31:T58e,function ephemeris_correction(tee) { // """Return Dynamical Time minus Universal Time (in days) for // moment, tee. Adapted from "Astronomical Algorithms" // by Jean Meeus, Willmann_Bell, Inc., 1991.""" const year = gregorian_year_from_fixed(ifloor(tee)); const c = gregorian_date_difference( gregorian_date(1900, JANUARY, 1), gregorian_date(year, JULY, 1) ) / 36525; let x; if (1988 <= year <= 2019) return (1 / 86400) * (year - 1933); else if (1900 <= year && year <= 1987) return poly(c, [ -0.00002, 0.000297, 0.025184, -0.181133, 0.553040, -0.861938, 0.677066, -0.212591 ]); else if (1800 <= year && year <= 1899) return poly(c, [ -0.000009, 0.003844, 0.083563, 0.865736, 4.867575, 15.845535, 31.332267, 38.291999, 28.316289, 11.636204, 2.043794 ]); else if (1700 <= year && year <= 1799) return ( (1 / 86400) * poly(year - 1700, [8.118780842, -0.005092142, 0.003336121, -0.0000266484]) ); else if (1620 <= year && year <= 1699) return (1 / 86400) * poly(year - 1600, [196.58333, -4.0675, 0.0219167]); else x = days_from_hours(12) + gregorian_date_difference( gregorian_date(1810, JANUARY, 1), gregorian_date(year, JANUARY, 1) ); return (1 / 86400) * ((x * x) / 41048480 - 15); }32:Tb9c,function solar_longitude(tee) { // """Return the longitude of sun at moment ’tee’. // Adapted from ’Planetary Programs and Tables from -4000 to +2800’ // by Pierre Bretagnon and Jean_Louis Simon, Willmann_Bell, Inc., 1986. // See also pag 166 of ’Astronomical Algorithms’ by Jean Meeus, 2nd Ed 1998, // with corrections Jun 2005.""" const c = julian_centuries(tee); const coefficients = [ 403406, 195207, 119433, 112392, 3891, 2819, 1721, 660, 350, 334, 314, 268, 242, 234, 158, 132, 129, 114, 99, 93, 86, 78, 72, 68, 64, 46, 38, 37, 32, 29, 28, 27, 27, 25, 24, 21, 21, 20, 18, 17, 14, 13, 13, 13, 12, 10, 10, 10, 10 ]; const multipliers = [ mpf(0.9287892), mpf(35999.1376958), mpf(35999.4089666), mpf(35998.7287385), mpf(71998.20261), mpf(71998.4403), mpf(36000.35726), mpf(71997.4812), mpf(32964.4678), mpf(-19.4410), mpf(445267.1117), mpf(45036.8840), mpf(3.1008), mpf(22518.4434), mpf(-19.9739), mpf(65928.9345), mpf(9038.0293), mpf(3034.7684), mpf(33718.148), mpf(3034.448), mpf(-2280.773), mpf(29929.992), mpf(31556.493), mpf(149.588), mpf(9037.750), mpf(107997.405), mpf(-4444.176), mpf(151.771), mpf(67555.316), mpf(31556.080), mpf(-4561.540), mpf(107996.706), mpf(1221.655), mpf(62894.167), mpf(31437.369), mpf(14578.298), mpf(-31931.757), mpf(34777.243), mpf(1221.999), mpf(62894.511), mpf(-4442.039), mpf(107997.909), mpf(119.066), mpf(16859.071), mpf(-4.578), mpf(26895.292), mpf(-39.127), mpf(12297.536), mpf(90073.778) ]; const addends = [ mpf(270.54861), mpf(340.19128), mpf(63.91854), mpf(331.26220), mpf(317.843), mpf(86.631), mpf(240.052), mpf(310.26), mpf(247.23), mpf(260.87), mpf(297.82), mpf(343.14), mpf(166.79), mpf(81.53), mpf(3.50), mpf(132.75), mpf(182.95), mpf(162.03), mpf(29.8), mpf(266.4), mpf(249.2), mpf(157.6), mpf(257.8), mpf(185.1), mpf(69.9), mpf(8.0), mpf(197.1), mpf(250.4), mpf(65.3), mpf(162.7), mpf(341.5), mpf(291.6), mpf(98.5), mpf(146.7), mpf(110.0), mpf(5.2), mpf(342.6), mpf(230.9), mpf(256.1), mpf(45.3), mpf(242.9), mpf(115.2), mpf(151.8), mpf(285.3), mpf(53.3), mpf(126.6), mpf(205.7), mpf(85.9), mpf(146.1) ]; const lam = deg(mpf(282.7771834)) + deg(mpf(36000.76953744)) * c + deg(mpf(0.000005729577951308232)) * sigma([coefficients, addends, multipliers], (x, y, z) => { x * sin_degrees(y + z * c); }); return mod(lam + aberration(tee) + nutation(tee), 360); }33:Tf27,function lunar_latitude(tee) { // """Return the latitude of moon (in degrees) at moment, tee. // Adapted