Rockets are big. Particles are small.
The Space Shuttle weighed about 2 million kilograms. A proton, which is mostly what CERN is slamming into things, weighs 1.6 x 10^-27 kg. That’s a difference of about 33 orders of magnitude.
For scale, the **entire Earth** weighs about 6 x 10^24 kg, so a rocket is as much bigger than a proton as the Earth is than a tiny speck of dust weighing micrograms.
> Alternatively, why can’t we put a particle accelerator on the back of a rocket and use that?
You could, and in fact, [we do](https://en.wikipedia.org/wiki/Ion_thruster). But because particles are so light, the amount of thrust generated is very very very very very very very VERY small. Such engines can’t even lift their own weight, much less a rocket attached to them.
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