At the risk of sounding like I don't have a sense of humor- it's not really arbitrary (at least not until you dig way deeper). Celebrating at a time when the earth has completed a revolution allows people to remember exactly when to celebrate- kind of an old-school time-management trick, so to speak. If we didn't have calendars, we could still have rocks sticking up with a line engraved somewhere on the ground to give us that same reminder- almost exactly once every year.
It's a convenience. ;)