you literally are trying to disprove that the latitudinal rotational speed of the earth does not influence rapid transition from daylight to darkness at the equator and slower towards the geographical poles unless you have not forgotten it is daily rotation which causes the transition from daylight to darkness while the spherical characteristics of a rotating earth generate the latitudinal specifics of that transition to believe otherwise is truly remarkable it is that twilight effect and the table of values which indicate the earth's rotation through degrees in hours and until you find a way to incorporate the hour minute second value for rotation through degrees you will have to consider that 'sidereal time' value and the reasoning behind it as invalid