31:T7d0,{ let dotplot = Plot.plot({ height: 470, width: 850, grid: true, marginLeft: 50, marginRight: 40, marginTop: 50, marginBottom: 75, insetTop: 0, insetBottom: 0, style: { fontSize: "17px", background: "#fff", color: "#000" }, x: { label: " ← Right ascension (RA), α ", tickPadding: 6, labelOffset: 64, transform: f => f/6, domain: [360/6,0], tickFormat: x => `${Math.round(6*x.toFixed(3))}°`, ticks: 10, tickSize: 9, tickRotate: 0 }, y: { label: "↑ Declination, δ", labelOffset: 35, tickFormat: x => x<=0 ?`${x}°`: `+${x}°`, ticks: 10, tickSize: 6, domain: [-30, 30] }, caption: html`
Figure 1: Theoretical astronomical coordinates of Mars for the period around the selected date.
⬤ Position of Mars at the selected date:
${date}.
┄ After selected date / ─ Before selected date
`, marks: [ Plot.frame({stroke: "black"}), Plot.ruleY([0]), Plot.line(ephemeris_mars_360_before, {x: "RA_deg", y: "Dec_deg", strokeWidth: 1.8, stroke: "crimson"} ), Plot.line(ephemeris_mars_360_after, {x: "RA_deg", y: "Dec_deg", strokeWidth: 2, strokeDasharray: "4,3", stroke: "crimson"} ), Plot.dot(ephemeris_mars_360_before, {x: coordinates_mars_selected_date.RA_deg, y: coordinates_mars_selected_date.Dec_deg, fill: "brown", r: 4.5}), Plot.text(ephemeris_mars_360_before, {x: coordinates_mars_selected_date.RA_deg , y: coordinates_mars_selected_date.Dec_deg, text: d => d.label, dx: 2, dy: -28, fill: "brown", fontSize: "28px"}), ] }) // Label in bold let select_labels = d3.select(dotplot) .selectAll("svg > g > text") .style("font-weight", "bold"); return dotplot; }32:T814,{ let dotplot = Plot.plot({ height: 470, width: 850, grid: true, marginLeft: 50, marginRight: 40, marginTop: 50, marginBottom: 75, insetTop: 0, insetBottom: 0, style: { fontSize: "17px", background: "#fff", color: "#000" }, x: { label: " ← Right ascension (RA), α ", tickPadding: 6, labelOffset: 64, transform: f => f/6, domain: [360/6,0], tickFormat: x => `${Math.round(6*x.toFixed(3))}°`, ticks: 10, tickSize: 9, tickRotate: 0 }, y: { label: "↑ Declination, δ", labelOffset: 35, tickFormat: x => x<=0 ?`${x}°`: `+${x}°`, ticks: 10, tickSize: 6, domain: [-30, 30] }, caption: html`
Figure 2: Theoretical astronomical coordinates of Mercury for the period around the selected date.
⬤ Position of Mercury at the selected date:
${date}.
┄ After selected date / ─ Before selected date
`, marks: [ Plot.frame({stroke: "black"}), Plot.ruleY([0]), Plot.line(ephemeris_mercury_360_before, {x: "RA_deg", y: "Dec_deg", strokeWidth: 1.8, stroke: "steelblue"} ), Plot.line(ephemeris_mercury_360_after, {x: "RA_deg", y: "Dec_deg", strokeWidth: 2, strokeDasharray: "4,3", stroke: "steelblue"} ), Plot.dot( ephemeris_mercury_360_before, {x: coordinates_mercury_selected_date.RA_deg , y: coordinates_mercury_selected_date.Dec_deg, fill: "black", r: 4.5}), Plot.text(ephemeris_mercury_360_before, {x: coordinates_mercury_selected_date.RA_deg , y: coordinates_mercury_selected_date.Dec_deg, text: d => d.label, dy: -25, fill: "steelblue", fontSize: "26px"}), ] }) // Label in bold let select_labels = d3.select(dotplot) .selectAll("svg > g > text") .style("font-weight", "bold"); return dotplot; }33:T622,ephemeris_planet = function(date,i){ let data = {}; data.name = planets[i].name; data.dRA = ephemeris.getAllPlanets(date,0, 0, 0).observed[planets[i].id].raw.position.apparent.dRA.toFixed(5); data.dDec = ephemeris.getAllPlanets(date,0, 0, 0).observed[planets[i].id].raw.position.apparent.dDec.toFixed(5); var RA_h = ephemeris.getAllPlanets(date,0, 0, 0).observed[planets[i].id].raw.position.apparent.ra.hours; var RA_min = ephemeris.getAllPlanets(date,0, 0, 0).observed[planets[i].id].raw.position.apparent.ra.minutes; RA_min = RA_min < 10? RA_min = "0" + RA_min: RA_min; var RA_sec = ephemeris.getAllPlanets(date,0, 0, 0).observed[planets[i].id].raw.position.apparent.ra.seconds; RA_sec = RA_sec < 10? RA_sec = "0" + RA_sec: RA_sec; data.RA = RA_h +"h " + RA_min +"m " + RA_sec + "s"; var dec_sign = Math.sign(ephemeris.getAllPlanets(date,0, 0, 0).observed[planets[i].id].raw.position.apparent.dDec) < 0? dec_sign = "-": dec_sign = "+"; var dec_deg = dec_sign + ephemeris.getAllPlanets(date,0, 0, 0).observed[planets[i].id].raw.position.apparent.dec.degree.toString(); var dec_min = ephemeris.getAllPlanets(date,0, 0, 0).observed[planets[i].id].raw.position.apparent.dec.minutes; dec_min = dec_min < 10? dec_min = "0" + dec_min: dec_min; var dec_sec = (ephemeris.getAllPlanets(date,0, 0, 0).observed[planets[i].id].raw.position.apparent.dec.seconds).toFixed(0); dec_sec = dec_sec < 10? dec_sec = "0" + dec_sec: dec_sec; data.DEC = dec_deg +"° " + dec_min +"' " + dec_sec +"''"; return data; }34:[{"id":"982dda2acfa5fb496dbcc9c0b3ca212f3cb240c53bb0637c571710e083f359a3519c47588d8c9d18d018bbe48bcc37d4508663de7a1528ddaaa07893df24cee0","href":"https://static.observableusercontent.com/files/982dda2acfa5fb496dbcc9c0b3ca212f3cb240c53bb0637c571710e083f359a3519c47588d8c9d18d018bbe48bcc37d4508663de7a1528ddaaa07893df24cee0","name":"ephemeris-2.0.0.js","type":"application/javascript","lastModified":1716159302545.378,"size":230067}] 2f:{"title":"Ephemerides (planets of the solar system)","cells":[{"id":0,"value":"# Ephemerides (planets of the solar system)","pinned":false,"hidden":false,"mode":"md"},{"id":426,"value":"

