Solstices: Determination and Celebration Christmas Is Celebrating What Birth? www.dioi.org/cs.pdf Dennis Rawlins 2019 May 29 [email protected]
A Historical Solstices: Why Does the Christian World Celebrate Christmas on December 25? A1 Unless Caesar Augustus thought Winter was an ideal time for the citizenry’s travel to pay taxes (Luke 2.1 4), it’s unlikely Jesus was born in late December. Almost no scholar thinks he was, in spite of traditional public celebration of Jesus’ nativity every December 25. It’s common knowledge among astronomers that Christmas is really celebrating Winter Solstice, when the noon Sun’s height ends its Autumn decline and, reborn, starts rising. [This occurs around December 20 21 in our time.] During the Christian Era, the Winter Solstice never fell on December 25. But it did so around the 4th century BC, which (though that’s before the official Julian calendar) might hint at a pagan origin for December 25. In any case a pagan was the emperor who chose December 25: Aurelian (ruler 270 275 AD) picked that date to honor the sun god Sol Invictus, the deity his army prayed to: successfully, in the sense that Aurelian won every war he entered; but unsuccessfully, in the sense that some among his army (sparked by forgery) conspired against him during an invasion of Persia and he was fragged in 275 AD [Gibbon Decline . . . Chap.11 (Mod.Libr.ed. 1910 1:274)]. A2 After Christianity became Rome’s official religion in the early 4th century AD, Church&government smoothened the transition to totalitarian theocracy by cooperatively absorbing/adopting/agreeing to Rome’s (& other regions’) traditional solstitial festivals. Just as the Church absorbed much of Roman law. (Including even such odd details as foetal ensoulment 40d after conception, a rule often misascribed to Aquinas over a millennium later.) Indeed, for the modern Church’s borrowing from 5th century Greece, 2 1/2 millennia ago: see below at §A4. A3 But noting solstices predates imperial Rome by centuries. While Babylon’s astrologer priests obtained solstices merely by indoor calculation (Neugebauer History of Ancient Mathematical Astronomy 1975 p.366), Greek astronomers attempted empirical determinations: the oldest known was by Meton of Athens in 432 BC to memorialize the onset of the Peloponnesian War (432 404 BC) which its scrupulous chronicler Thukydides called The Greatest. (Has any previous historian made the ultra obvious connexion of Meton’s solstice to the War?) It mayn’t be widely known that most of the world (early Egypt the solar exception) has lived by lunar calendars. A substantial fraction of it still does. A4 Meton dated his calendar from his solstice, 432 BC June 27 3/4 (sunset). But this time was merely the start (sunset by Athenian convention) of the day containing the solstice, which actually occurred 17h later, at June 28 11h; so Meton’s truncation to day start created a huge&fateful error. His calendar operated according to his 19y Metonic Cycle of 235 months in 6940d, which he codified by his Metonic lunisolar calendar rule (later adopted by Babylon in the 380s BC [Neugebauer op cit pp.354&366] & still used by Christians for fixing Easter):
19 years = 235 months (1) which could have lowered tensions between lunar and solar priests. (Even while enraging conservative playwright Aristophanes, whose Birds satirically calls Meton a “quack&imposter” while beating him & kicking him off the stage, and whose Clouds says his kind’s calendaric innovations starve the gods by confusing their festivals’ predictability.) When the month became exactly known c.280 BC (www.dioi.org/mn.pdf,§B2), Meton calendaric eq.1 made the year 6m too long, causing 1000y of severe consequences for accurate astronomy (www.dioi.org/pg.pdf,§D; www.dioi.org/bt.pdf, §A) as well as nuclear devastation upon the reputation of “The Greatest Astronomer of Antiquity”, Cloddiest Ptolemy (ibid §A2), whose loyal belief in the accuracy of the solar orbit he took from Hipparchos ultimately betrayed (ibid) his penchant for indoor computing solar positions from Hipparchan data, rather than outside observing the real Sun. A5 Alexander’s astronomer Kallippos launched a calendaric cycle, dating from his own observed dawn solstice 330 BC June 28 1/4 (www.dioi.org/jk02.pdf, eq.1), 102y after Meton’s solstice. He improved on Meton in a previously unnoted way by choosing a solstice less than 1h from a New Moon (Sun Moon conjunction) a