List of Illustrations

Figure 1.1. Dürer, The Northern and Southern Celestial Hemispheres 4

Figure 2.1. Diurnal arcs near the North Celestial Pole 14

Figure 2.2. The horizon system of spherical astronomical coordinates 15

Figure 2.3. The equatorial ("Chinese") system of spherical astronomical coordinates 16

Figure 2.4. A variant of the equatorial system, in which the hour angle is used 18

Figure 2.5. The equatorial and horizon systems and the "astronomical triangle" 19

Figure 2.6. The classic cosmological frameworks 20

Figure 2.7. Sky views of diurnal arcs: Dependence on declination and latitude 23

Figure 2.8. The effect of solar altitude on ground warming 23

Figure 2.9. The heliacal setting of the Pleiades in Jerusalem, ~132 b.c 24

Figure 2.10. The off-center circle Hipparchos model for the eccentric solar orbit 25

Figure 2.11. Constellations on the meridian at evening twilight, but two months apart 26

Figure 2.12. The ecliptic (or "Greek") system of astronomical coordinates . . . 28

Figure 2.13. The equatorial and ecliptic systems superposed 29

Figure 2.14. The phases of the Moon during the synodic month 30

Figure 2.15. The angular speed of an object moving across our line of sight 31

Figure 2.16. Elements and other properties of an elliptical orbit 32

Figure 2.17. Effects of the nodal regression of the lunar orbit 35

Figure 2.18. Apparent motion of Mars 37

Figure 2.19. Venus as an evening star and its telescopic appearance at elongation 38

Figure 2.20. Orientations of the ecliptic and celestial equator to the horizon . . . 39

Figure 2.21. The geocentric planetary configurations 40

Figure 2.22. Positions of planetary orbits relative to the Earth 41

Figure 2.23. Motions of an interior planet 41

Figure 2.24. Effect of parallax on the apparent direction to a planet 43

Figure 3.1. Plane-parallel atmosphere and the definition of air mass 50

Figure 3.2. Atmospheric refraction geometry 61

Figure 3.3. Snell's law: Refraction changes with medium 61

Figure 3.4. Novaya Zemyla effect on images of the setting Sun 63

Figure 3.5. Effects of dip and refraction on the altitude of the horizon 63

Figure 3.6. Topocentric versus geocentric coordinate systems and lunar parallax 64

Figure 3.7. Mercury as an evening star 66

Figure 3.8. Effects of precession on the vernal equinox and (a, 8) 67

Figure 3.9. Effects of precession on the north (and south) celestial poles . . . 68

Figure 3.10. NCP and SCP motion about the north and south ecliptic poles 69

Figure 3.11. Effect of precession on stars above the southern horizon 70

Figure 3.12. Proper motion simulation 72

Figure 3.13. Day-to-day horizon changes in the rising and setting Sun 72

Figure 3.14. The azimuth variation of sunrise over the year 73

Figure 3.15. The shaft of the passage grave at Newgrange 73

Figure 3.16. The gnomon and its use in solar measurements 74

Figure 3.17. The altitude of the noon Sun and the latitude 75

Figure 3.18. Heliacal and acronychal risings and settings 76

Figure 3.19. Front and back views of a sixteenth-century German astrolabe 78

Figure 3.20. Sketch of a medieval triquetrum 79

Figure 3.21. Chinese armillary spheres in Beijing 80

Figure 3.22. The solar clock tower of Chou Kung at Kao-chheng, China 80

Figure 3.23. Scenes of Ulugh Begh's observatory at Samarkand 81

Figure 3.24. Astronomical instruments at the Jaipur observatory, India 82

Figure 3.25. The "man in the moon" and the resolution of the human eye . . . 83

Figure 4.1. A modern cyclindrical sundial 87

Figure 4.2. Views of the Horologion, near the Plaka in Athens 88

Figure 4.3. A horizontal sundial from Beijing 89

Figure 4.4. A vertical sundial on a house in Switzerland 89

Figure 4.5. Sketch of a vertical sundial from Luxor 90

Figure 4.6. A stone sundial in the Forbidden City, Beijing 90

Figure 4.7. A sundial at the Jaipur observatory 90

Figure 4.8. Ecliptic movement of the Sun resolved into N-S and east motions 91

Figure 4.9. The equation of time 92

Figure 4.10. The analemma: Plotted; and incorporated in a modern sundial 93

Figure 4.11. A cosmological scheme and the days of the week 96

Figure 4.12. The tidal bulge and tidal friction 105

Figure 4.13. Shifting eclipse tracks from the slowing of Earth's rotation 106

Figure 5.1. The aurora borealis at Fort Yukon, Alaska 110

Figure 5.2. A Viking satellite view of the auroral oval 110

Figure 5.3. Arcs of primary and secondary rainbows 112

Figure 5.4. "Heiligenschein" around a shadow amidst steam 113

Figure 5.5. Sun column and sundog phenomena, including a vertical column of "multiple" Suns 113

