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The stars won't really be affected by anything - they're so far away that even the most powerful solar explosion simply won't reach them. The nearest star, Proxima Centauri, is four light-years away from us, and the blast wave from any solar explosion dies out at distances thousands of times closer than that. There won't be any pulling or pushing either - the Sun's gravitational influence after the explosion would remain roughly the same, just its mass would be distributed throughout space.

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