§731 The age of re-innovation is at hand (the first year of the 20th century): I-16.

I-16 (§731):

Scythe to the pond joined toward Sagittarius
In its high APSIDE of the exaltation,
Plague, famine, death from military hand:
The age of renovation is at hand.

(Faulx a l'estang joinct vers le Sagitaire
En son hault A V G E de l'exaltation,
Peste, famine, mort de main militaire:
Le siecle approche de renovation.
)

NOTES: [This article supposes the preceding ones of mine: §8, §9, §10, §11, §12, §13, §14 and §15 of A l’Entrée des Prophéties, first published on line in 2009.]

AVGE: = APSIDE (apsis). « auge, s.f., syn. d’apside (synonym of apsis).»
(Godefroy); « AUGE, s. f. - Astron. Auges s’emploie quelquefois comme synonyme d’apsides (AUGE, Astronomy. Auges is used sometimes as synonym of apsides).» (Landais); « APSIDES, subst. mas. plur. t. d’astron., les deux points de l’orbite d’une planète dans lesquels elle se trouve à la plus grande ou à la plus petite distance du soleil ou de la terre. - Apsides exprime proprement les deux sommets d’une courbe (APSIDES, term of astronomy, the two points of the orbit of a planet where its distance from the Sun or the Earth is either the greatest or the smallest).» (Landais).

Hault AVGE: = high apsis = aphelion; « apsis, n. (pl. apsides pr. -dēz), aphelion or perihelion of planet, apogee or perigee of satellite.» (Sykes); « apsis - n. (pl. apsides) the extremities of the major axis of an elliptic orbit, generic term for apogee and perigee: the higher apsis aphelion (of a planet); apogee (of the Moon)/ the lower apsis perihelion (of a planet); perigee (of the Moon).» (Koine).

Son hault AVGE: = the aphelion of Saturn.

Thus the first hemistich seems to concern an astronomical event as the astronomical terms of Sagittarius and APSIS suggest it. And In this context, scythe (faulx) refers « to Saturn, who (in astrological symbolism) carries a scythe.  The implement is a throwback to the origins of this planetary god as an agricultural deity, and as a descendant of the Greek time-god, Chronos. (The scythe-bearing ‘Father Time’ of modern imagery is cognate with this Saturn.).» (Ovason, 1997, p.91).

Estang: The original meaning of this French word is « a pond », but it has no astronomical connotation. If it has any meaning of the genre, it must be something of a planet because it is in conjunction with Saturn and what is in conjunction with a planet is itself another planet.  Here one can call for the so-called Latinism in Nostradamus, who sometimes seems to employ Latin words or etymologies in the guise of French usages. Then,
« a pond (estang = étang) » in Latin is stāgnum (Walde-Hofmann, s.v.), though the latter is not in fact the etymology of the former**, and « tin (étain) » in Latin is stagnum (Walde-Hofmann, s.v.), which is in fact the etymology of étain. Therefore,  estang = stāgnum as homograph of stagnum in Latin may suggest that the word estang (étang, pond) stands in reality for étain (tin) in the prophetic framework of Nostradamus. ** The etymology of étang is either a French verb étancher, to stop [the water current] (Bloch & Wartburg, s. v. ÉTANCHER) or a type of popular Latin stancum (thence the Low Latin verb stancare, Fr. étancher) (Scheler, p.65-66).

This procedure of interpretation, very reasonable in the field of studying Nostradamus because the Prophet has a mastery of mixed, multilingual, sometimes intelligently distorted  expressions
, does render useless the illegitimate effort of P. Brind'Amour who considers that all the editions are faulty and proposes his conjecture “estaing (étain)” in place of estang (Brind'Amour, 1996, p.69; 1993, p.212). But the word estaing does not exist in French.  However, the alternative way of thinking will have been able to admet the legitimate variant estain for estang because « in truth stancum should have been able to give estain as well as stagnum.» (Scheler, p.65-66). For « we see the [Latin] sound a replaced by ai in a large number of words where this vowel is followed by a complex of consonants whose first element is a simple or nasal guttural (g, c, ng, nc). Exemples: Pax = pacs) paix, tractus trait, sanctus saint, ...» (id., p.62-63). If stancum did not give  in fact estain, « it is, in all probablility, to elude the homonymy.» (id., p.66).

Now, as traditional astrology admets the respective correspondence of seven planets to seven principal metals as follows: the Sun = gold, the Moon = silver, Mercury = mercury, Venus = copper, Mars = iron, Jupiter = tin, Saturn = lead (Brind'Amour, 1993, p.162), the phrase “ Scythe to the pond joined ” concerns without doubt the conjunction of Saturn (scythe) with Jupiter (pond), i.e. a grand conjunction (cf. Brind'Amour, 1993, p.199). In fact, the French verb joindre à (to join to) forms a construction as follows: « Joignez cette pièce au dossier (Join this piece to the file). Joindre le geste à la parole (Join the practice to the word).» (Petit Robert).  Then, the interpretation of étang (pond) as « the sign of Aquarius (le signe du Verseau » (Ionescu, 1976, p.799; 1987, p.511; Wöllner, 1926, p.44; Centurio, 1953, p.34; Leoni, 1982, p.137; Cheetham, 1981, p.28; Dufresne, 1989, p.103), as « the aquatic zodiacal sign, Pisces » (Ovason, 1997, p.91) or as « Scorpio » (Lamont, 1944, p.330; Hogue, 1997, p.80; Fontbrune, 1999, p.219) is not pertinent in principle.

