Even if this weren't insanely expensive... The sun is far away in terms of delta-V. Getting to low-Earth orbit requires something like 9.4 km/s of delta-V. Get

Even if this weren't insanely expensive... The sun is far away in terms of delta-V. Getting to low-Earth orbit requires something like 9.4 km/s of delta-V. Getting from LEO to the Sun requires another 21.3 km/s of delta-V. There are probably transfer orbits that could use gravity assist to make this figure lower, but those orbits spend a lot of time looping around planets and generally hanging out in the solar system, which is probably not the best thing to do with our waste. It's actually cheaper to escape the solar system than to shoot for the Sun - around 18.15 km/s delta-V from ground to escape.