Could a particle accelerator launch a satellite?
Not entirely. You could theoretically get a satellite up to orbital speed with a linear accelerator, if you had a long enough run and used a high enough acceleration. But there are two large problems: First, the muzzle velocity of such a gun would have to be substantially greater than orbital speed (18000 miles per hour), and any object moving that fast generates a lot of heat. In effect, you’d be going the same speed leaving the atmosphere as a de-orbiting satellite goes when coming back into the atmosphere. So you’d need a heat shield just to launch the thing. Second, the orbit of such a satellite would have its perigee right back at the altitude of the muzzle of the accelerator. So you would still need to thrust the satellite once in orbit, to get the perigee up out of the atmosphere.