\n Right Ascension and Declination are essential astronomical coordinates that provide a consistent way to locate objects in the sky. For planets and stars, they are independent of the observer's location on Earth. \n

This notebook lists the Right Ascension (RA) and Declination (Dec) for the planets in our solar system. By default, it displays the positions for the current date. You can also manually enter a date or select one from the calendar (year range: ${Year_min}-${Year_max}).\n

","pinned":false,"hidden":false,"mode":"html"},{"id":43,"value":"viewof date = Inputs.datetime({label: htl.html`Input date:`, value: Date.now(), required: true, min: Year_min+\"-01-01\", max: Year_max+\"-12-31\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1079,"value":"
\n

Ephemerides

\nThe following table shows the calculated ephemerides for the date:\n
${date}.","pinned":false,"hidden":false,"mode":"html"},{"id":333,"value":"{\n \n return Inputs.table(ephemeris_planets, {\n columns: [\n \"name\",\n \"RA\", \n \"DEC\",\n \"empty\",\n \"dRA\",\n \"dDec\",\n ],\n \n header: {\n name: \"Name\",\n RA: \"RA, α (hours) \", \n DEC: \"Dec, δ (°)\",\n empty: \"\",\n dRA: \"RA, α (rad) \",\n dDec: \"Dec, δ (rad)\",\n\n\n\n },\n \n align: {\n name: \"left\",\n RA: \"right\",\n dRA: \"center\",\n DEC: \"right\",\n dDec: \"center\",\n\n },\n \n width: {\n name: 100,\n RA: 90,\n dRA: 90,\n empty: 50,\n DEC: 80,\n dDec: 80,\n },\n\n maxWidth: 600,\n maxHeight: 400,\n height: 200\n})\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":467,"value":"

