It is a myth that black holes are like a cosmic vacuum cleaner that just hoover everything up. The amount of gravity a black hole generates is still dependent on its mass, and the mass of a start doesn’t magically increase when it implodes and turns into a black hole.
I am pretty sure* that if the Sun were to implode into a black hole, and somehow that process itself wouldn’t destroy the planets, all the planets would just keep revolving around it. Sure, earth would become completely inhospitable for life due to the lack of solar energy, but the *orbit* of earth wouldn’t change.
* I am not an astronomer or physicist so I might be very mistaken though.
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