>>12128124>Why don’t we send satellites with ion thrusters to orbit some planet for a few years until it reaches relativistic speeds?
1. Ion thrusters use propellant and therefore obey the rocket equation. They get much more impulse per gram of propellant, but they still operate based on exhaust velocity and wet-dry mass ratio.
2. Ion thrusters don't have near the Isp necessary for a single stage to have enough delta V to achieve relativistic velocities. The highest Isp ever achieved in experimental electric thrusters on Earth is somewhere around 20,000 seconds, I think. Even if you designed a probe with a really good W/D ratio, 90% propellant by mass, that'd still only get you ~450 km/s of delta V. Good, in fact in a similar range as the single-stage delta V budget of a decent Orion nuclear pulse drive, but nowhere near relativistic.
3. Because ion thrusters have such low thrust, even if they had the efficiency necessary to get up to any significant fraction of light speed, it would take actual centuries of continuous thrust in order to accelerate that much. Ion drives continuously wear with use, because they're subjected to a low density wash of extremely fast ions the entire time they're operating, so you'd be very lucky to even get a decade out of a single thruster.
4. If you're accelerating, you're not going to be sticking around in orbit of a planet for very long. Orbits are literally defined by velocity and vector, so if you change velocity you change the orbit. You're not orbiting anything at relativistic speeds if it's less massive and dense than a heavy white dwarf star.