from "Astronomical Algorithms" by Jean Meeus, // Willmann_Bell, Inc., 1998.""" const c = julian_centuries(tee); const cap_L_prime = mean_lunar_longitude(c); const cap_D = lunar_elongation(c); const cap_M = solar_anomaly(c); const cap_M_prime = lunar_anomaly(c); const cap_F = moon_node(c); const cap_E = poly(c, [1, mpf(-0.002516), mpf(-0.0000074)]); const args_lunar_elongation = [ 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 4, 0, 0, 0, 1, 0, 0, 0, 1, 0, 4, 4, 0, 4, 2, 2, 2, 2, 0, 2, 2, 2, 2, 4, 2, 2, 0, 2, 1, 1, 0, 2, 1, 2, 0, 4, 4, 1, 4, 1, 4, 2 ]; const args_solar_anomaly = [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, -1, -1, -1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 0, -1, -2, 0, 1, 1, 1, 1, 1, 0, -1, 1, 0, -1, 0, 0, 0, -1, -2 ]; const args_lunar_anomaly = [ 0, 1, 1, 0, -1, -1, 0, 2, 1, 2, 0, -2, 1, 0, -1, 0, -1, -1, -1, 0, 0, -1, 0, 1, 1, 0, 0, 3, 0, -1, 1, -2, 0, 2, 1, -2, 3, 2, -3, -1, 0, 0, 1, 0, 1, 1, 0, 0, -2, -1, 1, -2, 2, -2, -1, 1, 1, -2, 0, 0 ]; const args_moon_node = [ 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 3, 1, 1, 1, -1, -1, -1, 1, -1, 1, -3, 1, -3, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 3, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1 ]; const sine_coefficients = [ 5128122, 280602, 277693, 173237, 55413, 46271, 32573, 17198, 9266, 8822, 8216, 4324, 4200, -3359, 2463, 2211, 2065, -1870, 1828, -1794, -1749, -1565, -1491, -1475, -1410, -1344, -1335, 1107, 1021, 833, 777, 671, 607, 596, 491, -451, 439, 422, 421, -366, -351, 331, 315, 302, -283, -229, 223, 223, -220, -220, -185, 181, -177, 176, 166, -164, 132, -119, 115, 107 ]; const beta = deg(1 / 1000000) * sigma( [ sine_coefficients, args_lunar_elongation, args_solar_anomaly, args_lunar_anomaly, args_moon_node ], (v, w, x, y, z) => v * pow(cap_E, abs(x)) * sin_degrees(w * cap_D + x * cap_M + y * cap_M_prime + z * cap_F) ); const venus = deg(175 / 1000000) * (sin_degrees(deg(mpf(119.75)) + c * deg(mpf(131.849)) + cap_F) + sin_degrees(deg(mpf(119.75)) + c * deg(mpf(131.849)) - cap_F)); const flat_earth = deg(-2235 / 1000000) * sin_degrees(cap_L_prime) + deg(127 / 1000000) * sin_degrees(cap_L_prime - cap_M_prime) + deg(-115 / 1000000) * sin_degrees(cap_L_prime + cap_M_prime); const extra = deg(382 / 1000000) * sin_degrees(deg(mpf(313.45)) + c * deg(mpf(481266.484))); return beta + venus + flat_earth + extra; }34:Tce1,function lunar_distance(tee) { // """Return the distance to moon (in meters) at moment, tee. // Adapted from "Astronomical Algorithms" by Jean Meeus, // Willmann_Bell, Inc., 2nd ed.""" const c = julian_centuries(tee); const cap_D = lunar_elongation(c); const cap_M = solar_anomaly(c); const cap_M_prime = lunar_anomaly(c); const cap_F = moon_node(c); const cap_E = poly(c, [1, mpf(-0.002516), mpf(-0.0000074)]); const args_lunar_elongation = [ 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 1, 0, 2, 0, 0, 4, 0, 4, 2, 2, 1, 1, 2, 2, 4, 2, 0, 2, 2, 1, 2, 0, 0, 2, 2, 2, 4, 0, 3, 2, 4, 0, 2, 2, 2, 4, 0, 4, 1, 2, 0, 1, 3, 4, 2, 0, 1, 2, 2 ]; const args_solar_anomaly = [ 0, 0, 0, 0, 1, 0, 0, -1, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, -2, 1, 2, -2, 0, 0, -1, 0, 0, 1, -1, 2, 2, 1, -1, 0, 0, -1, 0, 1, 0, 1, 0, 0, -1, 2, 1, 0, 0 ]; const args_lunar_anomaly = [ 1, -1, 0, 2, 0, 0, -2, -1, 1, 0, -1, 0, 1, 0, 1, 1, -1, 3, -2, -1, 0, -1, 0, 1, 2, 0, -3, -2, -1, -2, 1, 0, 2, 0, -1, 1, 0, -1, 2, -1, 1, -2, -1, -1, -2, 0, 1, 4, 0, -2, 0, 2, 1, -2, -3, 2, 1, -1, 3, -1 ]; const args_moon_node = [ 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2 ]; const cosine_coefficients = [ -20905355, -3699111, -2955968, -569925, 