Question

Would it be theoretically possible to create a hadron collider in space by orbiting particles around a planet?

Answer 1

Not by orbiting particles around a planet. The LHC needs a lot pf precision to work. The proton beams need to travel along the exact path we tell them to, and they must collide in a precise area. In space, due to the gravitational field being nonuniform (nearby massive bodies will cause perturbations which will change with time and be impossible to circumvent), we really can't do much about that. Aside from that, there are a lot of high energy particles traveling through space already (solar wind/etc).

That aside, we have no way of accelerating the particles. Particle colliders send the beams on a circular path. They are continuously accelerated, and after some number of laps, they are made to collide with a reverse beam. Orbiting particles can't be easily accelerated, without adding a superconducting ring. And, if we have a superconducting magnet ring, then we don't need the planet in the first place--we can keep the system anywhere.

In short a large particle collider can be built in space if we can amass the necessary resources -- but utilizing a planet's gravity for anything other than keeping the entire collider in orbit is a fools' errand -- so using the orbits is out of the question.