solstitial proximity which occurs only once in centuries, thus an ideal zero epoch for a lunisolar calendar. By dividing 102 into the 37255d1/2 interval between his own solstice & Meton’s calendaric solstice (not his observed solstice, sadly: §A4), Kallippos stumbled upon — originated — the 365d1/4 year (284y before Julius Caesar’s Sosigenes [§B4]) & believed it true, presumably because he knew his solstice was carefully observed. (Error just +3h, perhaps mostly from ancient 1d/4 precision rounding conventionfor solstices: ibid Table 3.) The 76y Kallippic Cycle of 27759d became canonical among astronomers and 2 centuries later was regularly used by Hipparchos to date his work. But its 365d1/4 yearlength’s . accuracy was vitiated by Meton’s −17h (§A4) truncation and his own +3h error, thus too high by c.+20h/102 = +0h.2: the very same error for which we now adjust the 365d1/4 calendar, thrice every 400y by Gregorian calendar rules (§C1). A6 Heliocentrist Aristarchos observed a 280 BC June 27 1/4 solstice: error 0h (ibid eq.2 & Table 3). He may’ve also launched the Dionysios calendar, based on a 285 BC solstice (B.L.van der Waerden Arch.Hist.ExactSci.29.2:125 130). A7 Hipparchos’ 1st solar orbit used solstice 158 BC June 26 18h (error 0h) & Kallippic motion, as Tihon found (Archimedes 23:2) in 2010, thus redeeming (www.dioi.org/jm02.pdf, §N19) DIO’s 2 unprecedented 1991 inductions (www.dioi.org/j139.pdf, §§K8 and K9&M4) that Hipparchos started with a 158 BC solstice and Kallippic solar motion. A8 History of science archons persistently & unregenerately hallucinate (www.dioi.org/hs.pdf, §G) that ancient equinoxes were more accurate than solstices. (Which prominent politician historians teach [idem] couldn’t be accu rately measured since the Sun was moving so little at solstice!) Aside from the highschool science involved here (idem or below at §D1), one is puzzled at historians’ historical unawareness that ALL Greek scientists knew better, preferring solstices not equinoxes to gauge yearlengths (sources for the Greek astronomers at www.dioi.org/jm02.pdf, fn 11): Meton, Euktemon, Kallippos, Aristarchos, Dionysios, Hipparchos, P.Fouad 267A, Astron. Cuneiform Text #210. 2 Solstices: Determination and Celebration www.dioi.org/cs.pdf 2019 May 29 Dennis Rawlins
B Sun God Rebirth: Rounding the Goalposts B1 The foregoing data are pre Christian. During the AD era, Claudius Ptolemy’s Almajest (c.160 AD), a handbook of the state’s Serapic religion, codified&disseminated the Hipparchan yearlength, 365d1/4 − 1/300, whose error is 6m/year, suspiciously close to Meton’s (§A4 & eq.1). Hipparchos’ tables and Ptolemy’s handbooks became canonical to the pagans. Hipparchos even appeared on coins minted by the state (G.Toomer DSB Hipparchus entry). The last pagan emperor, Julian the Apostate (d.363 AD), in his Hymn to the Sun lauds (LCL ed. 1:429) Hipparchos&Ptolemy’s solar orbits, & speaks of the Sun rounding the “goal posts” of Capricorn, reborn passing the Winter Solstice, starting its annual northing. Whether celebrants realize it or not, it is this “Birth” that all solstitial festivals are celebrating. B2 Within a century after Julian was killed while invading Persia in 363 AD (fragged? [§A1]), December 25 ◦ became evermore accepted as Jesus’ birth. Yet already by Julian’s time, the solar tables he glorified were more than 2 or 2d in error. But he remarks not the slightest problem with his sun cult’s idols, perhaps helping start a trend (which any remaining empirical astronomers of the time must have ironically scoffed would be VERY short lived) of hyping indoor Ptolemy as “The Greatest Astronomer of Antiquity”. B3 Once the West declined into the Dark Ages, empirical astronomy “died like a snuffed candle” to borrow the imagery of my late friend mathematician historian B.L.van der Waerden (Science Awakening 1 1963 p.291) regarding the simultaneous death of the Greek mathematical tradition. B4 Just as Islam’s holiest building, Hagia Sophia, was built by Christians (6th century AD), so Christians’ calendar was designed by the pagan Sosigenes, for Julius Caesar. This “Julian” calendar, unchanged for 1627y (46 BC to 1582 AD), was blindly followed by Christendom in spite of a confusing slippage of Christian feast dates (vs the outdoor sky) that would’ve have shaken the shade of Aristophanes. As at Babylon (§A3), “celestially based” holy days (e.g., Easter) were generated from indoor tables.