Figure 5.6. A lunar halo 114

Figure 5.7. The basic geometry of solar and lunar eclipses 115

Figure 5.8. The solar eclipse of October 24,1995, Lopburi, Thailand 116

Figure 5.9. Solar eclipse geometry 116

Figure 5.10. Nodes of the lunar orbit 118

Figure 5.11. The ecliptic limits 119

Figure 5.12. The basic geometry of a lunar eclipse 120

Figure 5.13. The Moon in partial umbral eclipse 120

Figure 5.14. Solar phenomena 128

Figure 5.15. Comet Halley as seen in March 1986 from Cancun, Mexico 133

Figure 5.16. The origin of a comet's "sunward" tail 134

Figure 5.17. The springtime visibility (in the Northern Hemisphere)

of zodiacal light 138

Figure 5.18. A telescopic view of the Pleiades 142

Figure 5.19. The winter sky showing Sirius and Betelgeuse near the horizon . . . 145

Figure 5.20. Sky simulation views of the 1054 supernova explosion 150

Figure 6.1. The megalithic monuments of Europe 159

Figure 6.2. The "Hill o' Many Stanes" at Mid Clyth, Caithness, Scotland________164

Figure 6.3. Megalithic constructs: The Ring of Brogar, Orkney, Scotland;

Avebury 165

Figure 6.4. A sketch of the construct features at Crucuno 165

Figure 6.5. Foresight and backsight, and a setting Moon at maximum standstill 166

Figure 6.6. One of the lintels of the passage grave at Gavr'inis 167

Figure 6.7. The funerary complex in the Boinne Valley, Ireland 169

Figure 6.8. Views of the passage grave monument at Newgrange 169

Figure 6.9. Views of kerbstones at Newgrange 170

Figure 6.10. Views of the ring of standing stones at Newgrange 171

Figure 6.11. Simulation of shadow effects involving a kerbstone and standing stones at Newgrange 172

Figure 6.12. The grave monument at Knowth, Ireland 173

Figure 6.13. A possible sundial among the kerbstones at Knowth 174

Figure 6.14. Ornamentation on kerbstone 52 shows possible lunar representations 174

Figure 6.15. Exterior and interior views of a tomb at Dowth, Ireland 175

Figure 6.16. Sectional panoramas of the Loughcrew funerary complex,

Ireland 176

Figure 6.17. Cairn L of the Loughcrew complex 177

Figure 6.18. Layout of the Cumbrian circle of Castlerigg, England 179

Figure 6.19. Sectional panoramas of Castlerigg, England, in the

Lake District 180

Figure 6.20. Panoramas of Long Meg and Her Daughters, near

Penrith, England 181

Figure 6.21. Long Meg addressing the assembled stones 182

Figure 6.22. Rain-darkened markings on Long Meg 182

Figure 6.23. Panoramic view of Arbor Low at Derbyshire, England 183

Figure 6.24. View from the NNE of Callanish, Isle of Lewis,

Outer Hebrides 183

Figure 6.25. Features of the Callanish site 184

Figure 6.26. The (symbolic) killing of the sacred wren on

Saint Stephen's Day 186

Figure 6.27. A few of the Standing Stones of Stenness, Mainland, Orkney . . . 186 Figure 6.28. Stonehenge and surroundings on the Salisbury Plain,

England 188

Figure 6.29. The general layout of Stonehenge 189

Figure 6.30. Views of the Heel Stone at Stonehenge 190

Figure 6.31. A plan view of the horizon and the standstills of the Moon 191

Figure 6.32. Possible use of the Aubrey holes Stonehenge as a stone age "abacus" 191

Figure 6.33. The parallactic shift in azimuth to observe a given shift in declination 197

