Khan has an axe to grind for arbitrary reasons?
Kirk abandoned him on a frozen hell hole, where Khan's wife died of exposure. How in the world could that possibly be called arbitrary?
um, this isn't accurate at all. Khan tried to take over Kirk's ship and kill Kirk himself. Far from "abandoning" him, Kirk let him choose exile in freedom over imprisonment for his crimes.
The shift in the planet's orbit happened months later. Why would Kirk be like "hey, I should really go check on the insane despot who tried to kill me and hijack my ship just to make sure he's doing okay?"