__PAGE
F 58 59 /D 37 38/__

A/ 9.18.2.2.0 4 Ahau 1,426,360 days

__- 12.11__
__- 251 days__

B/ /9.18.1.7.9/ 13 Muluc
1,426,109
days

C/ 9.12.11.11.0 4 Ahau 1,386,580
days

__- 1.7.11__
__- 511 days__

D/ /9.12.10.3.9/ 13 Muluc
1,386,069
days

A/ J.D. 2,048,621 October
26, 896

B/ J.D. 2,048,370 February
18, 896

C/ J.D. 2,008,841 November
28, 787

D/ J.D. 2,008,330 July
5, 786

The multiples of (1 to 9)x78, (1 to 18)x780
and (1 to 9)x14,820 days are added to dates B and D. Any multiple of 780 could be reached by mere addition through
their mutual combination.

The interval of 39,780 days is contained
between dates A and C. It contains with little differences of just a few days:

68 times Venus synodic circulation length rounded to 585 days.

177 times Venus siderial circulation length (224.700 640 days).

51 times Mars synodic circulation length rounded to 780 days.

58 times Mars siderial circulation length (686.979800 days)

17 times Venus and Mars basic conjunction cycle rounded to 2,340 days.

153 times the holy cycle tzolkin of 260 days.

Venus synodic circulation length is
moving between 577 to 592 days. Its real average length is 583.921 394 days.
Seemingly irregular sling movement of the planet 542 days forwards and 42 days
backwards arises from adding the movements of the Earth to the movements of the
Venus. Nearly the same movement is performed by Mars. Mars synodic
movement length is moving between 764 and 810 days. The direct movement is
about 706 days and the reverse one about 74 days. Mars average synodic
circulation length is 779.936 160 days. The basic theoretical cycle of the
Venus and Mars conjunction cycle is 2,340 days. And again, it moves between
2,315 and 2,360 days.

The Mayan astronomers were obviously aware
of Venus and Mars mutual complicated movements, so they have been
working with the rounded values, which enabled them determining the planets
conjunctions for a long period with little mistake. The position of Venus
and Mars is expressed in degrees of geocentric ecliptic co-ordinates.

A/ October 26, 896 Venus and Mars
conjunction.

The
Venus 176.267°

The
Mars 175.374°

The
distance of the planets was 0.893°

The
real conjunction held 2 days ago October 24,896

The
Venus 173.916°

The
Mars 174.117°

The
distance of both the planets was 0.201°.

C/ November 28, 787 Venus and Mars conjunction.

Venus 207.547°

The
Mars 204.765°

The
distance of the planets was 2.782°

The
real conjunction held 1 day ago November 27, 787

The
Venus 206.870°

The
Mars 204.115°

The
distance of both the planets was 2.755°.

In those cases the Mayan astronomers have
determined Venus and Mars conjunction a day or two later. The angle
distance has changed only slightly during this period, so it was not
observable. Their mutual shift of distance was only 0.692° and 0.027°.

If the conjunction is held during Venus
being as a morning star close to the eastern elongation with the Sun, then the
next conjunction is held around the western elongation, when Venus shines
as a morning star in the sky. The interval between two following conjunctions
is during those constellations very short and it moves between 206 and 295
days. The average value of this scatter is 251 days and it is to be found
between dates A and B.

The A date introduces Venus and the
Mars conjunction. At the same time Venus was after western elongation with
the Sun. Since this date, the time interval of 241 days (average time from the
last conjunction date B) is counted, till Venus was shortly before
eastern elongation with the Sun.

B/ February 18, 896
Venus and Mars conjunction.

The
Venus 10.896°

The
Mars 9.966°

The
distance of the planets was 0.93°

The
real conjunction held 2 days ago February 16,896

The
Venus 8.504°

The
Mars 8.507°

The
distance of both the planets was 0.003°.

In this case, the Mayan astronomers have
made a mistake of 0.897°, of which the planets receded since the real
conjunction.

In all three determined conjunctions the
Mayan astronomers have made a mistake
moving from 0.027°to 0.897°, of which the planets receded since the real
conjunction. It is so slight difference, that the planets movement on ecliptics
in such small angle distance was undiscoverable for the Mayan astronomers.

Mars and Jupiter conjunctions are
in average repeating after 2.21 years. They are together around their
oppositions with the Sun once in 49.14 years. It is the time of the best
conditions for their observation. Repetition of triple conjunctions or close
mutual approaches occurs during a short time period (tens of days) while the
planets in this position.

The D date, July 5, 786 expresses Mars
and Jupiter short-period maximal distance between two following
conjunctions. At the same time the
planets were close to their oppositions with the Sun.

The
first maximal approach May 4, 786.

The
Mars 256.336°

The
Jupiter 267.078°

The
distance of both the planets was 10.742°.

D/ July 5, 786
The maximal angle
distance after the first approach.

The
Mars 243.621°

The
Jupiter 260.162°

The
distance of both the planets was 16.541°

The
second conjunction August 22, 786.

The
Mars 258.101°

The
Jupiter 258.314°

The
distance of both the planets was 0.213°.

The Mayan astronomers have been observing
the mutual conjunctions of the outer planets (Mars, Jupiter, Saturn) during
their oppositions with the Sun. In these positions were the planets excellently
observable. We can say the same of dating Jupiter and the Saturn
conjunction on page F 45 (D 74).

The table of 780 days multiples follows
after the opening Mayan dates. It is slightly rounded length of Mars
synodic circulation (779.936 16 days). Through the mutual combination of those
multiples we can get any multiple of 780 days. The table serves to determining
the next conjunctions, or close approaches, of Mars and Venus, or the
Mars and Jupiter.

Mars and Venus conjunction is
repeating after three synodic circulations of Mars, i.e. 2.340 days. By
mere adding this cycle to the B date (February 18, 896), we get the time of the
next conjunction.

The mistake has increased and the planets
receded more and more after every cycle because of the Mayan astronomers
counting with the rounded values. In
spite of that the method was usable for 185.795 years with 29 basic cycles of
conjunctions. The angle distance of both the planets was after this time only
7.685°. But for calculation of the next conjunctions is the triple multiple of
780 days no longer usable.

For calculating the next conjunctions of
Mars and Venus, it is necessary to change for another cycle. 140
synodic circulations of Mars are again added to the starting Mayan date B.
140 synodic circulations of Mars are 109,200 days, i.e. nearly 299 years,
with 187 synodic circulations of Venus. The planets get into the near
approach after this time again. For a certain time, it is possible to add a
shorter basic interval of 2,340 days (3 times 780 days) to this conjunction to
get their conjunctions or close approaches, before the mistake grow shows
again. Out of the table of 780 days multiplies we can easily find out the multiply
of 140 and 780 days and the total of 103,740 and 5,460 days is 109,200 days.

The parallel positions of Mars and Jupiter nearby
their oppositions with the Sun (when they also get into mutual conjunction) are
repeating every 49.14 years with 23 synodic circulations of Mars, i.e.
17,940 days. Out of the table of 780
days multiplies we can find this value by adding 14,820 days to 3,120 days,
which is exactly 17,940 days. By
gradual adding the multiplies of this value to the initial Mayan date D (July 5,
786), Mars and Jupiter are always reaching the opposition with the Sun,
when they are good observable, but they are also situated approximately between
two following conjunctions. Because of working with average values of
astronomical data, the mistake grows approximately after 147.4 years.