2d:null 2e:["$","title",null,{"children":"Obliquity of the ecliptic | Igor A1 | Observable"}] 33:[] 31:{"id":"ddd1a4d36fde5ee2","slug":"obliquity-of-the-ecliptic","title":"Obliquity of the ecliptic","thumbnail":"559c8a98f8b42afa0756b01daa2aaeda4869a53d648ae857fa873423fe0ecc80","access_level":"public","create_time":"$D2020-02-24T13:54:33.205Z","update_time":"$D2020-02-26T00:13:55.685Z","view_time":null,"first_public_time":"$D2020-02-25T12:40:02.753Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"6c5efb1eab88987b","login":"igor-a1","name":"Igor A1","avatar_url":"https://avatars-next.observableusercontent.com/7f0055f4279565990ec1cc324da008037750cdcc99d774567c194b9e9898c62f","tier":"starter_2024"},"version":216,"publish_version":216,"role":null,"authored":false,"authors":[{"type":"individual","id":"4c750d0fb9bf5b48","login":"igor-a1","name":"Igor A1","avatar_url":"https://avatars-next.observableusercontent.com/7f0055f4279565990ec1cc324da008037750cdcc99d774567c194b9e9898c62f","tier":null}],"members":[{"type":"individual","id":"4c750d0fb9bf5b48","login":"igor-a1","name":"Igor A1","avatar_url":"https://avatars-next.observableusercontent.com/7f0055f4279565990ec1cc324da008037750cdcc99d774567c194b9e9898c62f","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":{"id":"55bd3dd6b0677799","slug":"astro","title":"Astro","owner":{"id":"6c5efb1eab88987b","login":"igor-a1","name":"Igor A1"}},"type":"notebook","body":{"title":"Obliquity of the ecliptic","cells":[{"id":0,"value":"md`# Obliquity of the ecliptic`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":65,"value":"html`From SunCalc@1.8.0 library:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":68,"value":"md`\n\\`\\`\\`javascript\ne = 23.4397 // obliquity of the Earth\n\\`\\`\\`\n*23.4397 = ${deg2dms(23.4397).dms}*`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"html`From Wikipedia article:`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":78,"value":"html`DE200 ephemerides model :
ε = 23° 26′ 21.448″ − 46.8150″ T − 0.00059″ T² + 0.001813″ T³`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":82,"value":"html`Astronomical Almanac 2010 :
ε = 23° 26′ 21.406″ − 46.836769″ T − 0.0001831″ T² + 0.00200340″ T³ − 5.76″ × 10⁻⁷ T⁴ − 4.34″ × 10⁻⁸ T⁵`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"html`J. Laskar :
ε = 23° 26′ 21.448″ − 4680.93″ t − 1.55″ t² + 1999.25″ t³ − 51.38″ t⁴ − 249.67″ t⁵ − 39.05″ t⁶ + 7.12″ t⁷ + 27.87″ t⁸ + 5.79″ t⁹ + 2.45″ t¹⁰`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"html`where here T is Julian centuries from J2000.0 and t is multiples of 10,000 Julian years from J2000.0

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":166,"value":"table(data,{})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":184,"value":"md`---\n### My obliquity formulae:\n\\`\\`\\`javascript\nconst obliquity = someDate => {\n const j2000 = 2000,\n jCentury = (someDate. getFullYear() - j2000) / 100,\n kSec = [-0.13004166666666667, -0.0000016388888888888889, 0.000005036111111111111];\n \n let result = 23.43929111111111;\n kSec.forEach((k, i) => result += k * jCentury ** (i + 1));\n return result;\n}\n\nconsole.log(obliquity(new Date())) // 23.413282752511112\n\\`\\`\\`\n---`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":163,"value":"import {table} from \"@tmcw/tables@444\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":134,"value":"data = earthObliquity(100)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":126,"value":"earthObliquity = (years) => {\n let data = []\n let year = 0\n while(year < years) {\n let T = year / jCentury\n let t = year / j100Centuries\n let e = obliquity(T, t)\n data.push({\n year: `${j2000 + year}`, \n de200: `${e[0]}`, \n dms: deg2dms(e[0]).dms, \n // equal to a2010: deg2dms(e[1]).dms, \n // equal to laskar: deg2dms(e[2]).dms\n diff: `${23.4397 > e[0] ? '-' : '+'}${deg2dms(23.4397 - e[0]).dms}`\n })\n year++\n }\n return data\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":116,"value":"j2000 = 2000","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":117,"value":"jCentury = 100","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":120,"value":"j100Centuries = 100 * jCentury","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":45,"value":"obliquity = (T, t) => {\n let result = [dms2deg(23, 26, 21.448), dms2deg(23, 26, 21.406), dms2deg(23, 26, 21.448)]\n kSec[0].forEach((d, i) => result[0] += d * T ** (i + 1))\n kSec[1].forEach((d, i) => result[1] += d * T ** (i + 1))\n kSec[2].forEach((d, i) => result[2] += d * t ** (i + 1))\n return result\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":40,"value":"kSec = [[-46.8150, -0.00059, 0.001813].map(s => s / 360), [-46.836769, -0.0001831, 0.00200340, -5.76 * 10 ** (-7), -4.34 * 10 ** (-8)].map(s => s / 360), [-4680.93, -1.55, 1999.25, -51.38, -249.67, -39.05, 7.12, 27.87, 5.79, 2.45].map(s => s / 360)]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":37,"value":"sec2deg = sec => sec / 360","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"dms2deg = (d, m, s) => d + m / 60 + s / (60 * 60)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"lead0 = n => n > 9 ? n : '0' + n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"deg2dms = deg => {\n let d = Math.floor(deg),\n m = Math.floor(60 * (deg - d)),\n s = Math.floor(3600 * (deg - d - m / 60)),\n dms = `${d}\\u00B0${lead0(m)}'${lead0(s)}\"`\n return {d: d, m: m, s: s, dms: dms}\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W33","stdlib":"1","titling":"auto"}} 32:"$31:body"