Mathematical facts concerning pyramids and stars in Orion ========================================================= output produced: 2021-08-19T18:50:47.385Z code written by Henk Reints MSc. -- http://Henk-Reints.nl %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Pyramids: (h = height, b = base, p = perimeter, be,ae = base,apex elevation above current sea level) ========= pyramid of Djoser | Geo: 29°52'16".36 = 29°.8712100N / 31°12'59".69 = 31°.2165800E | h: 119 cu = 62.3 m, b: 208,231 cu = 108.9, 120.9 m, p: 878 cu = 459.6 m, p/h: 7.378151, be,ae: 60, 122 m pyramid of Cheops/Khufu | Geo: 29°58'45".05 = 29°.9791813N / 31°08'03".11 = 31°.1341960E | h: 280 cu = 146.6 m, b: 440 cu = 230.3 m, p: 1760 cu = 921.4 m, p/h: 6.285714, be,ae: 69, 215 m pyramid of Chephren/Khafre | Geo: 29°58'33".55 = 29°.9759865N / 31°07'50".65 = 31°.1307354E | h: 274 cu = 143.4 m, b: 411 cu = 215.2 m, p: 1644 cu = 860.6 m, p/h: 6.000000, be,ae: 77, 220 m pyramid of Menkaure | Geo: 29°58'21".01 = 29°.9725014N / 31°07'41".73 = 31°.1282569E | h: 125 cu = 65.4 m, b: 200 cu = 104.7 m, p: 800 cu = 418.8 m, p/h: 6.400000, be,ae: 70, 135 m pyramid of Djedefre | Geo: 30°01'55".74 = 30°.0321500N / 31°04'29".53 = 31°.0748700E | h: 128 cu = 67.0 m, b: 202 cu = 105.7 m, p: 808 cu = 423.0 m, p/h: 6.312500, be,ae: 155, 222 m obelisk of Heliopolis | Geo: 30°07'45".66 = 30°.1293500N / 31°18'26".86 = 31°.3074600E | h: 21 cu = 11.0 m, b: 1.5 cu = 0.8 m, p: 6 cu = 3.1 m, p/h: 0.285714, be,ae: 13, 24 m bearings: from Menkaure SW to Menkaure NE : initial: 45°00', final: 45°00', distance: 148.1 m = 282.8 cu from Menkaure NE to Cheops SE : initial: 47°59', final: 47°59', distance: 856.0 m = 1635.2 cu from Menkaure SW to Cheops SE : initial: 47°33', final: 47°33', distance: 1003.9 m = 1917.7 cu from Menkaure NW to Chephren apex: initial: 41°07', final: 41°07', distance: 443.3 m = 846.9 cu from Chephren apex to Cheops apex: initial: 43°19', final: 43°19', distance: 486.8 m = 929.9 cu from Menkaure NW to Cheops apex : initial: 42°16', final: 42°16', distance: 930.0 m = 1776.4 cu misalignments: distance from Menkaure NE to line from Menkaure SW to Cheops SE : 6.6 m distance from Chephren apex to line from Menkaure NW to Cheops apex: 8.9 m %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Geodesic according to ellipsoidal geometry (Vincenty's inverse formula and WGS-84): =================================================================================== from: Geo: 29°58'45".05 = 29°.9791813N / 31°08'03".11 = 31°.1341960E / pyramid of Cheops/Khufu to: Geo: 30°07'45".66 = 30°.1293500N / 31°18'26".86 = 31°.3074600E / obelisk of Heliopolis > distance : 23 585.7 m = 45 053.9 cu > distance N-S: 16 646.7 m = 31 798.8 cu, intermediate: 16 531.1 m = 31 578.1 cu > distance E-W: 16 708.5 m = 31 916.9 cu, intermediate: 16 592.9 m = 31 696.2 cu > mean bearing: 45°06'22" = 45°.10617 (looking north, positive = clockwise) or: -134°53'38" = -134°.89383 (looking south, positive = clockwise) Geodesic according to ellipsoidal geometry (Vincenty's inverse formula and WGS-84): =================================================================================== from: Geo: 29°58'45".05 = 29°.9791813N / 31°08'03".11 = 31°.1341960E / pyramid of Cheops/Khufu to: Geo: 29°58'33".55 = 29°.9759865N / 31°07'50".65 = 31°.1307354E / pyramid of Chephren/Khafre > distance : 486.8 m = 929.9 cu > distance N-S: 354.2 m = 676.5 cu, intermediate: 131.4 m = 251.0 cu > distance E-W: 334.0 m = 638.0 cu, intermediate: 111.2 m = 212.5 cu > mean bearing: -136°40'46" = -136°.67934 (looking north, positive = clockwise) or: 43°19'14" = 43°.32066 (looking south, positive = clockwise) Geodesic according to ellipsoidal geometry (Vincenty's inverse formula and WGS-84): =================================================================================== from: