Space won't work for the kind of physics the LHC does. The fundamental problem is that collider physics relies on being able to create collisions of exactly kn

Space won't work for the kind of physics the LHC does. The fundamental problem is that collider physics relies on being able to create collisions of exactly known quantity as your input (eg in the LHC's case, proton-proton collisions at a 14TeV centre of mass energy). If you don't control the input, you can't extract any information about the output you detect, in the same way that you can't create a simulation of snooker by looking at the balls on the table, without knowing how they were set up before being hit. The other problem is that to probe the frontier of particle physics, you need truly immense statistics to get enough of the incredibly rare collisions. Think bunches of hundreds of billions of protons colliding tens of millions of times per second. The upshot is that you'd not only need to build the detectors in space (which are thousands of tonnes with extremely precise electronics that need whole server farms plugged directly into them to process the terabits of data coming out each second), but you'd also need to build the entire collider in space too. Even then it's a rather pointless endeavour, since the colliders require a colder temperature and higher vacuum than even interstellar space, nevermind within the solar system.