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Honest question could this be feasible with a few dozen satellites positioned above the Van Allen Belts to accelerate particles, and just letting the particles raw dog the solar wind and ride around Earth’s gravity well between each acceleration satellite? Cause that would be badass

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No, to orbit the earth at an height of let’s say 1000 km you would need a speed of around 7km/s. If you go faster, you don’t follow an circular orbit. Wirh around 11km/s you would be so fast to leave the gravity well of earth. The particles in those colliders are almost moving at the speed of light. To be exact, they move only 3.1m/s slower than the speed of light, so almost 300000km/s. They would fly almost straight and would be barely influenced by the gravity well.

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