And  the sign where this conjunction occurs is Capricorn because it is the exaltation of Saturn here. For the astrological term « exaltation » means «  the sign where a planet has the most virtue (le signe où une planète a le plus de vertu).» (Landais), and when it is in its exaltation, it is with dignity: « Dignity (Dignité), - In a term of astrology, situation of a planet in the sign where it has the most influence (En t. d’astrol., situation d’une planète dans le signe où elle a le plus d’influence).» (id.).  And as a traditonal rule Saturn has two exaltations, namely Capricorn and Aquarius (see below), of which the former well fits in with the context of the quatrain in question because it is where Saturn can take a certain move toward Sagittarius (vers le Sagitaire) in the narrowest sense of the term toward. Moreover, the move of Saturn in Capricorn toward Sagittarius must be, of course, its retrogradation, the latter preceding the former in the cycle of the zodiac.

The traditional doctrine of the exaltations of Seven Planets: « The thema mundi, the horoscope of the world, was very much more ancient than any of this. As it is presented in our late sources, it is strikingly consistent, which sauggests that it was long established and acepted. It is normally introduced to explain why Aries is regarded as the ‘beginning’ of the zodiac, although a circle has of course no beginning. So Macrobius (I-21, 23ff): ‘They say that when that day began which was the first of all and is therefore rightly called the world’s birthday, Aries was in the Midheaven; and because the Midheaven is as it were the vertex of the world, Aries was therefore held to be the first among them all, the one which appeared like the head of the world at the beginning of light. And they add the reason why theses twelve signs are assigned to the powers of different gods. For they say that in that same birth-chart of the world, Aries being as we have said in the Midheaven, the horoscopus of the world coming to birth was Cancer, bringing forth at that moment the Moon. The Sun was rising next with Leo, Virgo with Mercury, Libra with Venus, Mars was in Scorpio, Sagittarius had Jupiter and Saturn was wandering in Capricorn. So it came about that each was said to be the lord of that sign in which it was believed to be when the world was being born. To the two luminaries antiquity alloted only the signs, one to each, in which they had been then, Cancer to the Moon and Leo to the Sun. To the other five stars, however, besides those signs in which they then had been, ancient times so added the other five as to begin the new series at the end of the first. We said earlier that Saturn, last of all, was in Capricorn; so the second set of attributions made the previous last one first, and Aquarius, which follows Capricorn, was given to Saturn. To Jupiter, who preceded Saturn, Pisces was allocated’, and so on, thus explaining the ‘planetary houses’. All of which is found in other authorities; ... » (Tester, 1987, p.119-120).

At last, it is clear that in order to identify the date of the astronomical event predicted in this quatrain during the period of 1555 to 2000, the span which we suppose to be assigned by Nostradamus for the historical realization of his Prophecies, we should converge the following three conditions:

a) the conjunction of Saturn and Jupiter in Capricorn [
Scythe to the pond joined],

b) the retrogdadation of Saturn and Jupiter in Capricorn toward Sagittarius
[
toward Sagittarius] and

c) Saturn at its aphelion in Capricorn
[
Scythe at its high APSIDE of the exaltation].

Among these three, the most pertinent shall be the condition c), for the chronological change of the aphelion of Saturn is very slow, but with rapid and unexpected perturbations, which may allow us the chance of dating this event with more precision and facility during the period  relatively long.

a) The exact conjunctions [the congruence of their longitudes] of Saturn and Jupiter in Capricorn during the years 1555-2000.

During the period from 1555 to 2000 A.D., there are 23 exact conjunctions of Saturn and Jupiter, the so-called grand conjunctions as follows. N.B. These astronomic calculations have been done by means of the softwares: AstroArts Inc., StellaNavigator: Hyperreal astronomic simulation, ASCII Corp., Tokyo, 1993 and Tomas Kubec – OrionSoft, StarFisher, free astrology software, 2006-2011 (http://www.starfisher.cz/starfisher/EN/download.htm ).

Table §731a: Exact conjunctions of Saturn with Jupiter.

Year

Month

Day

LMT at
Paris:
2º.4 E,
48º.9 N

Longitude
of
conjunction

1

1563

8

25

17:00

119º 10ʹ

2

1583

5

2

22:00

350º 10ʹ

3

1603

12

18

05:00

248º 18ʹ

4

1623

7

16

20:00

126º 35ʹ

5

1643

2

24

22:00

355º 06ʹ

6

1663

10

16

22:00

252º 57ʹ

7

1683

5

18

00:00

134º 29ʹ

8

1702

5

21

20:00

6º 36ʹ

9

1723

1

5

13:00

263º 18ʹ

10

1742

8

30

18:00

147º 08ʹ

11

1762

3

18

14:00

12º 20ʹ

12

1782

11

5

07:00

268º 06ʹ

13

1802

7

17

21:00

155º 07ʹ

14

1821

6

19

14:00

24º 38ʹ

15

1842

1

26

03:00

278º 53ʹ

16

1861

10

21

10:00

168º 21ʹ

17

1881

4

18

12:00

31º 35ʹ

18

1901

11

28

15:00

283º 59ʹ

19

1921

9

10

01:00

176º 34ʹ

20

1941

2

15

05:00

39º 07ʹ

21

1961

2

18

21:17

295º 11ʹ

22

1980

12

31

14:00

189º 29ʹ

23

2000

5

28

15:00

52º 43ʹ


Of these 23, only 3 (cells in gray) are found to be in Capricorn (the longitude of Capricorn is from 270º to 300º):
15. 26 January 1842 03:00, 278º 53ʹ;
№18. 28 November 1901 15:00, 283º 59ʹ;
№21. 18 February 1961 21:17, 295º 11ʹ.

