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I think it is nearly impossible that the Babylonians thought there were 360 days in a year. I think you are implying that the number of degrees in a circle were chosen because the earth moves through almost one degree of its orbit each day. It's more likely that they chose 360 degrees as an outgrowth of their love for the number 60  because it has so many factors. If you choose 60 for the internal angle of an equilateral triangle you get 360 degrees in a circle.