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In order not to complicate matters more than necessary I will not use in my tables the outdated dates of our Gregorian calendar. It is enough to remember there was a 4 day difference. Furthermore, it may have been the positions of the stars as such rather than the dates which interested the creators of the rongorongo texts. Although the equinoxes and the solstices were clearly important:

... Far away, the Mangaians of old (Austral Islands, Polynesia), who kept the precessional clock running instead of switching over to 'signs', claim that only at the evening of the solstitial days can spirits enter heaven, the inhabitants of the northern parts of the island at one solstice, the dwellers in the south at the other ...

Ga5-1 (111) Ga5-2 Ga5-3 Ga5-4 Ga5-5
JULY 10 11 12 (193) 13 14
θ Crateris (175.0), υ Leonis (175.2), ω Virginis (175.3), ι Crateris (175.5) ο Hydrae (176.1) ζ Crateris, ξ Virginis  (177.0), λ Muscae (177.1), ν Virginis (177.2), μ Muscae (177.8) Al Sarfah-10 / Uttara Phalguni-12 / Zibbat A.-16 / Shēpu-arkū sha-A-17 Phekda, β Hydrae  (179.3), η Crateris (179.9)

Deneb Cygni

93 LEONIS (178.0), DENEBOLA (178.3), ALARAPH (178.6)
September 12 13 (256) 14 (*177) 15 16
NAKSHATRA DATES:
JANUARY 9 10 11 12 13 (378)
λ Piscium (358.0), MANUS CATENATA (358.1), Alrai, θ Phoenicis (358.4), κ Andromedae (358.7) ω Aquarii (359.2), 78 Pegasi (359.5) ψ Andromedae (360.1), σ Phoenicis (360.4) γ¹ Oct. (361.4). φ Pegasi (361.7) Dzaneb (362.4), γ² Oct.(362.8)
π March 15 16 (*360) 17 18 (77)
Ga5-6 Ga5-7 Ga5-8 (118) Ga5-9
JULY 15 (196) 16 (*118 = 4 * 29½) 18
no star listed (180) π Virginis (181.0), θ Crucis (181.5) 12h (182.6) ALCHITA, Ma Wei (183.1), Minkar (183.7), ρ Centauri (183.9)
ο Virginis (182.1), η Crucis (182.5)
September 17 (260) 18 19 20
NAKSHATRA DATES:
JANUARY 14 15 16 17 (382)
η Tucanae (363.0), ψ Pegasi (363.1), 32 Piscium (363.2), π Phoenicis (363.4), ε Tucanae (363.6), τ Phoenicis (363.9) θ Octantis (364.4) Al Fargh al Thāni-25 Uttara Bhādrapadā-27 / Wall-14
0h (365.25)
Caph, SIRRAH (0.5), ε Phoenicis (0.8) ALGENIB PEGASI (1.8)
March 19 (78) 20 EQUINOX 22

At the time of rongorongo the Gregorian calendar would still have pointed at heliacal Algenib Pegasi as the star which once upon a time was 378 (= 382 - 4) days from the beginning of the previous year. The synodic cycle of Saturn was 378 days and 365 + 13 = 378.

Ga5-8 could have referred to nakshatra Sirrah at the northern spring equinox (where birds should produce eggs). Or to heliacal 12h when south of the equator these birds would have arrived from the north. Birds on eggs tend to keep their beaks closed, to keep quiet in order not to reveal their positions for the predators.