But, these are all off the following three periods of common retrogradation of Saturn and Jupiter in Capricorn (see the table §731b below):
10 May 1842 18:10 – 9 September 1842 6:18,
1st May 1901 01:27 – 30 August 1901 22:59 and
12 August 1961 10:47 – 23 September 1961 15:37.

We then consider their conjunctions in a large sense, or loose conjunctions, namely conjunctions with indulgence (orbs of elongation) of ± 5°, i.e. 10° in sum (cf. Ishikawa, Genkou [
石川源晃], Introduction to astrology: Exercises, [実習占星学入門],  Hirakawashuppan [平河出版社], Tokyo, 1992. p.89).  

b) The common retrogradation of Saturn and Jupiter, in loose conjunction in Capricorn, toward Sagittarius during the period concerned.

Table §731b: Retrogradations of Saturn and Jupiter.

Year-Month
-Day

Longitude
of Saturn

Elong-
ation of
Saturn
from
Jupiter

Remarks

 

Hour: LMT
at Paris
(2.4º E,
48.9º N)

Longitude
of Jupiter

 

1842-1-26

278º 53ʹ

0º 00ʹ

Exact
conjunction
in progress

 

3:00

278º 53ʹ

 

1842-4-23

284º 25ʹ

7º 48ʹ

* Saturn
starting to
retrograde (*)

 

21:34

292° 13ʹ

 

1842-5-10

284º 12ʹ

8° 28ʹ

*# Jupiter starting to retrograde (#)

 

18:10

292° 40ʹ

 

1842-6-15

282º 27ʹ

8° 21ʹ

*#

 

0:00

290° 48ʹ

 

1842-7-20

279º 57ʹ

6° 37ʹ

*#

 

0:00

286° 34ʹ

 

1842-9-2

277º 54ʹ

5° 0

*#

 

13:10

282° 54ʹ

 

1842-9-9

277º 50ʹ

5° 0

*# Jupiter
finishing to
retrograde

 

6:18

282° 50ʹ

 

1842-9-12

277º 49ʹ

5º 02ʹ

* Saturn
finishing to
retrograde

 

6:08

282º 51ʹ

 

1901-4-26

286º 24ʹ

3º 23ʹ

* Saturn
starting to
retrograde

 

4:44

283º 01ʹ

 

1901-5-1

286º 22ʹ

3º 19ʹ

*# Jupiter
starting to
retrograde

 

1:27

283º 03ʹ

 

1901-6-1

285º 24ʹ

3º 49ʹ

*#

 

0:00

281º 35ʹ

 

1901-8-19

280º 20ʹ

6º 53ʹ

*#

 

2:00

273º 27ʹ

 

1901-8-30

279º 57ʹ

6º 44ʹ

*# Jupiter
finishing to
retrograde

 

22:59

273º 13ʹ

 

1901-9-7

279º 50ʹ

6º 32ʹ

*

 

0:00

273º 18ʹ

 

1901-9-14

279º 47ʹ

6º 13ʹ

* Saturn
finishing to
retrograde

 

14:19

273º 34ʹ

 

1901-11-28

283º 59ʹ

0º 00ʹ

Exact
conjunction
in progress

 

15:00

283º 59ʹ

 

1961-1-5

290º 05ʹ

5º 00ʹ

 

5:42

285º 05ʹ

 

1961-2-18

295º 11ʹ

0º 00ʹ

Exact
conjunction
in progress

 

21:17

295º 11ʹ

 

1961-3-15

297º 28ʹ

2º 32ʹ

Jupiter leaving
Capricorn
into Aquarius

 

7:04

300º 00ʹ

 

1961-5-9

299º 51ʹ

n/a

* Saturn
starting to
retrograde

 

16:31

306º 45ʹ

 

1961-5-25

299º 39ʹ

n/a

* Jupiter
starting to
retrograde

 

18:45

307º 09ʹ

 

1961-8-12

294º 51ʹ

5º 09ʹ

*# Jupiter
back into
Capricorn

 

10:47

300º 00ʹ

 

1961-9-23

293º 15ʹ

4º 04ʹ

*# Jupiter
finishing to
retrograde

 

15:37

297º 19ʹ

 

1961-9-27

293º 14ʹ

4º 07ʹ

* Saturn
finishing to
retrograde

 

19:41

297º 21ʹ

 


It is evident through this table
§731b that Saturn and Jupiter in loose conjunction (the elongations of Saturn from Jupiter under 10°) in Capricorn retrograde together during the following periods (cells in dark gray of the table §731b):
10 May 1842 18:10 – 9 September 1842 6:18,
1st May 1901 01:27 – 30 August 1901 22:59 and
12 August 1961 10:47 – 23 September 1961 15:37.
_______________________________________
© Koji Nihei Daijyo, 2017. All rights reserved. 
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§731(sequel-1) The age of re-innovation is at hand (the first year of the 20th century): I-16.

I-16 (§731 sequel-1).

Now it is to be examined if during these periods Saturn is at its aphelion [Sythe at its high APSIS in Capricorn] or not.

c) Astronomic calculation of the aphelion of Saturn during the period: 1555-2000.

Anyone has not given until now the astronomic calculations of the aphelion of Saturn in order to answer the question of this quatrain. Thus far, only the classical data have been invoked by interpreters of Nostradamus (e.g. Brind’Amour, 1993, p.212; Guinard, Le quatrain I.16 et l'annonce de la chute définitive de la Monarchie (1842-1848), 2007-2015). But those data of old times, are they truly correct and believable even now, in this age of the greatest innovation in science ?  Now, the so-called astronomic chronology, namely the investigation of astronomical truths of celestial phenomena in ancient records by means of the modernest theories and techniques of astronomy, will help us to treat this problem.