C Gregorian Salvation & the Tropical Year C1 Pope Gregory XIII in 1582 October converted from the old Julian calendar to his Gregorian calendar by adding 10d to all future dates and deputed Christopher Clavius, S.J., to correct §B4’s slow shift of Christian festivals due to the Julian 365d1/4 year’s excess, with the aim of restoring them to their position in Jesus’ day. Clavius proposed the excellent value 365d1/4 − 3/400 for the tropical year, very close to the real tropical yearlength then: 365d.2423. (For the era of Hipparchos the real yearlength was 365d.2425 and today it is 365d.2422.) Protestant nations resisted the improved calendar for over a century, causing the inconvenience of date differences when moving between nations. Upon Britain’s surrender, the “Eleven Day Riots” broke out, not lasting 11d but briefly intense since the public thought the added 11d (to accord with the Gregorian calendar) were part of a scheme to deny wages. Now, except for Greek&Russian orthodox churches, the West abides by the Gregorian calendar. [Note in passing that, for premodern yearlengths here, we include the effect of Earth spin deceleration on the day length temporal yardstick used.] C2 The term “tropical year” appears to refer to the time for a solar return to the Summer or Winter Tropic. But the tropical year is merely the time for one circuit of the mean Sun vs the mean equinox. In truth, each of the four cardinal points has its own year: e.g., the time between Summer Solstices differs from that between Winter Solstices. For 280 BC (www.dioi.org/d913.pdf, fn 18), expressing yearlength as 365d1/4 + 1/R, mean tropical year’s R = −133.
V.Eqx Rt = −129; S.Sol Rt = −124; A.Eqx Rt = −138; W.Sol Rt = −144. (Mean 2000 tropical year R = −128.) C3 When dealing with ancient estimates of yearlength from observations separated by centuries, §C2’s tiny ef fects accumulate to non negligibility. For applications of them to analyses, the interested reader is referred to www.dioi.org/jk02.pdf, our pioneering study of ancient solstices, which we’ll draw upon for our final section §D.
D How Ancients Determined Solstices — and How You Can Do It, Too D1 Relaying DIO’s mathematical solstice investigations, Wikipedia makes it clear: it is by now general knowledge [outside of history of science archondum: §A8] that ancients gauged solstices by Equal Altitudes, finding a Local Apparent Noon solar altitude d days ere Solstice (a few weeks — ideally c.20d for Hipparchos’ time: ibid eqs.19 21), then waiting until the Sun returns to that LAN altitude and taking the average of the two times. You can do this at home by tracking marking a fixed object’s solar shadows upon a fixed surface. D2 Wikipedia also performs the public service of disseminating our new formula for correcting Equal Altitude measurements for the slight ordmag 1h effect of the Earth’s orbital ellipticity. Near solstice, mean daily solar motion t t . ◦ d 1+ 2 m = (360 /365 1/4)(1 − 2e sin A). For Equal Altitude times t1 & t2, the MidPoint time tMidPt ≡ 2 ; and 2 Summer Solstice’s true time tSS is tMidPt corrected for H = −(2πme cos A)d /15 (www.dioi.org/jk02.pdf, eqs.10 13), tMidPt’s systematic error in hours from the elliptic effect of eccentricity e for solar apogee A. So Solstice time tSS is: t + t t + t t = t − H = 1 2 − [−(2πme cos A)d2/15] {= 1 2 + d2/345 for Hipparchos’ era} (2) SS MidPt 2 2 t −t 2 1 for t in hours and d = number of days ere&aft Solstice for Equal Altitudes. (Obviously, d = 2 .) Suggested reader exercises: [a] outdoor observe a Solstice; [b] find H for our era, using eq.2 and modern A = 103◦.3 & e = 0.0167. (From ibid fn 7, the correction’s sign flipped in 1245 AD, so H for our time will be positive.) We close by wishing you Successful Solsticing!