Geo: 29°58'45".05 = 29°.9791813N / 31°08'03".11 = 31°.1341960E / pyramid of Cheops/Khufu to: Geo: 29°58'21".01 = 29°.9725014N / 31°07'41".73 = 31°.1282569E / pyramid of Menkaure > distance : 936.4 m = 1 788.7 cu > distance N-S: 740.5 m = 1 414.5 cu, intermediate: 573.0 m = 1 094.5 cu > distance E-W: 573.2 m = 1 094.9 cu, intermediate: 405.7 m = 774.9 cu > mean bearing: -142°15'28" = -142°.25778 (looking north, positive = clockwise) or: 37°44'32" = 37°.74222 (looking south, positive = clockwise) Geodesic according to ellipsoidal geometry (Vincenty's inverse formula and WGS-84): =================================================================================== from: Geo: 29°58'33".55 = 29°.9759865N / 31°07'50".65 = 31°.1307354E / pyramid of Chephren/Khafre to: Geo: 29°58'21".01 = 29°.9725014N / 31°07'41".73 = 31°.1282569E / pyramid of Menkaure > distance : 454.4 m = 868.0 cu > distance N-S: 386.3 m = 738.0 cu, intermediate: 226.4 m = 432.5 cu > distance E-W: 239.2 m = 456.9 cu, intermediate: 79.3 m = 151.4 cu > mean bearing: -148°14'08" = -148°.23558 (looking north, positive = clockwise) or: 31°45'52" = 31°.76442 (looking south, positive = clockwise) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Celestial objects: ================== Betelgeuse | Equ: RA: 05:55:10.305 = 88°47'34".580 = 88°.79293900 / Dec: 7°24'25".430 = 7°.40706400 / 2000-01-01T12:00:00.000Z | magnV: 0.42 Meissa | Equ: RA: 05:35:08.278 = 83°47'04".164 = 83°.78449004 / Dec: 9°56'02".961 = 9°.93415586 / 2000-01-01T12:00:00.000Z | magnV: 3.66 Bellatrix | Equ: RA: 05:25:07.863 = 81°16'57".949 = 81°.28276354 / Dec: 6°20'58".932 = 6°.34970328 / 2000-01-01T12:00:00.000Z | magnV: 1.64 Alnitak | Equ: RA: 05:40:45.527 = 85°11'22".900 = 85°.18969442 / Dec: -1°56'33".265 = -1°.94257358 / 2000-01-01T12:00:00.000Z | magnV: 1.79 Alnilam | Equ: RA: 05:36:12.813 = 84°03'12".200 = 84°.05338896 / Dec: -1°12'06".909 = -1°.20191914 / 2000-01-01T12:00:00.000Z | magnV: 1.69 Mintaka | Equ: RA: 05:32:00.400 = 83°00'06".001 = 83°.00166704 / Dec: 0°17'56".742 = 0°.29909511 / 2000-01-01T12:00:00.000Z | magnV: 2.41 Saiph | Equ: RA: 05:47:45.389 = 86°56'20".833 = 86°.93912017 / Dec: -9°40'10".578 = -9°.66960492 / 2000-01-01T12:00:00.000Z | magnV: 2.06 Rigel | Equ: RA: 05:14:32.272 = 78°38'04".082 = 78°.63446708 / Dec: -8°12'05".898 = -8°.20163836 / 2000-01-01T12:00:00.000Z | magnV: 0.13 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Geodesic according to spherical geometry: ========================================= from: Rigel | Equ: RA: 05:14:32.272 = 78°38'04".082 = 78°.63446708 / Dec: -8°12'05".898 = -8°.20163836 / 2000-01-01T12:00:00Z Rigel | Hor: Az: 190°24'33".182 = 190°.40921719 / Alt: 51°18'10".449 = 51°.30290256 / 2000-01-01T20:52:54.766Z @Cheops/Khufu to: Betelgeuse | Equ: RA: 05:55:10.305 = 88°47'34".580 = 88°.79293900 / Dec: 7°24'25".430 = 7°.40706400 / 2000-01-01T12:00:00Z Betelgeuse | Hor: Az: 170°44'58".722 = 170°.74964489 / Alt: 67°10'31".737 = 67°.17548250 / 2000-01-01T20:52:54.766Z @Cheops/Khufu from azimuth,altitude: > angular separation: 18°36'21" = 18°.60596 > mean bearing : -32°41'36" = -32°.69322 (looking south, positive = clockwise) Geodesic according to spherical geometry: ========================================= from: Alnitak | Equ: RA: 05:40:45.527 = 85°11'22".900 = 85°.18969442 / Dec: -1°56'33".265 = -1°.94257358 / 2000-01-01T12:00:00Z Alnitak | Hor: Az: 179°59'46".837 = 179°.99634363 / Alt: 58°04'41".683 = 58°.07824540 / 2000-01-01T20:52:54.766Z @Cheops/Khufu to: Alnilam | Equ: RA: 05:36:12.813 = 84°03'12".200 = 84°.05338896 / Dec: -1°12'06".909 = -1°.20191914 / 2000-01-01T12:00:00Z Alnilam | Hor: Az: 182°11'22".945 = 182°.18970700 / Alt: 58°48'00".441 = 58°.80012258 / 2000-01-01T20:52:54.766Z @Cheops/Khufu from azimuth,altitude: > angular separation: 1°21'22" = 1°.35601 > mean bearing : 57°50'29" = 57°.84142 (looking south, positive = clockwise) Geodesic according to spherical geometry: ========================================= from: Alnitak | Equ: RA: 05:40:45.527 = 85°11'22".900 = 85°.18969442 / Dec: -1°56'33".265 = -1°.94257358 / 2000-01-01T12:00:00Z Alnitak | Hor: Az: 179°59'46".837 = 179°.99634363 / Alt: 58°04'41".683 = 58°.07824540 / 2000-01-01T20:52:54.766Z @Cheops/Khufu to: Mintaka | Equ: RA: 05:32:00.400 = 83°00'06".001 = 83°.00166704 / Dec: 0°17'56".742 = 0°.29909511 / 2000-01-01T12:00:00Z Mintaka | Hor: Az: 184°24'30".040 = 184°.40834438 / Alt: 60°14'49".377 = 60°.24704906 / 2000-01-01T20:52:54.766Z @Cheops/Khufu from azimuth,altitude: > angular separation: 3°07'56" = 3°.13224 > mean bearing : 46°12'57" = 46°.21581 (looking south, positive = clockwise) Geodesic according to spherical geometry: ========================================= from: Alnilam | Equ: RA: 05:36:12.813 = 84°03'12".200 = 84°.05338896 / Dec: -1°12'06".909 = -1°.20191914 / 2000-01-01T12:00:00Z Alnilam | Hor: Az: 182°11'22".945 = 182°.18970700 / Alt: 58°48'00".441 = 58°.80012258 / 2000-01-01T20:52:54.766Z @Cheops/Khufu to: Mintaka | Equ: RA: 05:32:00.400 = 83°00'06".001 = 83°.00166704 / Dec: 0°17'56".742 = 0°.29909511 / 2000-01-01T12:00:00Z Mintaka | Hor: Az: 184°24'30".040 = 184°.40834438 / Alt: 60°14'49".377 = 60°.24704906 / 2000-01-01T20:52:54.766Z @Cheops/Khufu from azimuth,altitude: > angular separation: 1°49'58" = 1°.83277 > mean bearing : 37°52'33" = 37°.87597 (looking south, positive = clockwise) Geodesic according to spherical geometry: ========================================= from: Saiph | Equ: RA: 05:47:45.389 = 86°56'20".833 = 86°.93912017 / Dec: -9°40'10".578 = -9°.66960492 / 2000-01-01T12:00:00Z Saiph | Hor: Az: 177°17'44".579 = 177°.29571648 / Alt: 50°18'55".475 = 50°.31540985 / 2000-01-01T20:52:54.766Z @Cheops/Khufu to: Bellatrix | Equ: RA: 05:25:07.863 = 81°16'57".949 = 81°.28276354 / Dec: 6°20'58".932 = 6°.34970328 / 2000-01-01T12:00:00Z Bellatrix | Hor: Az: 189°36'43".052 = 189°.61195885 / Alt: 66°05'11".131 = 66°.08642517 / 2000-01-01T20:52:54.766Z @Cheops/Khufu from azimuth,altitude: > angular separation: 16°58'54" = 16°.98166 > mean bearing : 22°30'35" = 22°.50961 (looking south, positive = clockwise) Geodesic according to spherical geometry: ========================================= from: Saiph | Equ: RA: 05:47:45.389 = 86°56'20".833 = 86°.93912017 / Dec: -9°40'10".578 = -9°.66960492 / 2000-01-01T12:00:00Z Saiph | Hor: Az: 177°17'44".579 = 177°.29571648 / Alt: 50°18'55".475 = 50°.31540985 / 2000-01-01T20:52:54.766Z @Cheops/Khufu to: Meissa | Equ: RA: 05:35:08.278 = 83°47'04".164 = 83°.78449004 / Dec: 9°56'02".961 = 9°.93415586 / 2000-01-01T12:00:00Z Meissa | Hor: Az: 184°01'38".461 = 184°.02735014 / Alt: 69°54'44".081 = 69°.91224469 / 2000-01-01T20:52:54.766Z @Cheops/Khufu from azimuth,altitude: > angular separation: 19°51'13" = 19°.85351 > mean bearing : 9°46'13" = 9°.77035 (looking south, positive = clockwise) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Bearings (axis w.r.t. meridian): ================================ Rigel/Belgeuse : -32°41'36" = -32°.69322 (looking south, positive = clockwise) Alnitak/Alnilam: 57°50'29" = 57°.84142 (looking south, positive = clockwise) Saiph/Bellatrix: 22°30'35" = 22°.50961 (looking south, positive = clockwise) Saiph/Meissa : 9°46'13" = 9°.77035 (looking south, positive = clockwise) Alnitak/Alnilam - Rigel/Belgeuse : 90°32'05" = 90°.53464 Alnitak/Alnilam - Saiph/Bellatrix: 35°19'55" = 35°.33181 Alnitak/Alnilam - Saiph/Meissa : 48°04'16" = 48°.07108 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Precession since last ice age (time of day = Alnitak's transit): # Betelgeuse # Rigel # clockwise skewness ================================================================ # --------------------------------- # --------------------------------- # at Alnitak's transit epoch: description # R.A. | decl. | azim | alt # R.A. | decl. | azim | alt # equatorial | horizontal ----------------------------------------------------------------- # -------+--------+--------+------- # -------+--------+--------+------- # -----------+----------- -15000 # 211°.8 | -30°.2 | 171°.6 | 29°.2 # 192°.0 | -39°.5 | 189°.2 | 19°.7 # -60°.4 | -59°.5 -14000 # 225°.7 | -34°.4 | 172°.3 | 25°.2 # 205°.4 | -44°.5 | 188°.7 | 14°.7 # -57°.3 | -56°.1 -13000 # 240°.6 | -37°.6 | 173°.2 | 22°.1 # 220°.3 | -49°.0 | 188°.2 | 10°.3 # -52°.7 | -50°.9 -12000 # 256°.5 | -39°.6 | 174°.3 | 20°.2 # 237°.1 | -52°.5 | 187°.6 | 6°.8 # -46°.4 | -44°.1 -11000 # 273°.0 | -40°.1 | 175°.7 | 19°.7 # 255°.7 | -54°.8 | 186°.9 | 4°.7 # -38°.8 | -36°.1 -10000 # 289°.4 | -39°.1 | 177°.1 | 20°.8 # 275°.4 | -55°.2 | 185°.9 | 4°.3 # -30°.7 | -27°.8 -9700: End of Younger Dryas (end of last ice age) # 294°.2 | -38°.5 | 177°.5 | 21°.4 # 281°.4 | -55°.0 | 185°.6 | 4°.6 # -28°.3 | -25°.5 -9359: Atlantis as described by Plato # 299°.7 | -37°.7 | 177°.9 | 22°.3 # 288°.0 | -54°.5 | 185°.3 | 5°.1 # -25°.7 | -22°.9 -9000 # 305°.3 | -36°.7 | 178°.4 | 23°.3 # 294°.9 | -53°.8 | 185°.0 | 5°.9 # -23°.1 | -20°.3 -8000 # 320°.2 | -33°.0 | 179°.4 | 27°.0 # 313°.0 | -50°.8 | 184°.3 | 9°.0 # -17°.0 | -14°.3 -7000 # 334°.2 | -28°.4 | 180°.2 | 31°.7 # 329°.1 | -46°.5 | 183°.8 | 13°.3 # -12°.6 | -10°.2 -6000 # 347°.3 | -23°.2 | 180°.7 | 36°.9 # 343°.5 | -41°.5 | 183°.5 | 18°.4 # -10°.1 | -7°.7 -5000 # 359°.9 | -17°.7 | 180°.9 | 42°.4 # 356°.6 | -36°.0 | 183°.6 | 23°.9 # -9°.2 | -6°.9 -4000 # 12°.1 | -12°.2 | 180°.8 | 47°.9 # 8°.7 | -30°.5 | 183°.9 | 29°.4 # -9°.7 | -7°.5 -3700: oldest known (cuneiform) writing # 15°.8 | -10°.5 | 180°.7 | 49°.5 # 12°.3 | -28°.9 | 184°.0 | 31°.0 # -10°.1 | -7°.9 -3300: Ötzi the iceman # 20°.6 | -8°.4 | 180°.5 | 51°.6 # 17°.0 | -26°.7 | 184°.2 | 33°.2 # -10°.9 | -8°.6 -3000: Stonehenge # 24°.3 | -6°.9 | 180°.3 | 53°.1 # 20°.4 | -25°.2 | 184°.4 | 34°.7 # -11°.5 | -9°.2 -2560: pyramid of Cheops/Khufu # 29°.6 | -4°.8 | 180°.0 | 55°.3 # 25°.5 | -22°.9 | 184°.8 | 37°.0 # -12°.6 | -10°.4 -2000 # 36°.6 | -2°.2 | 179°.4 | 57°.8 # 31°.9 | -20°.2 | 185°.3 | 39°.6 # -14°.3 | -12°.1 -1000 # 49°.1 | 1°.8 | 177°.9 | 61°.8 # 43°.3 | -15°.9 | 186°.4 | 43°.9 # -18°.1 | -16°.1 -0359: in 360 BCE, Plato described Atlantis as: "9000 years ago" # 57°.4 | 3°.9 | 176°.6 | 63°.9 # 50°.7 | -13°.5 | 187°.2 | 46°.2 # -20°.9 | -19°.2 0000 # 62°.1 | 4°.9 | 175°.8 | 64°.8 # 54°.9 | -12°.3 | 187°.7 | 47°.4 # -22°.6 | -21°.0 0001: incarnation & birth of Jesus # 62°.1 | 4°.9 | 175°.8 | 64°.8 # 54°.9 | -12°.3 | 187°.7 | 47°.4 # -22°.6 | -21°.0 1000 # 75°.3 | 6°.8 | 173°.3 | 66°.7 # 66°.7 | -9°.7 | 189°.1 | 49°.9 # -27°.7 | -26°.7 2000: J2000.0 # 88°.8 | 7°.4 | 170°.7 | 67°.2 # 78°.6 | -8°.2 | 190°.4 | 51°.3 # -33°.2 | -32°.7 2021: the current year # 89°.1 | 7°.4 | 170°.7 | 67°.2 # 78°.9 | -8°.2 | 190°.4 | 51°.3 # -33°.3 | -32°.8 3000 # 102°.3 | 6°.7 | 168°.8 | 66°.4 # 90°.7 | -7°.8 | 191°.4 | 51°.6 # -38°.8 | -38°.7 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Precession since last ice age (time of day = Alnitak's transit): # Alnitak # Alnilam # clockwise skewness ================================================================ # --------------------------------- # --------------------------------- # at Alnitak's transit epoch: description # R.A. | decl. | azim | alt # R.A. | decl. | azim | alt # equatorial | horizontal ----------------------------------------------------------------- # -------+--------+--------+------- # -------+--------+--------+------- # -----------+----------- -15000 # 203°.2 | -37°.3 | 180°.0 | 22°.7 # 202°.4 | -36°.2 | 180°.8 | 23°.8 # 30°.2 | 30°.6 -14000 # 217°.2 | -41°.9 | 180°.0 | 