Then, the longitude of the perihelion of the orbit of Saturn is one of its orbital elements. And its aphelion is in opposition to its perihelion. Therefore, the longitude of the aphelion is the sum of the longitude of the perihelion and
180º.

But
, Saturn and Jupiter, the two outer large planets, are subject especially to their mutual perturbations in their orbit that are not easy to be calculated with precision. We will follow the practice proposed by a leading tenant of astronomic chronology in Japan Dr. Kuniji Saito [斉藤国治] in his Astronomic Chronology [『古天文学』], KoseishaKoseikaku [恒星社厚生閣], Tokyo, 1989, p.57-75.

1. JD: Julian Days
2. Epoch: AD 1900 I 1.5 UT = JD2415021.d0  
3. C: JD of the date in question in term of century beginning with the epoch = (JD - 2415021)/36525
4. T: The year (Y) of the date in question in term of 10 centuries = Y/1000
5. PNL: The longitude of the perihelion of Saturn = 91º.09821 + 1º.958416C + 8º.26361·10-4C2 + 4º.61111·10-6C3
6. PNLp: The perturbative term = ( PS7 + PS8 ) / sin (3º.56 - 0º.175T - 0º.005T2)
7. PS7: The perturbative term of long period = - 0º.50 + B ( T ) sin { ( T - 0.54 ) 360º / 0.95} 
8. B(T) : Amplitude =
0º.10 - 0º.005T
9. PS8: The perturbative term of short period = To be calculated by means of the digital table VIIIc. Kurzperiodische Störungen 100 ψ8 of P. V. Neugebauer, Tafeln zur astronomischen Chronologie, II, J.C. Hinrichs’sche Buchhandlung, Leipzig, 1914, p.XI, p.60-61.
10. The digital table has two parameters: rETA [η] and rZETA [ζ].
11. ETA = 86º.1 + 0º.033459 ( JD - 1721057)
12. ZETA = 89º.1 + 0º.049630 ( JD - 1721057)
13. 1721057.d0: JD of AD 0 I 0, 12h UT
14. rETA: Reduction of ETA in large number to 0° - 360° = 360º ( ETA / 360 - INT(ETA / 360))
15. rZETA: Reduction of ZETA in large number to 0° - 360° =  360º ( ZETA / 360 - INT(ZETA / 360))
16. The longitude of the aphelion of Saturn = PNL + PNLp + 180º

Table §731c: Aphelions of Saturn.

Year

M
o
n
th

Day

Hour: LMT at Paris (2.4º E, 48.9º N).

Longitude
of the
aphelion
of Saturn
(heliocentric).

Capricorn:
270º-300º.

1555

1

1

0:00

265º.9921
(265° 59.5ʹ)

1600

1

1

0:00

269º.0255
(269° 02ʹ)

1650

1

1

0:00

268º.1589
(268° 10ʹ)

1700

1

1

0:00

266º.3398
(266° 20ʹ)

1750

1

1

0:00

269º.0382
(269° 02ʹ)

1770

1

1

0:00

271º.4780
(271° 29ʹ)

1800

1

1

0:00

272º.0609
(272º 04ʹ)

1810

1

1

0:00

269º.9867
(269º 59ʹ)

1820

1

1

0:00

267º.3515
(267º 21ʹ)

1830

1

1

0:00

270º.5510
(270º 33ʹ)

1840

1

1

0:00

272º.4163
(272º 25ʹ)

1841

1

1

0:00

271º.4036
(271º 24ʹ)

1842

1

1

0:00

270º.1088
(270º 07ʹ)

1842

1

26

3:00

270°.0208
(270º 01ʹ)

1842

2

1

0:00

270º.0003
(270º 00ʹ)

1842

2

5

0:00

269°.9863
(269º 59ʹ)

1842

2

10

0:00

269°.9688
(269º 58ʹ)

1842

2

20

0:00

269°.9334
(269º 56ʹ)

1842

3

20

0:00

269°.8284
(269º 50ʹ)

1842

4

23

21:34

269°.7064
(269º 42ʹ)

1842

4

30

21:00

269º.6473
(269º 39ʹ)

1842

5

10

18:10

269º.6473
(269º 39ʹ)

1842

6

15

0:00

269°.5239
(31ʹ)

1842

7

20

0:00

269º.4014
(
269° 24ʹ)

1842

9

2

13:10

269°.2455
(269° 15ʹ)

1842

9

9

6:18

269º.2221
(
269° 13ʹ)

1842

9

12

6:08

269°.2116
(269° 13ʹ)

1842

11

15

0:00

268º.9885
(
268° 59ʹ)

1842

12

10

0:00

269°.2569
(269° 15ʹ)

1843

1

1

0:00

268º.8240
(
268° 49ʹ)

1844

1

1

0:00

268º.0195
(
268° 01ʹ)

1845

1

1

0:00

268º.1027
(
268° 06ʹ)

1846

1

1

0:00

268º.8578
(
268° 51ʹ)

1847

1

1

0:00

269º.9061
(
269° 54ʹ)

1847

1

10

0:00

269º.9358
(
269° 56ʹ)

1847

1

18

0:00

269º.9622
(
269° 58ʹ)

1847

2

1

0:00

270º.0084
(
270° 00ʹ)

1847

3

1

0:00

270º.0931
(270º 06ʹ)

1847

4

1

0:00

270º.2010
(270º 12ʹ)

1847

8

15

0:00

270º.7208
(270º 43ʹ)

1848

1

1

0:00

271º.1395

(271º 08ʹ)

1849

2

15

0:00

272º.2387
(272º 14ʹ)

