On the reversal of the rotational momentum of Earth : a derivation and analysis of the Herodotus equation

Ancient texts contain statements about the change of the year length in days, requiring adjustments of the calendars, and the change of the location where the Sun rises and sets, implying a change of the direction of the rotational momentum of the Earth, more precisely a reversal if the positions of sunrise and sunset would exactly interchange. Mechanisms that may change the axis direction have been recently considered. Changes due to impact with a sufficiently large asteroid or comet have been studied by Barbiero [1]; changes due to the torque by a sufficiently large body passing near the Earth have been considered by Woelfli and Baltensperger [2]. Changes of the orbital parameters, hence of the length of the year, have been considered by Brunini [3] for the case of an impact. To our knowledge changes in both the rotation and revolution parameters, that are expected after this type of interaction, have never been modelled mathematically. Here we provide under simplifying assumptions such an analysis