48888, -3149, 246158, -152138, -170733, -204586, -129620, 108743, 104755, 10321, 0, 79661, -34782, -23210, -21636, 24208, 30824, -8379, -16675, -12831, -10445, -11650, 14403, -7003, 0, 10056, 6322, -9884, 5751, 0, -4950, 4130, 0, -3958, 0, 3258, 2616, -1897, -2117, 2354, 0, 0, -1423, -1117, -1571, -1739, 0, -4421, 0, 0, 0, 0, 1165, 0, 0, 8752 ]; const correction = sigma( [ cosine_coefficients, args_lunar_elongation, args_solar_anomaly, args_lunar_anomaly, args_moon_node ], (v, w, x, y, z) => v * pow(cap_E, abs(x)) * cos_degrees(w * cap_D + x * cap_M + y * cap_M_prime + z * cap_F) ); return mt(385000560) + correction; }35:Tead,function lunar_longitude(tee) { // """Return longitude of moon (in degrees) at moment tee. // Adapted from "Astronomical Algorithms" by Jean Meeus, // Willmann_Bell, Inc., 2nd ed., 1998.""" const c = julian_centuries(tee); const cap_L_prime = mean_lunar_longitude(c); const cap_D = lunar_elongation(c); const cap_M = solar_anomaly(c); const cap_M_prime = lunar_anomaly(c); const cap_F = moon_node(c); // # see eq. 47.6 in Meeus const cap_E = poly(c, [1, mpf(-0.002516), mpf(-0.0000074)]); const args_lunar_elongation = [ 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 1, 0, 2, 0, 0, 4, 0, 4, 2, 2, 1, 1, 2, 2, 4, 2, 0, 2, 2, 1, 2, 0, 0, 2, 2, 2, 4, 0, 3, 2, 4, 0, 2, 2, 2, 4, 0, 4, 1, 2, 0, 1, 3, 4, 2, 0, 1, 2 ]; const args_solar_anomaly = [ 0, 0, 0, 0, 1, 0, 0, -1, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, -2, 1, 2, -2, 0, 0, -1, 0, 0, 1, -1, 2, 2, 1, -1, 0, 0, -1, 0, 1, 0, 1, 0, 0, -1, 2, 1, 0 ]; const args_lunar_anomaly = [ 1, -1, 0, 2, 0, 0, -2, -1, 1, 0, -1, 0, 1, 0, 1, 1, -1, 3, -2, -1, 0, -1, 0, 1, 2, 0, -3, -2, -1, -2, 1, 0, 2, 0, -1, 1, 0, -1, 2, -1, 1, -2, -1, -1, -2, 0, 1, 4, 0, -2, 0, 2, 1, -2, -3, 2, 1, -1, 3 ]; const args_moon_node = [ 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0 ]; const sine_coefficients = [ 6288774, 1274027, 658314, 213618, -185116, -114332, 58793, 57066, 53322, 45758, -40923, -34720, -30383, 15327, -12528, 10980, 10675, 10034, 8548, -7888, -6766, -5163, 4987, 4036, 3994, 3861, 3665, -2689, -2602, 2390, -2348, 2236, -2120, -2069, 2048, -1773, -1595, 1215, -1110, -892, -810, 759, -713, -700, 691, 596, 549, 537, 520, -487, -399, -381, 351, -340, 330, 327, -323, 299, 294 ]; const correction = deg(1 / 1000000) * sigma( [ sine_coefficients, args_lunar_elongation, args_solar_anomaly, args_lunar_anomaly, args_moon_node ], (v, w, x, y, z) => v * pow(cap_E, abs(x)) * sin_degrees(w * cap_D + x * cap_M + y * cap_M_prime + z * cap_F) ); const A1 = deg(mpf(119.75)) + c * deg(mpf(131.849)); const venus = deg(3958 / 1000000) * sin_degrees(A1); const A2 = deg(mpf(53.09)) + c * deg(mpf(479264.29)); const jupiter = deg(318 / 1000000) * sin_degrees(A2); const flat_earth = deg(1962 / 1000000) * sin_degrees(cap_L_prime - cap_F); return mod( cap_L_prime + correction + venus + jupiter + flat_earth + nutation(tee), 360 ); }36:Tf2c,function nth_new_moon(n) { // """Return the moment of n-th new moon after (or before) the new moon // of January 11, 1. Adapted from "Astronomical Algorithms" // by Jean Meeus, Willmann_Bell, Inc., 2nd ed., 1998.""" const n0 = 24724; const k = n - n0; const c = k / mpf(1236.85); const approx = J2000 + poly(c, [ mpf(5.09766), MEAN_SYNODIC_MONTH * mpf(1236.85), mpf(0.0001437), mpf(-0.000000150), mpf(0.00000000073) ]); const cap_E = poly(c, [1, mpf(-0.002516), mpf(-0.0000074)]); const solar_anomaly = poly( c, deg([ mpf(2.5534), mpf(1236.85) * mpf(29.10535669), mpf(-0.0000014), mpf(-0.00000011) ]) ); const lunar_anomaly = poly( c, deg([ mpf(201.5643), mpf(385.81693528) * mpf(1236.85), mpf(0.0107582), mpf(0.00001238), mpf(-0.000000058) ]) ); const moon_argument = poly( c, deg([ mpf(160.7108), mpf(390.67050284) * mpf(1236.85), mpf(-0.0016118), mpf(-0.00000227), mpf(0.000000011) ]) ); const cap_omega = poly(c, [ mpf(124.7746), mpf(-1.56375588) * mpf(1236.85), mpf(0.0020672), mpf(0.00000215) ]); const E_factor = [ 0, 1, 0, 0, 1, 1, 2, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]; const solar_coeff = [ 0, 1, 0, 0, -1, 1, 2, 0, 0, 1, 0, 1, 1, -1, 2, 0, 3, 1, 0, 1, -1, -1, 1, 0 ]; const lunar_coeff = [ 1, 0, 2, 0, 1, 1, 0, 1, 1, 2, 3, 0, 0, 2, 1, 2, 0, 1, 2, 1, 1, 1, 3, 4 ]; const moon_coeff = [ 0, 0, 0, 2, 0, 0, 0, -2, 2, 0, 0, 2, -2, 0, 0, -2, 0, -2, 2, 2, 2, -2, 0, 0 ]; const sine_coeff = [ mpf(-0.40720), mpf(0.17241), mpf(0.01608), mpf(0.01039), mpf(0.00739), mpf(-0.00514), mpf(0.00208), mpf(-0.00111), mpf(-0.00057), mpf(0.00056), mpf(-0.00042), mpf(0.00042), mpf(0.00038), mpf(-0.00024), mpf(-0.00007), mpf(0.00004), mpf(0.00004), mpf(0.00003), mpf(0.00003), mpf(-0.00003), mpf(0.00003), mpf(-0.00002), mpf(-0.00002), mpf(0.00002) ]; const correction = deg(mpf(-0.00017)) * sin_degrees(cap_omega) + sigma( [sine_coeff, E_factor, solar_coeff, lunar_coeff, moon_coeff], (v, w, x, y, z) => v * pow(cap_E, w) * sin_degrees(x * solar_anomaly + y * lunar_anomaly + z * moon_argument) ); const add_const = [ mpf(251.88), mpf(251.83), mpf(349.42), mpf(84.66), mpf(141.74), mpf(207.14), mpf(154.84), mpf(34.52), mpf(207.19), mpf(291.34), mpf(161.72), mpf(239.56), mpf(331.55) ]; const add_coeff = [ mpf(0.016321), mpf(26.651886), mpf(36.412478), mpf(18.206239), mpf(53.303771), mpf(2.453732), mpf(7.306860), mpf(27.261239), mpf(0.121824), mpf(1.844379), mpf(24.198154), mpf(25.513099), mpf(3.592518) ]; const add_factor = [ mpf(0.000165), mpf(0.000164), mpf(0.000126), mpf(0.000110), mpf(0.000062), mpf(0.000060), mpf(0.000056), mpf(0.000047), mpf(0.000042), mpf(0.000040), mpf(0.000037), mpf(0.000035), mpf(0.000023) ]; const extra = deg(mpf(0.000325)) * sin_degrees(poly(c, deg([mpf(299.77), mpf(132.8475848), mpf(-0.009173)]))); const additional = sigma( [add_const, add_coeff, add_factor], (i, j, l) => l * sin_degrees(i + j * k) ); return universal_from_dynamical(approx + correction + extra + additional); }37:[] 2f:{"title":"Astronomical Lunar Calendars","cells":[{"id":0,"value":"md`# Astronomical Lunar Calendars`","pinned":false,"hidden":false,"mode":"ojs"},{"id":244,"value":"credits","pinned":false,"hidden":false,"mode":"ojs"},{"id":246,"value":"creditsMeeus","pinned":false,"hidden":false,"mode":"ojs"},{"id":254,"value":"html`

Notebook's image is a Lunar Volvelle from fol. 025r of Bodleian Library MS. Ashmole 370, CC-BY-NC 4.0 .

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":5,"value":"function jewish_dusk(date, location) {\n // \"\"\"Return standard time of Jewish dusk on fixed date, date,\n // at location, location, (as per Vilna Gaon).\"\"\"\n return dusk(date, location, angle(4, 40, 0));\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":12,"value":"function jewish_sabbath_ends(date, location) {\n // \"\"\"Return standard time of end of Jewish sabbath on fixed date, date,\n // at location, location, (as per Berthold Cohn).\"\"\"\n return dusk(date, location, angle(7, 5, 0));\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":14,"value":"function daytime_temporal_hour(date, location) {\n // \"\"\"Return the length of daytime temporal hour on fixed date, date\n // at location, location.\n // Return BOGUS if there no sunrise or sunset on date, date.