1850

3

15

0:00

272º.7442
(272º 45ʹ)

1860

1

1

0:00

273º.7869
(273º 47ʹ)

1870

1

1

0:00

270º.9814
(270º 59ʹ)

1880

1

1

0:00

267º.9729
(267º 58ʹ)

1890

1

1

0:00

270º.7616
(270º 46ʹ)

1900

1

1

0:00

272º.1963
(272º 12ʹ)

1901

1

1

0:00

271º.0742
(271º 04ʹ)

1901

4

26

4:44

270°.6599
(270º 40ʹ)

1901

5

1

01:27

270°.6428
(270º 39ʹ)

1901

6

1

0:00

270º.5340
(270º 32ʹ)

1901

7

10

0:00

270°.3971
(270º 24ʹ)

1901

8

19

2:00

270°.2563
(270º 15ʹ)

1901

8

21

0:00

270º.2495
(270º 15ʹ)

1901

8

21

5:00

270º.2488
 (270º 15ʹ)

1901

8

22

0:00

270º.2460
(270º 15ʹ)

1901

8

25

0:00

270º.2355

 (270º 14ʹ)

1901

8

30

22:59

270º.2147
(270º 13ʹ)

1901

9

7

0:00

270°.1898
(270º 11ʹ)

1901

9

14

14 :19

270°.1652
(270º 10ʹ)

1901

10

31

0:00

270°.0002
(270º 00ʹ)

1901

11

28

15:00

269º.8996
(269º 54ʹ)

1902

1

1

0:00

269º.7824
(269º 47ʹ)

1910

1

1

0:00

273º.5190
(273º 31ʹ)

1920

1

1

0:00

275º.1289
(275º 08ʹ)

1930

1

1

0:00

271º.8996
(271º 54ʹ)

1940

1

1

0:00

268º.8184
(268º 49ʹ)

1950

1

1

0:00

270º.8488
(270º 51ʹ)

1960

1

1

0:00

271º.9068
(271º 54ʹ)

1961

1

5

4:49

270°.6252
(270º 38ʹ)

1961

2

18

21:17

270°.4676
(270º 28ʹ)

1961

3

15

7:55

270°.3707
(270º 22ʹ)

1961

5

9

17:54

270°.1754
(270º 11ʹ)

1961

5

25

19:36

270°.1187
(270º 07ʹ)

1961

8

12

10:47

269°.8415
(269º 50ʹ)

1961

9

23

15:37

269°.6927
(269º 42ʹ)

1961

9

27

20:32

269°.6779
(269º 41ʹ)

1962

1

1

0:00

269°.3980
(269º 24ʹ)

1970

1

1

0:00

274º.0244
(274º 01ʹ)

1980

1

1

0:00

275º.9692
(275º 58ʹ)

1990

1

1

0:00

272º.9153
(272º 55ʹ)

1991

1

1

0:00

273°.5139
(273º 31ʹ)

1992

1

1

0:00

273°.7015
(273º 42ʹ)

2000

1

1

0:00

270º.0830
(270º 05ʹ)

2000

12

31

0:00

271º.6818
(271º 41ʹ)

2017

10

18

15:00

273°.7086
(273º 41ʹ)


_______________________________________
© Koji Nihei Daijyo, 2017. All rights reserved. 

§731 (sequel-2) The age of re-innovation is at hand (the first year of the 20th century): I-16.

I-16 (§731 sequel-2).

d) Comparison of our astronomical calculations with those by Horizons On-Line Ephemeris System (SSD, JPL, NASA) concerning the aphelion of Saturn.

In order to confirm the results of our astronomic calculations, we try to compare them with those pruduced by Horizons On-Line Ephemeris System, JPL, NASA (
http://ssd.jpl.nasa.gov/horizons.cgi, 2009; telnet ssd.jpl.nasa.gov 6775, 2017; https://ssd.jpl.nasa.gov/horizons.cgi, 2017). It is to be remarked that the Reference Epoch of these ephemerides is J2000.0 (: JD = 2451545.0), then, to compare their data with ours based upon the Reference Epoch of 1900 I 1.5 UT (: JD = 2415021.0), it is necessary to adjust these two Reference Epochs to one another. It is a problem of general precession.

General Precession (GP): According to Dr. Kho Nagasawa [
長澤工] in his Computation of positions of celestial bodies [『天体の位置計算』], Chijinshokan [地人書館], Tokyo, 1992, p.155, the calculating procedure of the general precession is formulated as follows: 0º.0139632t + 0º.0308333 × 10-6 t2 + 0º.056 × 10-9 t3. Now, t is the span of time measured since the epoch (= J2000.0) in terms of one Besselian year of 365.242194 days. Horizons On-Line Ephemeris System offers us the orbital elements of Saturn, whose OM (OMEGA: longitude of the ascendant node, in degrees) and W (w, argument of the perifocus = argument of the perihelion, in degrees) makes the longitude of perihelion of Saturn. The value of this longitude of perihelion must be revised by means of subtraction of that of general precession in the perspective of the past starting from the epoch: 2000-1-1-00:00 CT (: JD = 2451544.5). Then, the longitude of aphelion (in opposition to its perihelion) of Saturn is the sum of OM + W + GP (negative value) + 180º (reduced to 0º - 360º). (The cells in gray represent the time of retrogradation of Saturn).

Table §731d: Computations by Horizons.

Year

M
o
n
th

Day

Hour:
LMT at
 Paris (2.4º E, 48.9º N).

