1: To drive or punish one's ass by whipping; but without the force necessary to fully regret the act.
2: Atonement in a half assed way
Mary: "Did you hear what Brad did to Angelina?"
Genivieve: "No, but i bet he'll asternithin himself to get back with her!"
Sarah: "Oh my GOD! Did you hear how Bill crawled back to Hillary?"
Elizabeth: "Ha! I Bet he just went through Asternithin to get out of paying alimony."