\"\"\"\n if (sunrise(date, location) == BOGUS || sunset(date, location) == BOGUS)\n return BOGUS;\n else return (sunset(date, location) - sunrise(date, location)) / 12;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":17,"value":"function nighttime_temporal_hour(date, location) {\n // \"\"\"Return the length of nighttime temporal hour on fixed date, date,\n // at location, location.\n // Return BOGUS if there no sunrise or sunset on date, date.\"\"\"\n if (sunrise(date + 1, location) == BOGUS || sunset(date, location) == BOGUS)\n return BOGUS;\n else return (sunrise(date + 1, location) - sunset(date, location)) / 12;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":20,"value":"function standard_from_sundial(tee, location) {\n // \"\"\"Return standard time of temporal moment, tee, at location, location.\n // Return BOGUS if temporal hour is undefined that day.\"\"\"\n const date = fixed_from_moment(tee);\n const hour = 24 * mod(tee, 1);\n let h;\n if (6 <= hour <= 18) {\n h = daytime_temporal_hour(date, location);\n } else if (hour < 6) {\n h = nighttime_temporal_hour(date - 1, location);\n } else {\n h = nighttime_temporal_hour(date, location);\n }\n\n if (h == BOGUS) return BOGUS;\n else if (6 <= hour <= 18) return sunrise(date, location) + (hour - 6) * h;\n else if (hour < 6) return sunset(date - 1, location) + (hour + 6) * h;\n else return sunset(date, location) + (hour - 18) * h;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":28,"value":"function jewish_morning_end(date, location) {\n // \"\"\"Return standard time on fixed date, date, at location, location,\n // of end of morning according to Jewish ritual.\"\"\"\n return standard_from_sundial(date + days_from_hours(10), location);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":30,"value":"function asr(date, location) {\n // \"\"\"Return standard time of asr on fixed date, date, at location, location.\"\"\"\n const noon = universal_from_standard(midday(date, location), location);\n const phi = latitude(location);\n const delta = declination(noon, deg(0), solar_longitude(noon));\n const altitude = delta - phi - deg(90);\n const h = arctan_degrees(\n tan_degrees(altitude),\n 2 * tan_degrees(altitude) + 1\n );\n // # For Shafii use instead:\n // # tangent_degrees(altitude) + 1)\n return dusk(date, location, -h);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":32,"value":"function universal_from_dynamical(tee) {\n // \"\"\"Return Universal moment from Dynamical time, tee.\"\"\"\n return tee - ephemeris_correction(tee);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":35,"value":"function dynamical_from_universal(tee) {\n // \"\"\"Return Dynamical time at Universal moment, tee.\"\"\"\n return tee + ephemeris_correction(tee);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":169,"value":"function sidereal_from_moment(tee) {\n // \"\"\"Return the mean sidereal time of day from moment tee expressed\n // as hour angle. Adapted from \"Astronomical Algorithms\"\n // by Jean Meeus, Willmann_Bell, Inc., 1991.\"\"\"\n const c = (tee - J2000) / mpf(36525);\n return mod(\n poly(\n c,\n deg([\n mpf(280.46061837),\n mpf(36525) * mpf(360.98564736629),\n mpf(0.000387933),\n mpf(-1) / mpf(38710000)\n ])\n ),\n 360\n );\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":51,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":79,"value":"function equation_of_time(tee) {\n // \"\"\"Return the equation of time (as fraction of day) for moment, tee.\n // Adapted from \"Astronomical Algorithms\" by Jean Meeus,\n // Willmann_Bell, Inc., 1991.