Сравнение Эспенака и Такесако

Автор сообщения: gorm
Дата и время сообщения: 22 December 2006 at 20:01:13:

В ответ на сообщение: Re: Конференция_Астрономия

Я нашел ссылку на сравнительное обсуждение точности этих расчетов в листе рассылки о котором я говорил. Таких обсуждений было еще несколько.

Арбитром здесь выступает известнейший специалист по астрономическим расчетам - Jean Meeus, автор собственных печатных канонов затмений и блестящих книг "Astronomical Algorithms" (раннее издание в версии для калькуляторов даже была переведена на русский),, "Mathematical astronomy morsels", "More Mathematical astronomy morsels".


From : John Tilley

To : Sent: Wednesday, October 04, 2000 5:53 PM
Subject: [SE] 5000 year Lists of Solar Eclipses

I was trying to combine data from two lists of Solar Eclipses - one produced by Fred Espenak (NASA - A 5000 year list of Solar Eclipses) and the other by Takesako Shinobu (EMAPWIN - Besselian data files - 6000 years) - and to my surprise found a number of differences. Fred has six partial eclipses that are not eclipses in Takesako's list and vice versa. As a result the total number of solar eclipses for the period 2000BC to 3000AD should be the same in both lists - ie 11897 - however Takesako managed to lose the final eclipse (9 Oct 3000).I can think of three reasons for the twelve partial eclipses being different: - Different ephemeris used - Allowance made/not made for centre of mass of moon and centre of figure of lunar disk not being coincident - Different algorithms for the calculation I think they are due to the fact that Fred used Newcomb [1895] for his Solar Ephemeris and Brown[1919] for his Lunar Ephemeris with the 1954 improvements. However Takesako-san used the JPL DE406 ephemeris - The latter is of course more accurate. As a result some of Fred's eclipses are not eclipses in Takesako's list and vice versa. All such eclipses are of course partial eclipses of very small magnitude at the start/end of a Saros. (In his Fifty Year Canon - Fred compares the accuracy of his ephemeris with JPL DE200). There are also a large number of eclipses in the two lists where the date differs by one day - I haven't yet worked out why. (I know that Fred dates the eclipse as the day when greatest eclipse occurs - I don't know how Takesakosan dates his eclipses) Espenak eclipses that aren't eclipses according to Takesako
-1295 8 25
-742 11 28
-727 2 20
-716 7 15
-702 10 8
1107 7 21
(all have positive gamma) Takesako eclipses that aren't in Espenak list
-1979 5 2
-1719 10 31
-1686 7 30
-1140 3 28
-1028 3 19
2883 8 23
(all have negative gamma - except the eclipse of -1719) It would be good to have a definitive Espenak list produced using the JPL ephemeris which covers 3000BC to 3000AD - with centre of lunar mass correction applied
From : Jean Meeus

John Tilley mentions the long lists of solar eclipses by Espenak and Takesako, and found six Espenak eclipses missing in Takesako, and six Takesako eclipses missing in Espenak. I have none of those two lists, as I have calculated my own list of solar eclipses, from - 2000 to the year +3400. My calculations are based on the following sources :
--- for the Sun, the modern VSOP87 planetary theory by Bretagnon (Bureau des Longitudes, Paris);
--- for the Moon, the modern ELP lunar theory by Chapront (Bureau des longitudes), but with improved mean elements for the Moon's orbit as given by Chapront in January 1998. However, I applied a correction of -0.6 arcsecond to the Moon's latitude in order to take into account the fact that the center of figure of the lunar disk does not exactly coincide with the Moon's center of mass.
Actually, for the Moon I reglected all *very* small periodic terms, retaining (for the three coordinates) a total of "only" approximately 5000 periodic terms, instead of Chapront's approximately 37000. However, this can hardly affect the results.
I found that, indeed, the six Espenak "eclipses" missing in the list by Takesako do NOT exist. Sorry, Fred...! On the other hand, the six Takesako eclipses missing in Espenak's list DO exist. For these very small six eclipses I
find the following values for greatest magnitude :
-1979 May 2 0.010
-1719 Nov 1 0.008
-1686 Jul 31 0.006
-1140 Mar 28 0.009
-1028 Mar 19 0.005
+2883 Aug 23 0.001
Note that these dates are in the time scale of Dynamic Time, not Universal Time,

which may explain the difference of one day for two cases (-1719 Oct 31 and -1686 Jul 30 according to Takesako).
Jean Meeus

Обратите внимание, что ошибки у Эспенака как раз того же порядка (меньше процента), что и в случае различения кольцеобразные - полные.
Можете для интереса проверить те же затмения в RedShift.

2506. Равноденственные и «косые» часы - АнТюр 09:54 20.12.06 (101)
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