Figure 6.34. Thom's proposed triangle method for interpolation 198

Figure 6.35. Thom's proposed sector method for interpolation 198

Figure 6.36. The Tal Qadi stone 201

Figure 6.37. Pillar markings at Mnajdra Temple III on Malta 202

Figure 6.38. The tumulus and menhirs of Mzorah, North Africa 204

Figure 6.39. Views of three principal Medicine Wheels 207

Figure 6.40. The Minton Turtle effigy, south-central Saskatchewan 208

Figure 7.1. Mesopotamian representations of the constellations superimposed on a simulation of the sky of 2500 b.c 214

Figure 7.2. A monument of King Esarhaddon of Assyria, Zinjirli 214

Figure 7.3. A Kassite boundary-stone and possible constellations 227

Figure 7.4. The fragments of a cuneiform tablet from Babylon (No. 5) 232

Figure 7.5. Solar motion according to Babylon: Plot of column II (B)

versus month number from Tablet No. 5 232

Figure 7.6. Sun's angular speed: Differences between entries of

Column B 232

Figure 7.7. A zigzag function of System B from Babylon Tablet No. 120,

Column A (solar motion per month) 235

Figure 7.8. The zigzag function found from data in Column F of

Tablets 5 and 120 236

Figure 7.9. Another zigzag function: Column ® of Tablet 5 236

Figure 7.10. Planetary phenomena as understood in Babylonian astronomy . . 237 Figure 7.11. Ruins of the temple of Olympian Zeus at Akragas

(now Agrigento), Sicily 241

Figure 7.12. Sketch of the concentric spheres cosmological concept of

Eudoxus 242

Figure 7.13. The rolling motion of one planetary sphere on another:

The hippopede 242

Figure 7.14. Aristarchos's method to find the ratio of distances of the

Moon and Sun from Earth 244

Figure 7.15. Eratosthenes's method to determine the circumference of the Earth 245

Figure 7.16. Mercury's epicycle and eccentric deferent, according to

Ptolemy 247

Figure 8.1. Depiction of the 75 manifestations of Re from the reigns of

Thutmose III and Seti I 265

Figure 8.2. A coffin lid interior from ~2100 b.c., illustrating the diagonal calendar 266

Figure 8.3. Details from Dendera, and the coffin lid of Heter 267

Figure 8.4. Petrie's star map of Egyptian constellations 270

Figure 8.5. Constellations from the tomb of Seti I and Locher's attempt to correlate star patterns with outlines of depictions 271

Figure 8.6. The geometry of the Lunar "gates" 272

Figure 8.7. Possible representations of planetary gods, from the

Tuareg-related peoples in the Sahara 273

Figure 8.8. Dogon cosmology according to Marcel Griaule 274

Figure 9.1. Temples carved from solid rock near Mahabalipuram, southern India 284

Figure 9.2. View from the southwest of the shore temple at

Mahabalipuram 285

Figure 9.3. The temples at Kanchipuram, India 285

Figure 9.4. Temples of Bhubaniswar, India 286

Figure 9.5. The Sun god Surya in his chariot, a chlorite sculpture at

Konarak, on the Bay of Bengal 287

Figure 9.6. The Jagomohana or great hall at Konarak 287

Figure 9.7. Two of the 12 great stone chariot wheels at Konarak 288

Figure 9.8. One of the remaining horses lining the stairway of the chariot-temple at Konarak 288

Figure 9.9. Erotic sculpture from the solar temple at Konarak 288

Figure 9.10. The Observatories of the Maharajah Jai Singh at

Jaipur and New Delhi 295

Figure 9.11. Temples of the Wat Phra Si Sanphet in Ayutthaya, Thailand . . . . 302 Figure 9.12. A chedi in the Wat Phra That Doi Suthep in Chiang Mai,

Thailand 303

Figure 9.13. Elements of a pelelintangan rearranged into ten-week sequences 305

Figure 9.14. 68 Burmese asterisms; and a subset with names of Balinese bintang parallels 306

Figure 9.15. The planetary gods housed in a structure at Konarak 309

Figure 9.16. Silk coffin shrouds from Astana on the ancient Silk Road to China 311

Figure 10.1. Pairings of the Xius according to Saussure (1930) 316

Figure 10.2. Elimination of Vega from the Xius because of precession 317

Figure 10.3. Animal series known as the "rat zodiac," from a Chinese mirror rubbing 318

