Well, you need a rotor and a stator. Alternators work by transferring energy to the stator, which is extracted as an electrical current thanks to it being held

Well, you need a rotor and a stator. Alternators work by transferring energy to the stator, which is extracted as an electrical current thanks to it being held in place. You cannot really "hold" something in place (barring an external propulsion system that costs energy), so while you could extract some energy at first due to inertia, you will slow the orbiter down and barely collect more (if any) than you needed to put it there in the first place. An alternative but close system was described in Stephen Baxter's Sapce (Manifold series), with (IIRC) superconducting loops around Io, to collect energy from Jupiter's magnetic field, technically extracting energy from Io's momentum.