Aphelion
by
Horizons:
OM + W
+ GP
(CT+
0:09:36)

OM

GP

W

1600

1

1

0:00

268°.1391

114.7571

-5.5839

340.2742

1650

1

1

0:00

269.4474

114.633

-4.8857

338.3918

1700

1

1

0:00

266.5334

114.4954

-4.1876

336.2256

1750

1

1

0:00

269.1915

114.4507

-3.4897

338.2305

1770

1

1

0:00

270.0919

114.3194

-3.2105

338.983

1800

1

1

0:00

271.1026

114.2435

-2.7918

339.6509

1810

1

1

0:00

270.0143

114.204

-2.6522

338.4625

1820

1

1

0:00

267.2161

114.1858

-2.5127

335.543

1830

1

1

0:00

270.1676

114.1313

-2.3731

338.4094

1840

1

1

0:00

272.8952

114.0631

-2.2335

341.0656

1841

1

1

0:00

271.9028

114.0854

-2.2195

340.0369

1842

1

1

0:00

270.5075

114.1102

-2.2056

338.6029

1842

1

26

3:00

270.4835

114.1274

-2.2046

338.5607

1842

2

1

0:00

270.4131

114.1186

-2.2044

338.4989

1842

2

5

0:00

270.2245

114.0918

-2.2042

338.3369

1842

2

10

0:00

270.3688

114.1192

-2.204

338.4536

1842

2

20

0:00

270.185

114.0964

-2.2037

338.2923

1842

3

20

0:00

270.2391

114.1232

-2.2026

338.3185

1842

4

23

21:34

269.9392

114.103

-2.2013

338.0375

1842

4

30

21:00

270.032

114.1183

-2.201

338.1147

1842

5

10

18:10

269.8341

114.0989

-2.2006

337.9358

1842

6

15

0:00

269.7023

114.101

-2.1993

337.8006

1842

7

20

0:00

269.7151

114.1196

-2.1979

337.7934

1842

9

2

13:10

269.3421

114.1031

-2.1962

337.4352

1842

9

9

6:18

269.5514

114.1255

-2.196

337.6219

1842

9

12

6:08

269.4064

114.1151

-2.1959

337.4872

1842

11

15

0:00

269.1614

114.1152

-2.1934

337.2396

1842

12

10

0:00

269.1353

114.1156

-2.1925

337.2122

1843

1

1

0:00

269.0588

114.1176

-2.1916

337.1328

1844

7

1

0:00

267.6062

114.1293

-2.1707

335.6476

1845

1

1

0:00

268.0422

114.0921

-2.1637

336.1138

1846

1

1

0:00

268.6644

114.0921

-2.1497

336.722

1847

1

1

0:00

269.6609

114.1187

-2.1358

337.678

1847

1

10

0:00

269.4423

114.1645

-2.1355

337.4133

1847

1

18

0:00

269.8048

114.0969

-2.1351

337.843

1847

2

1

0:00

269.6754

114.1382

-2.1346

337.6718

1847

3

1

0:00

269.5288

114.1899

-2.1335

337.4724

1847

4

1

0:00

269.6662

114.1855

-2.1323

337.613

1847

8

15

0:00

270.535

114.0807

-2.1272

338.5815

1848

1

1

0:00

270.7057

114.1678

-2.1218

338.6597

1849

2

15

0:00

271.724

114.2093

-2.1061

339.6208

1850

3

15

0:00

272.8308

114.0709

-2.0911

340.851

1860

1

1

0:00

272.6634

114.0435

-1.9544

340.5743

1870

1

1

0:00

270.6109

114.0108

-1.8147

338.4148

1880

1

1

0:00

267.4939

114.0347

-1.6752

335.1344

1890

1

1

0:00

270.4136

113.9968

-1.5356

337.9524

1900

1

1

0:00

272.8121

113.9536

-1.396

340.2545

1901

1

1

0:00

271.511

113.9344

-1.3821

338.9587

1901

4

26

4:44

271.2085

113.9575

-1.3777

338.6287

1901

5

1

01:27

271.0764

113.9450

-1.3775

338.5090

1901

6

1

0:00

270.9906

113.9492

-1.3763

338.4177

1901

7

10

0:00

270.6536

113.9309

-1.3748

338.0975

1901

8

19

2:00

270.676

113.9504

-1.3733

338.0989

1901

8

21

0:00

270.5602

113.942

-1.3732

337.9914

1901

8

21

5:00

270.5495

113.9412

-1.3732

337.9815

1901

8

22

0:00

270.508

113.9381

-1.3732

337.9431

1901

8

25

0:00

270.4039

113.93

-1.373

337.8469

1901

8

30

22:59

270.6476

113.9501

-1.3728

338.0704

1901

9

7

0:00

270.4271

113.9379

-1.3725

337.8617

1901

9

14

14 :19

270.5199

113.9448

-1.3723

337.9474

1901

10

31

0:00

270.2234

113.9389

-1.3705

337.655

1901

11

28

15:00

269.9872

113.9344

-1.3694

337.4222

1902

1

1

0:00

269.896

113.9367

-1.3681

337.3274

1910

1

1

0:00

273.4645

113.9162

-1.2564

340.8047

1920

1

1

0:00

274.5728

113.9472

-1.1169

341.7425

1930

1

1

0:00

271.8031

113.8868

-0.9772

338.8935

1940

1

1

0:00

268.6216

113.7445

-0.8377

335.7148

1950

1

1

0:00

270.5393

113.868

-0.698

337.3693

1960

1

1

0:00

272.3541

113.7833

-0.5584

339.1292

1961

1

5

4:49

270.7065

113.7679

-0.5443

337.4829

1961

2

18

21:17

270.7254

113.7711

-0.5426

337.4969

1961

3

15

7:55

270.4926

113.7693

-0.5417

337.265

1961

5

