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Given enough time, the Earth will be incinerated by the sun as it expands into a red giant. Solved the plastic problem!

Though as you said, I'm sure we'll have a few hundred (thousand) landfill planets by then.

On a smaller scale, how about using a mass accelerator to dispose of trash by shooting it into the sun?

I think the sun is further away in terms of energy required than one would expect. You don't just have to escape the Earth, you also need to cancel or redirect its orbital velocity around the sun to get a trajectory that reaches the sun.

Then throw it into space, whatever the direction. The universe is so vast, even if the entirety of the earth was garbage it would be nothing compared to it ;)

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