There is another and similar such silent bird 41 days later, but with another kind of offspring. Her position corresponded to that of nakshatra Bharani:

37
Ga6-17 (157) Ga6-18 Ga6-19 Ga6-20
AUGUST 25 26 27 (*159) 28 (240)
ρ Lupi (221.0), TOLIMAN (221.2), π Bootis (221.8), ζ Bootis (221.9) 31 Bootis (222.0), Yang Mun (222.1), RIJL AL AWWA (222.5), ο Bootis (222.9) Izar (223.0), 109 VIRGINIS, α Apodis (223.3) Al Zubānā-14a / Visakha-16 / Root-3
ZUBEN ELGENUBI (224.2), ξ Bootis, ο Lupi (224.5)
October 28 29 30 31 (304)
NAKSHATRA DATES:
FEBRUARY 24 (420) 25 26 (*342) 27
μ Arietis (39.4), Head of the Fly (39.6), Kaffaljidhma (39.8) π Ceti, ο Arietis (40.0), μ Ceti, Angetenar (40.2), Right Wing (40.9) Bharani-2 / Stomach-17 no star listed (42)
π Arietis (41.2), BHARANI (41.4), τ² Eridan, σ Arietis (41.7)
April 29 30 (120) May 1 2
ARIES:
1 Ashvini β and γ Arietis Horse's head 27 = 16 + 11
wife of the Ashvins Sheratan and Mesarthim April 17 (107)
2 Bharani 35, 39, and 41 Arietis Yoni, the female organ of reproduction 41 = 27 + 14
the bearer  Musca Borealis May 1 (121)

Symmetry could have demanded a contrast in form of a bird's egg sheltered down on the ground compared to Atlas with his great 'sky egg' held high. The pair of silent birds could have indicated the dates March 21 respectively May 1- whereas Atlas would have arrived in May 16 = 8 weeks after Sirrah and 15 days after Bharani.

A nakshatra reading probably stretched from Manus Catenata, and possibly at the beginning of 40 + 40 rainy days:

Ga5-1 (111) Ga5-2 Ga5-3 Ga5-4 Ga5-5
MANUS CATENATA     φ PEGASI  
π March 15 16 (*360) 17 18 (77)
Egyptian bread, (-t, female determinant) Phoenician qoph Greek phi Φ(φ)

... is the 21st letter of the Greek alphabet ... Its origin is uncertain but it may be that phi originated as the letter qoppa ... In traditional Greek numerals, phi has a value of 500 or 500000 ...

Isaac Taylor, History of the Alphabet: Semitic Alphabets, Part 1, 2003: 'The old explanation, which has again been revived by Halévy, is that it denotes an 'ape,' the character Q being taken to represent an ape with its tail hanging down. It may also be referred to a Talmudic root which would signify an 'aperture' of some kind, as the 'eye of a needle,' ... Lenormant adopts the more usual explanation that the word means a 'knot' ...

... The king, wearing now a short, stiff archaic mantle, walks in a grave and stately manner to the sanctuary of the wolf-god Upwaut, the 'Opener of the Way', where he anoints the sacred standard and, preceded by this, marches to the palace chapel, into which he disappears. A period of time elapses during which the pharaoh is no longer manifest.

When he reappears he is clothed as in the Narmer palette, wearing the kilt with Hathor belt and bull's tail attatched. In his right hand he holds the flail scepter and in his left, instead of the usual crook of the Good Shepherd, an object resembling a small scroll, called the Will, the House Document, or Secret of the Two Partners, which he exhibits in triumph, proclaiming to all in attendance that it was given him by his dead father Osiris, in the presence of the earth-god Geb. 'I have run', he cries, 'holding the Secret of the Two Partners, the Will that my father has given me before Geb. I have passed through the land and touched the four sides of it. I traverse it as I desire.' ...

31
Ga5-6 Ga5-7 Ga5-8 (4 * 29½) Ga5-9 (119) Ga6-11 (151)
    SIRRAH ALGENIB PEGASI ARCTURUS
March 19 (78) 20 EQUINOX 22 October 22 (295)
5 22
Ga6-17 (157) Ga6-18 Ga6-19 Ga6-20
    BHARANI  
April 29 30 (120) May 1 2
Ga7-14 (183) Ga7-15 Ga7-16 Ga7-17 Ga7-18 Ga7-19
SEPTEMBER 20 21 (*184) EQUINOX 23 24 25 (268)
Heart-5 ρ Ophiuchi (248.1), Aldibain (248.2), Kajam (248.3), χ Ophiuchi (248.5), She Low, ι Tr. Austr. (248.7), ζ Tr. Austr. (248.8) Al Kalb-16 / Jyeshtha-18

