"For a spacecraft to launch toward the sun, it must accelerate to nearly match the Earth’s velocity—in the opposite direction."

Source: https://www.theatlantic.com/science/archive/2018/08/parker-s...

> If nuclear rockets or reactors are built in space, would this be a possible way of handling nuclear waste from reactors already in space?

If you're not already falling towards the Sun, it must mean you're in some sort of orbit around it. So you'd still need to cancel that out.