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[Star Wars] How would Vader and Luke go about taking out the Emperor?

Had Luke decided to join Vader while on Bespin, what would their plan be? How would they assassinate the Emperor? What would they do to ensure continuance if government?
gpt
I've posited before that, as soon as Vader learned concretely that the pilot who destroyed the death star was his son, Vader planned on murdering Palpatine. After all, Palpatine's lies about Padme dying and taking the unborn child with her was what broke him as a human being, and left behind the superpowered puppet that eradicated the last of the known jedi. During the conversation on the Executor, Vader pleaded with Palpatine to make Luke into an ally, rather than kill him like all the others. So there was *something* there inside of Anakin even back then.  

So it's possible that Vader would have absconded with Luke the instant he agreed to join Vader, and they would have gone somewhere Vader thought would be hidden from Palpatine's view. (perhaps Mortis?) There, Luke would have been fully trained in Vader's view of Sith philosophy, had his immense potential in the force unlocked, and forged into a weapon meant to kill one man. 

And honestly, with the chosen one and his son, both of whom had potentially limitless abilities with the force so long as they believed in themselves and their power, they might have stood a good chance against the Emperor. I've also speculated that Luke had just as much potential power as Anakin, but without the glaring personality flaws that prevented him from fully committing. So if anyone in the galaxy had the raw power to defeat Palpatine in a stand-up duel, it would be Luke. (and also Leia, if she was ever trained)

As far as continuance of government, Anakin has always held a childishly naive view of power, and would have assumed things would run as they had for the last several decades. He might have assumed that he could maintain power by being tough, intimidating, and powered by the force. He would have been dead wrong.

Or, if he had matured since his talk with Padme about being cool with total dictatorships, he would leave the running of the Empire to the Grand Moffs or other group of leaders, and taken Luke somewhere secluded where they could delve deeper into the philosophy of the Sith and further their knowledge of the dark side.