18°.1 # 216°.3 | -40°.7 | 180°.8 | 19°.3 # 33°.5 | 34°.0 -13000 # 232°.7 | -45°.6 | 180°.0 | 14°.4 # 231°.5 | -44°.6 | 180°.9 | 15°.4 # 38°.6 | 39°.1 -12000 # 249°.6 | -48°.3 | 180°.0 | 11°.7 # 248°.2 | -47°.3 | 181°.0 | 12°.7 # 45°.2 | 45°.9 -11000 # 267°.6 | -49°.4 | 180°.0 | 10°.6 # 266°.0 | -48°.6 | 181°.1 | 11°.4 # 53°.1 | 53°.8 -10000 # 285°.9 | -48°.8 | 180°.0 | 11°.2 # 284°.1 | -48°.2 | 181°.2 | 11°.8 # 61°.2 | 62°.0 -9700: End of Younger Dryas (end of last ice age) # 291°.2 | -48°.3 | 180°.0 | 11°.7 # 289°.4 | -47°.7 | 181°.2 | 12°.3 # 63°.6 | 64°.4 -9359: Atlantis as described by Plato # 297°.2 | -47°.6 | 180°.0 | 12°.5 # 295°.4 | -47°.0 | 181°.3 | 13°.0 # 66°.1 | 66°.9 -9000 # 303°.4 | -46°.6 | 180°.0 | 13°.4 # 301°.6 | -46°.1 | 181°.3 | 13°.9 # 68°.6 | 69°.4 -8000 # 319°.6 | -43°.0 | 180°.0 | 17°.0 # 317°.9 | -42°.6 | 181°.4 | 17°.4 # 74°.4 | 75°.2 -7000 # 334°.4 | -38°.4 | 180°.0 | 21°.6 # 332°.7 | -38°.1 | 181°.4 | 21°.9 # 78°.4 | 79°.2 -6000 # 348°.0 | -33°.2 | 180°.0 | 26°.9 # 346°.4 | -32°.9 | 181°.5 | 27°.1 # 80°.7 | 81°.5 -5000 # 0°.6 | -27°.7 | 180°.0 | 32°.4 # 359°.1 | -27°.5 | 181°.6 | 32°.5 # 81°.4 | 82°.1 -4000 # 12°.7 | -22°.2 | 180°.0 | 37°.9 # 11°.2 | -21°.9 | 181°.7 | 38°.1 # 80°.7 | 81°.5 -3700: oldest known (cuneiform) writing # 16°.2 | -20°.6 | 180°.0 | 39°.5 # 14°.8 | -20°.3 | 181°.7 | 39°.7 # 80°.2 | 81°.0 -3300: Ötzi the iceman # 20°.9 | -18°.5 | 180°.0 | 41°.6 # 19°.5 | -18°.2 | 181°.8 | 41°.8 # 79°.5 | 80°.3 -3000: Stonehenge # 24°.5 | -16°.9 | 180°.0 | 43°.1 # 23°.1 | -16°.7 | 181°.8 | 43°.3 # 78°.8 | 79°.6 -2560: pyramid of Cheops/Khufu # 29°.6 | -14°.8 | 180°.0 | 45°.2 # 28°.3 | -14°.5 | 181°.9 | 45°.5 # 77°.6 | 78°.5 -2000 # 36°.2 | -12°.2 | 180°.0 | 47°.8 # 34°.9 | -11°.9 | 182°.0 | 48°.1 # 75°.9 | 76°.7 -1000 # 48°.1 | -8°.1 | 180°.0 | 51°.9 # 46°.8 | -7°.7 | 182°.1 | 52°.3 # 72°.0 | 73°.0 -0359: in 360 BCE, Plato described Atlantis as: "9000 years ago" # 55°.9 | -6°.0 | 180°.0 | 54°.0 # 54°.6 | -5°.5 | 182°.2 | 54°.5 # 69°.2 | 70°.1 0000 # 60°.3 | -5°.0 | 180°.0 | 55°.0 # 59°.0 | -4°.5 | 182°.2 | 55°.5 # 67°.5 | 68°.4 0001: incarnation & birth of Jesus # 60°.3 | -5°.0 | 180°.0 | 55°.0 # 59°.0 | -4°.5 | 182°.2 | 55°.5 # 67°.5 | 68°.4 1000 # 72°.6 | -2°.9 | 180°.0 | 57°.1 # 71°.4 | -2°.3 | 182°.2 | 57°.7 # 62°.4 | 63°.3 2000: J2000.0 # 85°.2 | -1°.9 | 180°.0 | 58°.1 # 84°.1 | -1°.2 | 182°.2 | 58°.8 # 56°.9 | 57°.8 2021: the current year # 85°.5 | -1°.9 | 180°.0 | 58°.1 # 84°.3 | -1°.2 | 182°.2 | 58°.8 # 56°.8 | 57°.7 3000 # 97°.8 | -2°.2 | 180°.0 | 57°.8 # 96°.8 | -1°.4 | 182°.0 | 58°.6 # 51°.4 | 52°.2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Precession since last ice age (time of day = Alnitak's transit): # Saiph # Bellatrix # clockwise skewness ================================================================ # --------------------------------- # --------------------------------- # at Alnitak's transit epoch: description # R.A. | decl. | azim | alt # R.A. | decl. | azim | alt # equatorial | horizontal ----------------------------------------------------------------- # -------+--------+--------+------- # -------+--------+--------+------- # -----------+----------- -15000 # 200°.5 | -45°.0 | 182°.0 | 15°.0 # 203°.5 | -28°.2 | 179°.8 | 31°.8 # -7°.9 | -6°.9 -14000 # 215°.0 | -49°.6 | 181°.5 | 10°.3 # 216°.8 | -32°.7 | 180°.4 | 27°.3 # -4°.6 | -3°.4 -13000 # 231°.5 | -53°.5 | 180°.7 | 6°.5 # 231°.3 | -36°.5 | 181°.3 | 23°.5 # 0°.5 | 1°.7 -12000 # 250°.0 | -56°.2 | 179°.8 | 3°.8 # 246°.7 | -39°.3 | 182°.4 | 20°.6 # 7°.3 | 8°.5 -11000 # 270°.0 | -57°.2 | 178°.7 | 2°.8 # 263°.1 | -40°.8 | 183°.6 | 19°.1 # 15°.5 | 16°.5 -10000 # 290°.2 | -56°.3 | 177°.6 | 3°.6 # 279°.8 | -40°.7 | 184°.9 | 19°.1 # 23°.9 | 24°.8 -9700: End of Younger Dryas (end of last ice age) # 296°.0 | -55°.7 | 177°.3 | 4°.3 # 284°.8 | -40°.4 | 185°.2 | 19°.4 # 26°.3 | 27°.2 -9359: Atlantis as described by Plato # 302°.5 | -54°.8 | 177°.0 | 5°.1 # 290°.4 | -39°.8 | 185°.6 | 19°.9 # 28°.9 | 29°.8 -9000 # 309°.0 | -53°.6 | 176°.6 | 6°.2 # 296°.2 | -39°.1 | 185°.9 | 20°.6 # 31°.4 | 32°.3 -8000 # 325°.9 | -49°.6 | 175°.9 | 10°.2 # 311°.9 | -36°.0 | 186°.8 | 23°.6 # 37°.3 | 38°.2 -7000 # 340°.8 | -44°.7 | 175°.3 | 15°.1 # 326°.5 | -31°.9 | 187°.6 | 27°.7 # 41°.2 | 42°.3 -6000 # 354°.1 | -39°.4 | 174°.9 | 20°.4 # 340°.2 | -26°.9 | 188°.2 | 32°.6 # 43°.4 | 44°.6 -5000 # 6°.4 | -33°.8 | 174°.7 | 26°.0 # 353°.1 | -21°.6 | 188°.9 | 37°.9 # 44°.1 | 45°.4 -4000 # 18°.0 | -28°.4 | 174°.5 | 31°.4 # 5°.5 | -16°.0 | 189°.6 | 43°.5 # 43°.4 | 44°.9 -3700: oldest known (cuneiform) writing # 21°.4 | -26°.9 | 174°.4 | 32°.9 # 9°.1 | -14°.4 | 189°.8 | 45°.1 # 42°.9 | 44°.6 -3300: Ötzi the iceman # 26°.0 | -24°.8 | 174°.4 | 35°.0 # 14°.0 | -12°.2 | 190°.0 | 47°.3 # 42°.1 | 43°.9 -3000: Stonehenge # 29°.4 | -23°.4 | 174°.4 | 36°.4 # 17°.6 | -10°.6 | 190°.2 | 48°.9 # 41°.5 | 43°.3 -2560: pyramid of Cheops/Khufu # 34°.3 | -21°.3 | 174°.4 | 38°.5 # 23°.0 | -8°.3 | 190°.5 | 51°.2 # 40°.3 | 42°.3 -2000 # 40°.6 | -18°.9 | 174°.5 | 41°.0 # 29°.8 | -5°.6 | 190°.9 | 53°.9 # 38°.5 | 40°.7 -1000 # 52°.0 | -15°.1 | 174°.8 | 44°.7 # 42°.2 | -1°.1 | 191°.4 | 58°.4 # 34°.7 | 37°.3 -0359: in 360 BCE, Plato described Atlantis as: "9000 years ago" # 59°.3 | -13°.2 | 175°.1 | 46°.7 # 50°.3 | 1°.3 | 191°.5 | 60°.8 # 31°.9 | 34°.7 0000 # 63°.4 | -12°.3 | 175°.4 | 47°.7 # 54°.9 | 2°.5 | 191°.4 | 62°.0 # 30°.2 | 33°.1 0001: incarnation & birth of Jesus # 63°.5 | -12°.3 | 175°.4 | 47°.7 # 54°.9 | 2°.5 | 191°.4 | 62°.0 # 30°.1 | 33°.0 1000 # 75°.1 | -10°.4 | 176°.2 | 49°.5 # 68°.0 | 5°.0 | 190°.9 | 64°.6 # 25°.0 | 28°.1 2000: J2000.0 # 86°.9 | -9°.7 | 177°.3 | 50°.3 # 81°.3 | 6°.3 | 189°.6 | 66°.1 # 19°.5 | 22°.5 2021: the current year # 87°.2 | -9°.7 | 177°.3 | 50°.3 # 81°.6 | 6°.4 | 189°.6 | 66°.1 # 19°.4 | 22°.4 3000 # 98°.8 | -10°.1 | 178°.5 | 49°.9 # 94°.8 | 6°.4 | 187°.6 | 66°.3 # 13°.9 | 16°.6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Precession since last ice age (time of day = Alnitak's transit): # Saiph # Meissa # clockwise skewness ================================================================ # --------------------------------- # --------------------------------- # at Alnitak's transit epoch: description # R.A. | decl. | azim | alt # R.A. | decl. | azim | alt # equatorial | horizontal ----------------------------------------------------------------- # -------+--------+--------+------- # -------+--------+--------+------- # -----------+----------- -15000 # 200°.5 | -45°.0 | 182°.0 | 15°.0 # 207°.7 | -26°.0 | 175°.2 | 33°.9 # -17°.1 | -18°.2 -14000 # 215°.0 | -49°.6 | 181°.5 | 10°.3 # 221°.1 | -30°.3 | 176°.2 | 29°.6 # -13°.6 | -14°.6 -13000 # 231°.5 | -53°.5 | 180°.7 | 6°.5 # 235°.5 | -33°.9 | 177°.4 | 26°.1 # -8°.5 | -9°.3 -12000 # 250°.0 | -56°.2 | 179°.8 | 3°.8 # 250°.8 | -36°.3 | 179°.0 | 23°.7 # -1°.6 | -2°.3 -11000 # 270°.0 | -57°.2 | 178°.7 | 2°.8 # 266°.7 | -37°.5 | 180°.8 | 22°.6 # 6°.5 | 5°.9 -10000 # 290°.2 | -56°.3 | 177°.6 | 3°.6 # 282°.8 | -37°.1 | 182°.6 | 22°.9 # 14°.7 | 14°.3 -9700: End of Younger Dryas (end of last ice age) # 296°.0 | -55°.7 | 177°.3 | 4°.3 # 287°.6 | -36°.6 | 183°.1 | 23°.3 # 17°.1 | 16°.7 -9359: Atlantis as described by Plato # 302°.5 | -54°.8 | 177°.0 | 5°.1 # 293°.0 | -36°.0 | 183°.7 | 23°.9 # 19°.6 | 19°.3 -9000 # 309°.0 | -53°.6 | 176°.6 | 6°.2 # 298°.7 | -35°.2 | 184°.3 | 24°.7 # 22°.0 | 21°.8 -8000 # 325°.9 | -49°.6 | 175°.9 | 10°.2 # 313°.8 | -32°.0 | 185°.6 | 27°.8 # 27°.6 | 27°.8 -7000 # 340°.8 | -44°.7 | 175°.3 | 15°.1 # 328°.0 | -27°.7 | 186°.7 | 32°.0 # 31°.4 | 31°.9 -6000 # 354°.1 | -39°.4 | 174°.9 | 20°.4 # 341°.3 | -22°.7 | 187°.7 | 36°.9 # 33°.5 | 34°.3 -5000 # 6°.4 | -33°.8 | 174°.7 | 26°.0 # 354°.1 | -17°.3 | 188°.4 | 42°.3 # 34°.1 | 35°.1 -4000 # 18°.0 | -28°.4 | 174°.5 | 31°.4 # 6°.4 | -11°.8 | 189°.1 | 47°.8 # 33°.3 | 34°.6 -3700: oldest known (cuneiform) writing # 21°.4 | -26°.9 | 174°.4 | 32°.9 # 10°.1 | -10°.1 | 189°.2 | 49°.5 # 32°.9 | 34°.2 -3300: Ötzi the iceman # 26°.0 | -24°.8 | 174°.4 | 35°.0 # 15°.0 | -8°.0 | 189°.5 | 51°.6 # 32°.1 | 33°.5 -3000: Stonehenge # 29°.4 | -23°.4 | 174°.4 | 36°.4 # 18°.7 | -6°.4 | 189°.6 | 53°.2 # 31°.4 | 32°.9 -2560: pyramid of Cheops/Khufu # 34°.3 | -21°.3 | 174°.4 | 38°.5 # 24°.1 | -4°.1 | 189°.7 | 55°.5 # 30°.2 | 31°.8 -2000 # 40°.6 | -18°.9 | 174°.5 | 41°.0 # 31°.1 | -1°.4 | 189°.9 | 58°.2 # 28°.4 | 30°.2 -1000 # 52°.0 | -15°.1 | 174°.8 | 44°.7 # 43°.7 | 3°.0 | 189°.7 | 62°.7 # 24°.6 | 26°.4 -0359: in 360 BCE, Plato described Atlantis as: "9000 years ago" # 59°.3 | -13°.2 | 175°.1 | 46°.7 # 52°.0 | 5°.3 | 189°.2 | 65°.0 # 21°.7 | 23°.5 0000 # 63°.4 | -12°.3 | 175°.4 | 47°.7 # 56°.7 | 6°.4 | 188°.8 | 66°.2 # 19°.9 | 21°.7 0001: incarnation & birth of Jesus # 63°.5 | -12°.3 | 175°.4 | 47°.7 # 56°.7 | 6°.4 | 188°.8 | 66°.2 # 19°.9 | 21°.7 1000 # 75°.1 | -10°.4 | 176°.2 | 49°.5 # 70°.1 | 8°.8 | 186°.9 | 68°.7 # 14°.7 | 16°.1 2000: J2000.0 # 86°.9 | -9°.7 | 177°.3 | 50°.3 # 83°.8 | 9°.9 | 184°.0 | 69°.9 # 9°.2 | 9°.8 2021: the current year # 87°.2 | -9°.7 | 177°.3 | 50°.3 # 84°.1 | 9°.9 | 184°.0 | 69°.9 # 9°.1 | 9°.6 3000 # 98°.8 | -10°.1 | 178°.5 | 49°.9 # 97°.6 | 9°.7 | 180°.7 | 69°.8 # 3°.6 | 3°.2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% North Pole shift (earth crust shift) according to ellipsoidal geometry (Vincenty's inverse formula and WGS-84): =============================================================================================================== observer: Geo: 29°58'45".05 = 29°.9791813N / 31°08'03".11 = 31°.1341960E / pyramid of Cheops/Khufu old pole: Geo: 76°00'00".00 = 76°.0000000N / 47°06'00".00 = -47°.1000000W / former North Pole II, see https://mariobuildreps.com/orientation-pyramids-former-north-poles/ > meridian rotation : -16°13'40" = -16°.22782 > angular distance to old NP: 58°14'49" = 58°.24704 > former latitude : 31°45'11" = 31°.75296 > current latitude : 29°58'45" = 29°.97918 > latitude change : -1°46'26" = -1°.77378 In case of a north pole shift (due to earth crust shift) to its current location the southern sky would have risen by ~2° and tilted left by ~16°. The latter is also the amount by which the celestial meridian would have turned right. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Göbekli Tepe: ============= North Pole shift (earth crust shift) according to ellipsoidal geometry (Vincenty's inverse formula and WGS-84): =============================================================================================================== observer: Geo: 37°13'23".00 = 37°.2230556N / 38°55'21".00 = 38°.9225000E / Göbekli Tepe old pole: Geo: 76°00'00".00 = 76°.0000000N / 47°06'00".00 = -47°.1000000W / former North Pole II, see https://mariobuildreps.com/orientation-pyramids-former-north-poles/ > meridian rotation : -17°35'50" = -17°.59716 > orientation of enclosure C: -16°, see https://mariobuildreps.com/gobekli-tepe-true-age/ > angular distance to old NP: 53°12'42" = 53°.21158 > former latitude : 36°47'18" = 36°.78842 > current latitude : 37°13'23" = 37°.22306 > latitude change : 0°26'05" = 0°.43464 In case of a north pole shift (due to earth crust shift) to its current location the southern sky would have sunk by ~0° and tilted left by ~18°. The latter is also the amount by which the celestial meridian would have turned right. North Pole shift (earth crust shift) according to ellipsoidal geometry (Vincenty's inverse formula and WGS-84): =============================================================================================================== observer: Geo: 37°13'23".00 = 37°.2230556N / 38°55'21".00 = 38°.9225000E / Göbekli Tepe old pole: Geo: 82°54'00".00 = 82°.9000000N / 47°06'00".00 = -47°.1000000W / former North Pole pointed to at Göbekli Tepe, see https://mariobuildreps.com/gobekli-tepe-true-age/ > meridian rotation : -8°56'44" = -8°.94551 > orientation of enclosure D: -9°, see https://mariobuildreps.com/gobekli-tepe-true-age/ > angular distance to old NP: 52°42'51" = 52°.71414 > former latitude : 37°17'09" = 37°.28586 > current latitude : 37°13'23" = 37°.22306 > latitude change : 0°03'46" = 0°.06280 In case of a north pole shift (due to earth crust shift) to its current location the southern sky would have risen by ~0° and tilted left by ~9°. The latter is also the amount by which the celestial meridian would have turned right. North Pole shift (earth crust shift) according to ellipsoidal geometry (Vincenty's inverse formula and WGS-84): =============================================================================================================== observer: Geo: 37°13'23".00 = 37°.2230556N / 38°55'21".00 = 38°.9225000E / Göbekli Tepe old pole: Geo: 72°12'00".00 = 72°.2000000N / 47°06'00".00 = -47°.1000000W / former North Pole III, see https://mariobuildreps.com/orientation-pyramids-former-north-poles/ > meridian rotation : -22°17'30" = -22°.29155 > orientation of enclosure B: -21°, see https://mariobuildreps.com/gobekli-tepe-true-age/ > angular distance to old NP: 53°45'08" = 53°.75214 > former latitude : 36°14'52" = 36°.24786 > current latitude : 37°13'23" = 37°.22306 > latitude change : 0°58'31" = 0°.97520 In case of a north pole shift (due to earth crust shift) to its current location the southern sky would have sunk by ~1° and tilted left by ~22°. The latter is also the amount by which the celestial meridian would have turned right. North Pole shift (earth crust shift) according to ellipsoidal geometry (Vincenty's inverse formula and WGS-84): =============================================================================================================== observer: Geo: 37°13'23".00 = 37°.2230556N / 38°55'21".00 = 38°.9225000E / Göbekli Tepe old pole: Geo: 64°06'00".00 = 64°.1000000N / 47°06'00".00 = -47°.1000000W / former North Pole IV, see https://mariobuildreps.com/orientation-pyramids-former-north-poles/ > meridian rotation : -32°01'14" = -32°.02067 > angular distance to old NP: 55°30'02" = 55°.50069 > former latitude : 34°29'58" = 34°.49931 > current latitude : 37°13'23" = 37°.22306 > latitude change : 2°43'25" = 2°.72374 In case of a north pole shift (due to earth crust shift) to its current location the southern sky would have sunk by ~3° and tilted left by ~32°. The latter is also the amount by which the celestial meridian would have turned right. North Pole shift (earth crust shift) according to ellipsoidal geometry (Vincenty's inverse formula and WGS-84): =============================================================================================================== observer: Geo: 37°13'23".00 = 37°.2230556N / 38°55'21".00 = 38°.9225000E / Göbekli Tepe old pole: Geo: 52°12'00".00 = 52°.2000000N / 47°06'00".00 = -47°.1000000W / former North Pole V, see https://mariobuildreps.com/orientation-pyramids-former-north-poles/ > meridian rotation : -45°24'20" = -45°.40569 > orientation of enclosure A: -45°, see https://mariobuildreps.com/gobekli-tepe-true-age/ > angular distance to old NP: 59°22'43" = 59°.37860 > former latitude : 30°37'17" = 30°.62140 > current latitude : 37°13'23" = 37°.22306 > latitude change : 6°36'06" = 6°.60166 In case of a north pole shift (due to earth crust shift) to its current location the southern sky would have sunk by ~7° and tilted left by ~45°. The latter is also the amount by which the celestial meridian would have turned right.