6. Insight dawns. First I wish to correct a mistake: ... With Gienah rising heliacally 186 days beyond spring equinox north of the equator the star should somewhat later have lagged behind Sun and be visible in the late night before sunrise. Gienah should be crossing the meridian at midnight ca 90 days after September 23 ... My conclusion is false, because Gienah is following Sun all through the day (September 23). The natural way to count days beyond September 23 is to move half a year ahead because the daytime culmination of Gienah is at noon and not at dawn. Next problem is a bit more complicated. Via Cartes du Ciel I apparently received confirmation of my ideas, viz. that the culmination of Gienah in the night would occur not far from 180º. However, this result is doubtful because I don't know how time is processed in the program and I don't know what its grid of lines means. Instead I wish to think anew and combine my idea above of 90º difference between midnight and dawn in the same night with a measure for nighttime culminations half a year later. When Earth moves around Sun it also turns around creating day and night. There are 365 dawns in a year but in a year Earth has to turn 365 + 1 times because it also moves in a cycle around Sun. Both movements are counterclockwise if seen from 'above':
This means the quarter of a turn between dawn and midnight in a single night has to be extended when we measure from dawn in September 23 to midnight half a year later. Otherwise the stars crossing the meridian at midnight would be such which have lower right ascensions than Gienah. Gienah will cross the meridian in the night at different times depending on the date. When 1 extra turn is needed for Earth in a year it means ½ of an extra turn is necessary for 6 months in order to keep the orientation. Therefore the midnight culmination of Gienah will not be 6 months after September 23 but later. If we wish to follow Gienah from dawn in September 23 to its midnight culmination at a later date it will take more then 90 days. The distance from dawn to midnight is half the night and a quarter of the diurnal cycle. 1 / 4 (of the diurnal cycle) * 1 / 2 (the addition of half a day in 6 months) = 1 / 8. 1 / 8 * 365¼ = ca 46 days. 365¼ / 2 + 46 = ca 229 days. I am satisfied for the moment, but there are details which remain to be considered. Winter is shorter north of the equator than south of the equator and the orbit of Earth around Sun is not a perfect circle. Therefore a rule of adding 229 days cannot be exact but must depend on where in the orbit the addition will take place. |