9

17:54

270.3694

113.7688

-0.5395

337.1401

1961

5

25

19:36

271.8274

113.945

-0.5389

338.4213

1961

8

12

10:47

270.0278

113.7645

-0.5359

336.7992

1961

9

23

15:37

269.7651

113.7707

-0.5343

336.5287

1961

9

27

20:32

269.9148

113.7613

-0.5341

336.6876

1962

1

1

0:00

269.5895

113.7576

-0.5305

336.3624

1970

1

1

0:00

274.0254

113.7637

-0.4188

340.6805

1980

1

1

0:00

275.4515

113.7365

-0.2792

341.9942

1990

1

1

0:00

272.5459

113.6735

-0.1396

339.012

1991

1

1

0:00

273.2075

113.678

-0.1256

339.6551

1992

1

1

0:00

273.6481

113.6624

-0.1117

340.0974

2000

1

1

0:00

269.5931

113.6931

0

335.9

2000

12

31

0:00

271.1437

113.6332

0.0139

337.4966


_______________________________________
© Koji Nihei Daijyo, 2017. All rights reserved.

§731(sequel-3) The age of re-innovation is at hand (the first year of the 20th century): I-16.

I-16 (§731 sequel-3).

Table §731e: Parallels.

Y
e
a

r

M

o

n

th

D
a
y

Hour:

LMT at

 Paris (2.4º E, 48.9º N)

Longitude

of the

aphelion

of Saturn: our results

Aphelion by

Horizons:

OM + W

+ PG.

 

CT +

00:09:36

1600

1

1

0:00

269°.0255

268°.1391

1650

1

1

0:00

268°.1589

269°.4474

1700

1

1

0:00

266°.3398

266°.5334

1750

1

1

0:00

269°.0382

269°.1915

1770

1

1

0:00

271°.4780

270°.0919

1800

1

1

0:00

272°.0609

271°.1026

1810

1

1

0:00

269°.9867

270°.0143

1820

1

1

0:00

267°.3515

267°.2161

1830

1

1

0:00

270°.5510

270°.1676

1840

1

1

0:00

272°.4163

272°.8952

1841

1

1

0:00

271°.4036

271°.9028

1842

1

1

0:00

270°.1088

270°.5075

1842

1

26

3:00

270°.0208

270°.4835

1842

2

1

0:00

270°.0003

270°.4131

1842

2

5

0:00

269°.9863

270°.2245

1842

2

10

0:00

269°.9688

270°.3688

1842

2

20

0:00

269°.9334

270°.1850

1842

3

20

0:00

269°.8284

270°.2391

1842

4

23

21:34

269°.7064

269°.9392

1842

4

30

21:00

269°.6473

270°.0320

1842

5

10

18:10

269°.6473

269°.8341

1842

6

15

0:00

269°.5239

269°.7023

1842

7

20

0:00

269°.4014

269°.7151

1842

9

2

13:10

269°.2455

269°.3421

1842

9

9

6:18

269°.2221

269°.5514

1842

9

12

6:08

269°.2116

269°.4064

1842

11

15

0:00

268°.9885

269°.1614

1842

12

10

0:00

269°.2569

269°.1353

1843

1

1

0:00

268°.8240

269°.0588

1844

7

1

0:00

268°.0195

267°.6062

1845

1

1

0:00

268°.1027

268°.0422

1846

1

1

0:00

268°.8578

268°.6644

1847

1

1

0:00

269°.9061

269°.6609

1847

1

10

0:00

269°.9358

269°.4423

1847

1

18

0:00

269°.9622

269°.8048

1847

2

1

0:00

270°.0084

269°.6754

1847

3

1

0:00

270°.0931

269°.5288

1847

4

1

0:00

270°.2010

269°.6662

1847

8

15

0:00

270°.7208

270°.5350

1848

1

1

0:00

271°.1395

270°.7057

1849

2

15

0:00

272°.2387

271°.7240

1850

3

15

0:00

272°.7442

272°.8308

1860

1

1

0:00

273°.7869

272°.6634

1870

1

1

0:00

270°.9814

270°.6109

1880

1

1

0:00

267°.9729

267°.4939

1890

1

1

0:00

270°.7616

270°.4136

1900

1

1

0:00

272°.1963

272°.8121

1901

1

1

0:00

271°.0742

271°.5110

1901

4

26

4:44

270°.6599

271°.2085

1901

5

1

01:27

270°.6428

271°.0764

1901

6

1

0:00

270°.5340

270°.9906

1901

7

10

0:00

270°.3971

270°.6536

1901

8

19

2:00

270°.2563

270°.6760

1901

8

21

0:00

270°.2495

270°.5602

1901

8

21

5:00

270°.2488

270°.5495

1901

8

22

0:00

270°.2460

270°.5080

1901

8

25

0:00

270°.2355

270°.4039

1901

8

30

22:59

270°.2147

270°.6476

1901

9

7

0:00

270°.1898

270°.4271

1901

9

14

14 :19

270°.1652

270°.5199

1901

10

31

0:00

270°.0002

270°.2234

1901

11

28

15:00

269°.8996

269°.9872

1902

1

1

0:00

269°.7824

269°.8960

1910

1

1

0:00

273°.5190

273°.4645

1920

1

1

0:00

275°.1289

274°.5728

1930

1

1

0:00

271°.8996

271°.8031

1940

1

1

0:00

268°.8184

268°.6216

1950

1

1

0:00

270°.8488

270°.5393

1960

1

1

0:00

271°.9068

272°.3541

1961

1

5

4:49

270°.6252

270°.7065

1961

2

18

21:17

270°.4676

270°.7254

1961

3

15

7:55

270°.3707

270°.4926

1961

5

9

17:54

270°.1754

270°.3694

1961

5

25

19:36

270°.1187

271°.8274

1961

8

12

7:26

(269°.8419)