ANA-MUA

γ Apodis (250.1), σ Herculis (250.3), θ Tr. Austr. (250.6), τ Scorpii (250.7) Han (251.0) ζ Herculis, η Tr. Austr. (252.1), η Herculis, β Apodis (252.5)
σ SCORPII (247.0), Hejian (247.2), ψ Ophiuchi (247.7) ANTARES (249.1), Marfik, φ Ophiuchi (249.5),  ω Ophiuchi (249.8)
November 23 24 25 26 27 28 (332)
NAKSHATRA DATES:
MARCH 22 23 24 25 26 (85) 27
Net-19 no star listed (66) no star listed (67) Rohini-4 / Pidnu-sha-Shame-5

ANA-MURI

no star listed (69) no star listed (70)
θ² Tauri, AIN, θ¹ Tauri (65.7) ALDEBARAN (68.2), Theemin (68.5)
May 25 26 27 28 29 30 (150)
Ga7-20 Ga7-21 Ga7-22 (191) Ga7-23 Ga7-24
SEPTEMBER 26 27 (270) 28 29 30 (*193)
ATRIA (253.9) Tail-6 ι Ophiuchi (255.3), Grafias (255.4) κ Ophiuchi (256.2), ζ Arae (256.5), ε Arae (256.8), Cujam (256.9) no star listed (257)
Wei, η Arae (254.3), DENEBAKRAB (254.7)
November 29 30 December 1 2 (336) 3
NAKSHATRA DATES:
MARCH 28 29 30 31 (90) APRIL 1
Tabit (71.7), π² Orionis (71.9) π4 Orionis (72.1), ο¹ Orionis (72.4), π5 Orionis (72.8) π¹ Orionis (73.0),ο² Orionis (73.4), HASSALEH (73.6), π6 Orionis (73.9) Almaaz (74.7), HAEDUS I (74.8) HAEDUS II (75.9)
May 31 June 1 2 3 4 (155)

However, the last 8 of these presumtive 80 days - from number 183 up to and including number 190 - were evidently special. Glyph 183 (Ga7-14) corresponded to the 5th Chinese station Heart and clearly this could be a place for changing from nakshatra to heliacal reading - until Rei in Ga7-22.

There were 8 dark nights before Venus returned in the eastern sky. Nakshatra σ Sciorpii was at the zero position of the text:

no glyph
Ga1-1 Ga1-2
0h (80) MARCH 22 23
HYADUM II (δ¹ Tauri) (64.2) Net-19 no star listed (66)
AIN, θ¹ Tauri, θ² Tauri (65.7)
May 24 25 26 (146)
NAKSHATRA DATES:
SEPTEMBER 20 21 (*184) EQUINOX
Heart-5 ρ Ophiuchi (248.1), ALDIBAIN (248.2), Kajam (248.3), χ Ophiuchi (248.5), She Low, ι Tr. Austr. (248.7), ζ Tr. Austr. (248.8) Al Kalb-16 / Jyeshtha-18 / ANA-MUA
σ SCORPII (247.0), Hejian (247.2), ψ Ophiuchi (247.7) ANTARES (249.1), Marfik, φ Ophiuchi (249.5),  ω Ophiuchi (249.8)
November 23 24 25 (329)
Ga1-3 Ga1-4 Ga1-5 Ga1-6
MARCH 24 25 (84) 26 27
no star listed (67) Rohini-4 / Pidnu-sha-Shame-5

ANA-MURI

no star listed (69) no star listed (70)
ALDEBARAN (68.2), Theemin (68.5)
May 27 28 (148) 29 30
NAKSHATRA DATES:
SEPTEMBER 23 24 25 (268) 26
γ Apodis (250.1), σ Herculis (250.3), θ Tr. Austr. (250.6), τ Scorpii (250.7) HAN (251.0) ζ Herculis, η Tr. Austr. (252.1), η Herculis, β Apodis (252.5) ATRIA (253.9)
November 26 27 28 29 (333)

