Re: Equinox discrepancy

[Gianni Ferrari]

Hello All, the differences that sometimes we may found on the instants of the Solstices and the Equinoxes depend, in my opinion, on the fact that the Mean Geocentric Longitude and the Apparent Geocentric Longitude of the Sun. are often confused among them or considered equal The Apparent Geocentric position of the Sun is the position in which it would actually be seen from the center of the Earth, displaced by the light aberration and referred to the coordinate system determined by the instantaneous equator, ecliptic and equinox ( i.e. corrected for nutation and obliquity) The geocentric apparent position is therefore the direction in which an observer at the center of the Earth would see the Sun. The Mean Geocentric position of the Sun is the position referred to the mean equinox of date ( not to that of the instant of observation and to mean obliquity) and not corrected for the aberration The difference from Apparent and Mean Longitude of the Sun are very little ( 20-30" ) and the instants in which these quantities became = 0 , differs for few minutes ( about 10 - 30) For example , in The Nautical Almanac we find the Mean Longitude of the Sun referred to the mean equinox of date and not the Apparent Longitude. This value can be reduced to the true equinox, obtaining the Apparent Longitude, by adding the nutation in Longitude at date diminished by aberration. Since the Mean Longitude of the Sun can be easily calculated, with a simple series with 3 terms, in many programs, for simplicity, the Apparent Longitude is not calculated and the instants of the Solstices and Equinoxes are found making equal to 0, 90, 180,270° these quantities. Therefore the instants obtained in this way differ of about twenty minutes, from the correct instants obtained making equal to 0 the Apparent Longitude.   The declination of the Sun at the Equinoxes is always very small and if we calculate the instants of the Equinoxes making equal to 0 the declination, we have instants very near to those calculated correctly For instance on September 22 2001, in the instant of the Equinox, at 23h 4m (GMT Greenwich Mean Time) the Sun has a declination of around +0.18" and since the declination changes of 23' 22" = 1402"/ day, the Declination would become =0 around 11 seconds after the instant written above. Using the Mean Longitude instead, we obtain, for the instant of the Equinox, the time 22h 48m GMT that is near to the value reported by Bill Gottesman   A wish to all for the next "Feriem Augusti" day  ( August 15) Best Gianni Ferrari