\"\"\"\n const c = julian_centuries(tee);\n const lamb = poly(c, deg([mpf(280.46645), mpf(36000.76983), mpf(0.0003032)]));\n const anomaly = poly(\n c,\n deg([mpf(357.52910), mpf(35999.05030), mpf(-0.0001559), mpf(-0.00000048)])\n );\n const eccentricity = poly(c, [\n mpf(0.016708617),\n mpf(-0.000042037),\n mpf(-0.0000001236)\n ]);\n const varepsilon = obliquity(tee);\n const y = pow(tan_degrees(varepsilon / 2), 2);\n const equation =\n (1 / 2 / PI) *\n (y * sin_degrees(2 * lamb) +\n -2 * eccentricity * sin_degrees(anomaly) +\n 4 * eccentricity * y * sin_degrees(anomaly) * cos_degrees(2 * lamb) +\n -0.5 * y * y * sin_degrees(4 * lamb) +\n -1.25 * eccentricity * eccentricity * sin_degrees(2 * anomaly));\n return signum(equation) * min(abs(equation), days_from_hours(mpf(12)));\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":114,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":190,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":162,"value":"function lunar_altitude(tee, location) {\n // \"\"\"Return the geocentric altitude of moon at moment, tee,\n // at location, location, as a small positive/negative angle in degrees,\n // ignoring parallax and refraction. Adapted from ’Astronomical\n // Algorithms’ by Jean Meeus, Willmann_Bell, Inc., 1998.\"\"\"\n const phi = latitude(location);\n const psi = longitude(location);\n const lamb = lunar_longitude(tee);\n const beta = lunar_latitude(tee);\n const alpha = right_ascension(tee, beta, lamb);\n const delta = declination(tee, beta, lamb);\n const theta0 = sidereal_from_moment(tee);\n const cap_H = mod(theta0 + psi - alpha, 360);\n const altitude = arcsin_degrees(\n sin_degrees(phi) * sin_degrees(delta) +\n cos_degrees(phi) * cos_degrees(delta) * cos_degrees(cap_H)\n );\n return mod(altitude + deg(180), 360) - deg(180);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":195,"value":"function mean_lunar_longitude(c) {\n // \"\"\"Return mean longitude of moon (in degrees) at moment\n // given in Julian centuries c (including the constant term of the\n // effect of the light-time (-0\".70).\n // Adapted from eq. 47.1 in \"Astronomical Algorithms\" by Jean Meeus,\n // Willmann_Bell, Inc., 2nd ed. with corrections, 2005.\"\"\"\n return normalized_degrees(\n poly(\n c,\n deg([\n mpf(218.3164477),\n mpf(481267.88123421),\n mpf(-0.0015786),\n mpf(1 / 538841),\n mpf(-1 / 65194000)\n ])\n )\n );\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":198,"value":"function lunar_elongation(c) {\n // \"\"\"Return elongation of moon (in degrees) at moment\n // given in Julian centuries c.\n // Adapted from eq. 47.2 in \"Astronomical Algorithms\" by Jean Meeus,\n // Willmann_Bell, Inc., 2nd ed. with corrections, 2005.\"\"\"\n return normalized_degrees(\n poly(\n c,\n deg([\n mpf(297.8501921),\n mpf(445267.1114034),\n mpf(-0.0018819),\n mpf(1 / 545868),\n mpf(-1 / 113065000)\n ])\n )\n );\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":203,"value":"function lunar_parallax(tee, location) {\n // \"\"\"Return the parallax of moon at moment, tee, at location, location.\n // Adapted from \"Astronomical Algorithms\" by Jean Meeus,\n // Willmann_Bell, Inc., 1998.\"\"\"\n const geo = lunar_altitude(tee, location);\n const Delta = lunar_distance(tee);\n const alt = mt(6378140) / Delta;\n const arg = alt * cos_degrees(geo);\n return arcsin_degrees(arg);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":208,"value":"$34","pinned":false,"hidden":false,"mode":"ojs"},{"id":206,"value":"function lunar_position(tee) {\n // \"\"\"Return the moon position (geocentric latitude and longitude [in degrees]\n // and distance [in meters]) at moment, tee.\n // Adapted from \"Astronomical Algorithms\" by Jean Meeus,\n // Willmann_Bell, Inc., 2nd ed.