Figure 10.4. Supernatural figures associated with the 28 Xiu in the

Jade Box Scriptures 323

Figure 10.5. A Tang "magic mirror" with the 28 Xiu, 8 trigrams, rat zodiac, and four great directional animals 324

Figure 10.6. Another Tang "magic mirror," showing the 28 Xiu as animals in CCW order 324

Figure 10.7. The Suchow planisphere from the southern Sung Dynasty 325

Figure 10.8. A map of the walls of the Chinese imperial city Chang-An 326

Figure 10.9. The four directional animals represent divisions of the year as asterisms 329

Figure 10.10. A Han forerunner of a shih with unequal divisions of the 28 xiu 330

Figure 10.11. A recently discovered shih (diviner's plate) of the

Sui Dynasty 330

Figure 10.12. Champsong-dae or "Star Tower" near Kyongju, Korea 333

Figure 11.1. The Mamari Tablet from Easter Island 340

Figure 11.2. A mnemonic navigation image: The sky pictured as a giant house 343

Figure 11.3. Star Compass of the Bugis navigators of Sulawesi and the

Indonesian archipelago 345

Figure 11.4. The crescent moon as a seasonal direction indicator 345

Figure 11.5. A navigational gourd from Hawaii, according to

David Malo Kupihea 345

Figure 11.6. Views from Cape Kumukahi, easternmost point of Hawaii 348

Figure 11.7. Heaven and the Underworld, according to the

Tuamotuan Paiore 349

Figure 12.1. The Mesoamerica region with major sites noted 354

Figure 12.2. A Jaina Island figurine, possibly of an observer with optical aid 354

Figure 12.3. Borgia Codex glyphs of the day names and ruling deities of the days 357

Figure 12.4. Writing of a date ( 12 Lamat 1 Muan), in inscriptions or codices 359

Figure 12.5. Glyphs from the Yaxchilan ballcourt: The date of a cosmic ball game 362

Figure 12.6. Planetary band glyphs from the coffin of Pacal, ruler of Palenque 362

Figure 12.7. Drawings of some planetary and eclipse gods 367

Figure 12.8. Versions of the Feathered Serpent 368

Figure 12.9. The Vase of the Seven Gods 369

Figure 12.10. The structure of the Dresden Codex Venus Table 371

Figure 12.11. Hun Hunahpu and the other gods emerging 372

Figure 12.12. A prototype Moon god from Teotihuacan and the head of a Mayan Sun god as a gourd 379

Figure 12.13. God L in the house of Jaguar Snakes with five

Moon goddesses 382

Figure 12.14. Princeton Vase 4: Decapitation at an eclipse 382

Figure 12.15. The possible eclipse symbols of the Borgia Codex 389

Figure 12.16. A four-sided vase [K5113] of the Classic Period 390

Figure 12.17. Year 1 Reed, day 4 Earthquake, the Sun God, on his throne, interpreted as winter solstice, 936 a.d 395

Figure 12.18. Stela 3 of Caracol, Belize, an integration of Mayan astronomy and dynastic history 399

Figure 12.19. The Aztec "calendar stone" 401

Figure 12.20. The relationships of the sequences of the Trecenas and the

Nine Lords of the Night to segments of the sky 403

Figure 12.21. The Palace of the Governor at Uxmal 404

Figure 12.22. The Pyramid of the Magician at Uxmal 404

Figure 12.23. Monte Alban: Photographic and plan views 406

Figure 12.24. Simulations of the heliacal rise of Capella at Monte Alban 406

Figure 12.25. The zenith distance at a transit of six stars of the Pleiades 408

Figure 12.26. The Caracol at Chichen Itza 409

Figure 13.1. A rock cut overhang in Chaco Canyon, pictographs, possibly, on the 1054 supernova event 413

Figure 13.2. Map of the Chaco Canyon area, U.S. southwest 415

Figure 13.3. Two Navajo sky charts from sand-paintings 416

Figure 13.4. A sand-painting with asterisms, and Father Sky 417

Figure 13.5. A possible Navajo star map on a rock wall 417

Figure 13.6. Black Point Ceremonial Pathway, relating astronomy and cosmology 418

Figure 13.7. An Ipai ground painting of the Earth and Sky 419

Figure 13.8. Burro Flats, California: A Sun-illuminated spiral, not long after winter solstice; and Sapaksi cave: Sun daggers at equinox 420

