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If the earth stopped rotating, days would be about 365x longer.
I wanted to figure out a more exact answer, but I'm hung up on the fact that the length of a day is influenced by rotation and revolution together.
I have a feeling this requires calculus. If Sir Isaac Newton were here, I think he'd know what to do.
It could be tidally locked to the sun too. Then days would truly cease to exist, you'd just have a hot side and a cold side.
It could, and eventually would, but the premise of this comic is "the earth has stopped rotating", not "the earth is now rotating at 1 revolution per year".
Tidal locking still requires the planet to be rotating
365x24=8760
Open 8760 hours a day, 7 days a week
365.25 days I believe is the better approximation because it's the rough time it takes Earth to be in the same spot - hence the leap years