270°.0337

1961

8

12

10:47

269°.8415

270°.0278

1961

9

23

15:37

269°.6927

269°.7651

1961

9

27

20:32

269°.6779

269°.9148

1962

1

1

0:00

269°.3980

269°.5895

1970

1

1

0:00

274°.0244

274°.0254

1980

1

1

0:00

275°.9692

275°.4515

1990

1

1

0:00

272°.9153

272°.5459

1991

1

1

0:00

273°.5139

273°.2075

1992

1

1

0:00

273°.7015

273°.6481

2000

1

1

0:00

270°.0830

269°.5931

2000

12

31

0:00

271°.6818

271°.1437

 

Table §731f: Extended detailed data by Horizons.

Year

M
o
n
th

Day

Hour:
LMT
at Paris:
2.4º E,
48.9º N.

Longitude of
 the aphelion
of Saturn
by Horizons.

Capricorn:
270°-300°

1842

4

23

21:34

269°.9393

1842

4

24

21:00

269°.8958

1842

4

25

21:00

269°.8663

1842

4

26

21:00

269°.8739

1842

4

27

21:00

269°.8934

1842

4

28

21:00

269°.9319

1842

4

29

21:00

269°.9809

1842

4

30

0:00

269°.9876

1842

4

30

3:00

269°.9943

1842

4

30

4:00

269°.9965

1842

4

30

4:30

269°.9975

1842

4

30

5:00

269°.9986

1842

4

30

5:35

269°.9999

1842

4

30

5 :40

270°.0001

1842

4

30

6:00

270°.0008

1842

4

30

6:30

270°.0019

1842

4

30

7:00

270°.003

1842

4

30

7:30

270°.004

1842

4

30

8:00

270°.0051

1842

4

30

9:00

270°.0072

1842

4

30

10:00

270°.0093

1842

4

30

11:00

270°.0114

1842

4

30

12:00

270°.0135

1842

4

30

21:00

270°.032

1842

5

1

20:00

270°.0831

1842

5

2

20:00

270°.1144

1842

5

3

20:00

270°.1181

1842

5

4

20:00

270°.106

1842

5

5

20:00

270°.0784

1842

5

6

20:00

270°.0329

1842

5

7

0:00

270°.0247

1842

5

7

6:00

270°.0131

1842

5

7

12:00

270°.0013

1842

5

7

12:30

270°.0002

1842

5

7

12:40

269°.9998

1842

5

7

13:00

269°.9991

1842

5

7

20:00

269°.9828

1842

5

8

20:00

269°.9158

1842

5

9

20:00

269°.881

1842

5

10

18:10

269°.8343

1961

8

12

10:47

270°.0278

1961

8

12

18:00

270°.0121

1961

8

12

21:00

270.0043

1961

8

12

22:00

270.0016

1961

8

12

22:30

270.0003

1961

8

12

23:00

269°.9989

1961

8

13

0:00

269°.9961

1961

8

14

0:00

269°.9176

1961

8

15

0:00

269°.8483

1961

8

31

0:00

269°.7889


Of these cases are excluded those whose dates (cells in gray) are off the periods determined by the condition of common retrogradation of Saturn and Jupiter: 10 May 1842 18:10 – 9 September 1842 6:18, 1st May 1901 01:27 – 30 August 1901 22:59 and 12 August 1961 10:47 – 23 September 1961 15:37 and also those whose data of aphelion are under 270° 00ʹ (cells in dark gray) are excluded.

Then, the cases legitimate for the condition of the common retrogradation of Saturn and Jupiter in loose conjunction and the condition of Saturn’s aphelion in Capricorn are as follows (table §731g of the following sequel-4).
_______________________________________
© Koji Nihei Daijyo, 2017. All rights reserved.

§731(sequel-4) The age of re-innovation is at hand (the first year of the 20th century): I-16.

I-16 (§731 sequel-4).

e) The cases legitimate for the condition of the common retrogradation of Saturn and Jupiter in loose conjunction and for the condition of Saturn’s aphelion in Capricorn are as follows:

Table §731g: The screened cases (validly extended).

Year

M
o
n
th

Day

Hour:

LMT
at
Paris (2.4º E, 48.9º N)

Aphelion (heliocentric)

by Horizons:

OM + W + PG

+ 180°.

Hour: CT + 00:09:36

( ): geocentric longitude of Saturn.

1901

5

1

01:271

271°.0764 (286º 22ʹ)

1901

6

1

0:00

270°.9906 (285º 24ʹ)

1901

7

10

0:00

270°.6536 (282º 47ʹ)

1901

8

10

0:00

270.4916 (280º 46ʹ)

1901

8

19

2:00

270°.6760 (280º 20ʹ)

1901

8

21

0:00

270°.5602 (280º 16ʹ)

1901

8

21

5:00

270°.5495 (280º 15ʹ)

1901

8

22

0:00

270°.5080 (280º 14ʹ)

1901

8

25

0:00

270°.4039 (280º 07ʹ)

1901

8

30

22:59

270°.6476 (279° 57ʹ)

1961

8

12

7:26

270°.0337 (294° 52ʹ)

1961

8

12

10:47

270°.0278 (294° 51ʹ)

1961

8

12

18:00

270°.0121 (294° 50ʹ)

1961

8

12

21:00

270.0043 (294°49ʹ)

1961

8

12

22:00

270.0016 (294°49ʹ)

1961

8

12

22:30

270.0003 (294° 49ʹ)

1961