Figure 13.9. A diagram of the Pawnee scaffold and associations 422

Figure 13.10. An Osage drawing of the cosmos 426

Figure 14.1. Identifications of South American sites 432

Figure 14.2. The Sierra Madre region and the locations of Kogi villages 432

Figure 14.3. A Tairona ceremonial building 433

Figure 14.4. The pispiska, used by Kogi priests to relate the calendar to astronomy 436

Figure 14.5. The Lanzon at Chavin de Huantar 439

Figure 14.6. Burial of a woman in a step pyramid, amid possible astronomical themes 443

Figure 14.7. Possible depictions of a myth involving the central star of Orion's Belt as a captive 444

Figure 14.8. The Thunder Twin in five scenes from a pot 445

Figure 14.9. A rattle with representations of four seasonal "grand scenes" . . . 445 Figure 14.10. Gods with war clubs and the prisoner on the same serpent frame 445

Figure 14.11. The "Bridge of Cords" or "The Spider Path to Heaven" 446

Figure 14.12. The Thunder Twin (two versions) 446

Figure 14.13. The two-headed fox snake as the litter-of-the-Sun 447

Figure 14.14. The two-headed fox snake as an image of the rainbow 448

Figure 14.15. Moche depiction of two corncobs with deity heads 448

Figure 14.16. Quechua games of chance, played with beans as counters 448

Figure 14.17. Moche "grand scene" involves races analogous to an initiation ritual at the time of the December solstice 449

Figure 14.18. The Moche myth of the Flood and the "Revolt of the

Artifacts" 449

Figure 14.19. A Moche pot suggests a relationship between the

Moon and stars 450

Figure 14.20. Paired water craft 450

Figure 14.21. A fisher god on a flying (bird-borne) boat 451

Figure 14.22. Warriors at the Festival of Coya Raymi (Quechua) 451

Figure 14.23. A Chimu representation of the birth of a tree 451

Figure 14.24. The Weavers, including Venus? 452

Figure 14.25. A Moche pot with Fox-Snake, which should represent the ecliptic at an equinox or solstice point, at the bottom 452

Figure 14.26. A pre-Columbian instrument, possibly used for surveying and astronomical observation 453

Figure 14.27. The types and locations of the terraglyph figures on the

Nazca plains, Peru 454

Figure 14.28. The schematic contents of a Nazca textile described as a calendar 457

Figure 14.29. Individual images from the "Paracas" textile 458

Figure 14.30. The Akapana monument at Tiahuanaco, Bolivia 461

Figure 14.31. The Bennett Stela of Tiahuanaco, Bolivia 461

Figure 14.32. The cosmological map of Pachacuti, Yamqui Salcamayhua 465

Figure 14.33. A nineteenth-century drawing of a possible star map on a carved rock from Pedra Lavrada, Paraiba 468

Figure 14.34. Barasana constellations 469

Figure 14.35. The asterisms of the Wayana of Surinam and

French Guiana 470

Figure 15.1. Comparisons of Greco-Roman Judaic and Mesoamerican astronomical and astrological symbolism 477

Figure 15.2. Bird breasts in the form of bearded human heads representing star deities 477

Figure 15.3. The "lion horoscope," from the west terrace of Nemrud Dag,

Turkey 479

Figure 15.4. The recreation of the "lion horoscope" sky 480

Figure 15.5. Simulations of conjunctions of Venus and Jupiter, noteworthy candidates for the Star of Bethlehem 485

Figure 15.6. Versions of the Cosmic Churn from Angkor Wat and the Totonac 489

Figure 15.7. Bound turtle imagery from Bali, India, and the Bataks of Indonesia 489

Figure 15.8. Mayan representations of a similar theme 490

Figure 15.9. The Cosmic Churn in India 490

Figure 15.10. Indian and Tibetan turtles as world supporter 491

Figure 15.11. A Tibetan plaque of the Cosmic Turtle bearing the magic square 491

Figure 15.12. An Assyrian amulet in the form of a turtle-like "monster"

with stellar symbolism 492

Figure 15.13. The Cosmic Turtle and snake, as one of the four great directional deities, from China 492

Figure 15.14. Turtles and magic squares, from China 492

Figure 15.15. The kan cross of Mesoamerica and the magic square of 5 493

Figure 15.16. Other Mesoamerican references to turtles 493

Figure B.1. The equatorial region of the sky, equinox 2000.0 509

Figure B.2. North celestial pole region, equinox 2000.0, and south celestial pole region, equinox 2000.0 510

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