.

[lazide]

You might want to do the actual math.

[Anotheroneagain]

Did you do it? That maneuvre would take decades to millenia, and when you use something that far, it may be more efficient to push it into a retrograde orbit so that it hits Earth heads on, instead of chasing after it. It's just absurdly impractical.

Anyway, if you really want to destroy a planet, you want sonething small but fast. It penetrates into the planet, and rips surface on the other side.

[lazide]

Read my comment. Yes I did. Time was in the hundreds of hours.

Dropping things is way easier than throwing things up. This is easy to verify yourself too.