Atria is α in the Southern Triangle, which constellation came later than the Southern Fly (Musca Australis) - and not earlier as the Northern Fly compared to the pair of Northern Triangles:

The Northern Triangles began with Metallah (α) which rose in the same day as Polaris. From Metallah to Atria there were 333 (November 29) - 106 (April 16) = 227 days (alluding to π). From nakshatra Metallah to heliacal Atria, however, there were only 45 days (= 227 - 182):

Ga6-3 Ga6-4 Ga6-5 (145)
AUGUST 11 12 13 (225)
no star listed (207) τ Bootis (208.2), BENETNASH (208.5), ν Centauri (208.7), μ Centauri, υ Bootis (208.8) no star listed (209)
October 14 15 (288) 16
NAKSHATRA DATES:
FEBRUARY 10 11 (42) 12 (408)
no star listed (25) ANA-NIA Al Sharatain-1 / Ashvini-1 / Bond-16 / Mahrū-sha-rishu-ku-2
χ Ceti (26.1), POLARIS, Baten Kaitos (26.6), METALLAH (26.9)  Segin, Mesarthim, ψ Phoenicis (27.2), SHERATAN, φ Phoenicis (27.4)
April 15 16 (471) 17 (107)
37
Ga6-6 Ga6-7 Ga6-8 Ga6-9 Ga6-10 (150) Ga6-11
AUGUST 14 15 16 17 (229) 18 19
MUPHRID (210.1), ζ Centauri (210.3) φ Centauri (211.0), υ¹ Centauri (211.1), υ² Centauri (211.8), τ Virginis (211.9) Agena (212.1), θ Apodis (212.5), THUBAN (212.8) 14h (213.1) Neck-2 Al Ghafr-13 / Svāti-15

TAHUA-TAATA-METUA-TE-TUPU-MAVAE

π HYDRAE, χ Centauri (213.0), Menkent (213.1) ASELLUS TERTIUS, κ VIRGINIS, 14 Bootis (214.8) 15 Bootis (215.2), ARCTURUS (215.4), ASELLUS SECUNDUS (215.5), SYRMA, λ Bootis (215.6), η Apodis (215.8)
October 17 18 19 20 21 22 (295)
NAKSHATRA DATES:
FEBRUARY 13 2-14 (45) 15 16 (413 = 14 * 29½) 18
ι Arietis (28.0), λ Arietis (28.2), υ Ceti (28.8) ALRISHA, χ Phoenicis (29.2), Alamak (29.7) Arku-sha-rishu-ku-2 η Arietis (31.9) no star listed (32) θ Arietis (33.3), MIRA (33.7)
2h (30.4)
κ Arietis (30.3), HAMAL (30.5)

Alkes

April 18 (108) 19 (*29) 20 (475) 21 22 23
Ga7-20 Ga7-21 Ga7-22 (191) Ga7-23 Ga7-24
SEPTEMBER 26 27 (270) 28 29 30 (*193)
ATRIA (253.9) Tail-6 ι Ophiuchi (255.3), Grafias (255.4) κ Ophiuchi (256.2), ζ Arae (256.5), ε Arae (256.8), Cujam (256.9) no star listed (257)
Wei, η Arae (254.3), DENEBAKRAB (254.7)
November 29 30 December 1 2 (336) 3
NAKSHATRA DATES:
MARCH 28 29 30 31 (90) APRIL 1
Tabit (71.7), π² Orionis (71.9) π4 Orionis (72.1), ο¹ Orionis (72.4), π5 Orionis (72.8) π¹ Orionis (73.0),ο² Orionis (73.4), HASSALEH (73.6), π6 Orionis (73.9) Almaaz (74.7), HAEDUS I (74.8) HAEDUS II (75.9)
May 31 June 1 2 3 4 (155)