\"\"\"\n return lunar_latitude(tee), lunar_longitude(tee), lunar_distance(tee);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":201,"value":"function topocentric_lunar_altitude(tee, location) {\n // \"\"\"Return the topocentric altitude of moon at moment, tee,\n // at location, location, as a small positive/negative angle in degrees,\n // ignoring refraction.\"\"\"\n return lunar_altitude(tee, location) - lunar_parallax(tee, location);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":193,"value":"$35","pinned":false,"hidden":false,"mode":"ojs"},{"id":216,"value":"function lunar_phase(tee) {\n // \"\"\"Return the lunar phase, as an angle in degrees, at moment tee.\n // An angle of 0 means a new moon, 90 degrees means the\n // first quarter, 180 means a full moon, and 270 degrees\n // means the last quarter.\"\"\"\n const phi = mod(lunar_longitude(tee) - solar_longitude(tee), 360);\n const t0 = nth_new_moon(0);\n const n = iround((tee - t0) / MEAN_SYNODIC_MONTH);\n const phi_prime =\n deg(360) * mod((tee - nth_new_moon(n)) / MEAN_SYNODIC_MONTH, 1);\n if (abs(phi - phi_prime) > deg(180)) return phi_prime;\n else return phi;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":221,"value":"$36","pinned":false,"hidden":false,"mode":"ojs"},{"id":128,"value":"md`---\n**TODO**`","pinned":false,"hidden":false,"mode":"ojs"},{"id":121,"value":"function solar_latitude(tee) {\n // \"\"\"Return the latitude of Sun (in degrees) at moment, tee.\n // Adapted from \"Astronomical Algorithms\" by Jean Meeus,\n // Willmann_Bell, Inc., 1998.\"\"\"\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":124,"value":"function solar_distance(tee) {\n // \"\"\"Return the distance of Sun (in degrees) at moment, tee.\n // Adapted from \"Astronomical Algorithms\" by Jean Meeus,\n // Willmann_Bell, Inc., 1998.\"\"\"\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":131,"value":"md`---`","pinned":false,"hidden":false,"mode":"ojs"},{"id":134,"value":"function solar_position(tee) {\n // \"\"\"Return the position of the Sun (geocentric latitude and longitude [in degrees]\n // and distance [in meters]) at moment, tee.\n // Adapted from \"Astronomical Algorithms\" by Jean Meeus,\n // Willmann_Bell, Inc., 2nd ed.\"\"\"\n return solar_latitude(tee), solar_longitude(tee), solar_distance(tee);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":140,"value":"function aberration(tee) {\n // \"\"\"Return the aberration at moment, tee.\"\"\"\n const c = julian_centuries(tee);\n return (\n deg(mpf(0.0000974)) *\n cos_degrees(deg(mpf(177.63)) + deg(mpf(35999.01848)) * c) -\n deg(mpf(0.005575))\n );\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":136,"value":"function nutation(tee) {\n // \"\"\"Return the longitudinal nutation at moment, tee.\"\"\"\n const c = julian_centuries(tee);\n const cap_A = poly(c, deg([mpf(124.90), mpf(-1934.134), mpf(0.002063)]));\n const cap_B = poly(c, deg([mpf(201.11), mpf(72001.5377), mpf(0.00057)]));\n return (\n deg(mpf(-0.004778)) * sin_degrees(cap_A) +\n deg(mpf(-0.0003667)) * sin_degrees(cap_B)\n );\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":173,"value":"function lunar_anomaly(c) {\n // \"\"\"Return mean anomaly of moon (in degrees) at moment\n // given in Julian centuries c.\n // Adapted from eq. 47.4 in \"Astronomical Algorithms\" by Jean Meeus,\n // Willmann_Bell, Inc., 2nd ed. with corrections, 2005.\"\"\"\n return normalized_degrees(\n poly(\n c,\n deg([\n mpf(134.9633964),\n mpf(477198.8675055),\n mpf(0.0087414),\n mpf(1 / 69699),\n mpf(-1 / 14712000)\n ])\n )\n );\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":118,"value":"function geometric_solar_mean_longitude(tee) {\n // \"\"\"Return the geometric mean longitude of the Sun at moment, tee,\n // referred to mean equinox of the date.