The reason why they don't take nuclear waste up is because it costs $10,000 per pound of weight on the shuttle to be taken up. Every pound needs its weight of fuel, and that fuel's fuel, and so forth. The tether would be a solution to that. Then, when the time of day is right, just launch lots of nuclear waste towards the sun, not like it'll be hurt by it.
A tether system made throughout our solar system would be amazing. Imagine just flying to Mars or Titan on a giant sling shot. Also, hydrocarbon fuels could be shipped over to Mars (if there is enough O2 in its atmosphere to merit combustion) and we have an on going shake and bake colony to terraform Mars.
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