\"\"\"\n const c = julian_centuries(tee);\n return poly(c, deg([mpf(280.46646), mpf(36000.76983), mpf(0.0003032)]));\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":183,"value":"function moon_node(c) {\n // \"\"\"Return Moon’s argument of latitude (in degrees) at moment\n // given in Julian centuries ’c’.\n // Adapted from eq. 47.5 in \"Astronomical Algorithms\" by Jean Meeus,\n // Willmann_Bell, Inc., 2nd ed. with corrections, 2005.\"\"\"\n return normalized_degrees(\n poly(\n c,\n deg([\n mpf(93.2720950),\n mpf(483202.0175233),\n mpf(-0.0036539),\n mpf(-1 / 3526000),\n mpf(1 / 863310000)\n ])\n )\n );\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":186,"value":"function solar_anomaly(c) {\n // \"\"\"Return mean anomaly of sun (in degrees) at moment\n // given in Julian centuries c.\n // Adapted from eq. 47.3 in \"Astronomical Algorithms\" by Jean Meeus,\n // Willmann_Bell, Inc., 2nd ed. with corrections, 2005.\"\"\"\n return normalized_degrees(\n poly(\n c,\n deg([\n mpf(357.5291092),\n mpf(35999.0502909),\n mpf(-0.0001536),\n mpf(1 / 24490000)\n ])\n )\n );\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":226,"value":"function estimate_prior_solar_longitude(lam, tee) {\n // \"\"\"Return approximate moment at or before tee\n // when solar longitude just exceeded lam degrees.\"\"\"\n const rate = MEAN_TROPICAL_YEAR / deg(360);\n const tau = tee - rate * mod(solar_longitude(tee) - lam, 360);\n const cap_Delta = mod(solar_longitude(tau) - lam + deg(180), 360) - deg(180);\n return min(tee, tau - rate * cap_Delta);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":75,"value":"md`### Constants`","pinned":false,"hidden":false,"mode":"ojs"},{"id":39,"value":"J2000 = days_from_hours(12) + gregorian_new_year(2000)","pinned":false,"hidden":false,"mode":"ojs"},{"id":66,"value":"MEAN_TROPICAL_YEAR = 365.242189","pinned":false,"hidden":false,"mode":"ojs"},{"id":69,"value":"MEAN_SIDEREAL_YEAR = 365.25636","pinned":false,"hidden":false,"mode":"ojs"},{"id":72,"value":"MEAN_SYNODIC_MONTH = 29.530588861","pinned":false,"hidden":false,"mode":"ojs"},{"id":229,"value":"SPRING = deg(0)","pinned":false,"hidden":false,"mode":"ojs"},{"id":232,"value":"SUMMER = deg(90)","pinned":false,"hidden":false,"mode":"ojs"},{"id":235,"value":"AUTUMN = deg(180)","pinned":false,"hidden":false,"mode":"ojs"},{"id":238,"value":"WINTER = deg(270)","pinned":false,"hidden":false,"mode":"ojs"},{"id":7,"value":"md`## Technical details`","pinned":false,"hidden":false,"mode":"ojs"},{"id":10,"value":"import {\n angle,\n arcsin_degrees,\n creditsMeeus,\n days_from_hours,\n declination,\n deg,\n dusk,\n julian_centuries,\n latitude,\n longitude,\n midday,\n mpf,\n mt,\n normalized_degrees,\n obliquity,\n right_ascension,\n sunset,\n sunrise,\n tan_degrees,\n sin_degrees,\n cos_degrees,\n arctan_degrees,\n signum,\n universal_from_standard,\n PI\n} from \"@espinielli/calcal-time-astronomy\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":24,"value":"import {\n abs,\n credits,\n fixed_from_moment,\n ifloor,\n iround,\n min,\n mod,\n poly,\n pow,\n sigma,\n BOGUS\n} from \"@espinielli/calcal-foundation\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":44,"value":"import {\n gregorian_date,\n gregorian_date_difference,\n gregorian_year_from_fixed,\n gregorian_new_year,\n JANUARY,\n JULY\n} from \"@espinielli/calcal-gregorian\"","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W37","stdlib":"1","titling":"auto"}