\n Please note that these ephemerides are estimations calculted using the JavaScript code ephemeris-2.0.0.js.\n

You may compare it with the Observer Tables found in the NASA HORIZONS system, which should definitely provide more accurate values.\n

","pinned":false,"hidden":false,"mode":"html"},{"id":754,"value":"
\n

Illustration 1: The planet Mars (♂)

\n The following graph plots the theoertical path of Mars around the selected date.\n Notice the occasional loops, which occur because Mars undergoes apparent retrograde motion approximately once every 26 months (~2.1 years).\n

\n

","pinned":false,"hidden":false,"mode":"html"},{"id":704,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":866,"value":"

\n

Illustration 2: The planet Mercury (☿)

\n The following graph plots the theoertical path of Mercury around the selected date.\n Notice the frequent loops, which occur because Mercury undergoes apparent retrograde motion approximately three to four times a year.\n

\n

","pinned":false,"hidden":false,"mode":"html"},{"id":870,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":485,"value":"
\n

","pinned":false,"hidden":false,"mode":"html"},{"id":421,"value":"## Appendix","pinned":false,"hidden":false,"mode":"md"},{"id":1053,"value":"Year_min = 1950","pinned":false,"hidden":false,"mode":"ojs"},{"id":1056,"value":"Year_max = 2100","pinned":false,"hidden":false,"mode":"ojs"},{"id":538,"value":"dates = function(i) {\n\n function UT(d) { return Date.parse(d)};\n \n var date_i = new Date(UT(date)+86400000*i)\n return date_i \n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":85,"value":"planets = [\n {id:\"mercury\", name:\"Mercury (☿)\"},\n {id:\"venus\", name:\"Venus (♀)\"},\n {id:\"mars\", name:\"Mars (♂)\"},\n {id:\"jupiter\", name:\"Jupiter (♃)\"},\n {id:\"saturn\", name: \"Saturn (♄)\"},\n {id:\"uranus\", name:\"Uranus (⛢)\"},\n {id:\"neptune\", name:\"Neptune (♆)\"}]","pinned":false,"hidden":false,"mode":"ojs"},{"id":854,"value":"ephemeris_mercury = {\n var data = []\n var i_min = -40;\n var i_max = 60;\n for(var i = i_min; i < i_max; i++) {\n data[i-i_min] = ephemeris_planet_raw(dates(i*2),0)\n }\n return data\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":857,"value":"ephemeris_mercury_360_before = ephemeris_mercury.filter(d => d.date <= date).map(d => d.RA_deg <= 2 || d.RA_deg >= 358 ? NaN : d);","pinned":false,"hidden":false,"mode":"ojs"},{"id":859,"value":"ephemeris_mercury_360_after = ephemeris_mercury.filter(d => d.date >= date).map(d => d.RA_deg <= 2 || d.RA_deg >= 358 ? NaN : d);","pinned":false,"hidden":false,"mode":"ojs"},{"id":863,"value":"coordinates_mercury_selected_date = {\n let data = ephemeris_mercury.filter(d => d.date <= date && d.date >= date)[0];\n data.label = \"☿\";\n return data;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":534,"value":"ephemeris_mars = {\n var data = []\n var i_min = -60;\n var i_max = 75;\n for(var i = i_min; i < i_max; i++) {\n data[i-i_min] = ephemeris_planet_raw(dates(i*5),2)\n }\n return data\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":712,"value":"ephemeris_mars_360_before = ephemeris_mars.filter(d => d.date <= date).map(d => d.RA_deg <= 2 || d.RA_deg >= 358 ? NaN : d);","pinned":false,"hidden":false,"mode":"ojs"},{"id":779,"value":"ephemeris_mars_360_after = ephemeris_mars.filter(d => d.date >= date).map(d => d.RA_deg <= 2 || d.RA_deg >= 358 ? NaN : d);","pinned":false,"hidden":false,"mode":"ojs"},{"id":735,"value":"coordinates_mars_selected_date = {\n let data = ephemeris_mars.filter(d => d.date <= date && d.date >= date)[0];\n data.label = \"♂\";\n return data;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":339,"value":"ephemeris_planets = {\n var data = []\n for(var i = 0; i < planets.length; i++) {\n data[i] = ephemeris_planet(date,i)\n }\n return data\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":633,"value":"ephemeris_planet_raw = function(date,i) {\n \n let data = {};\n\n data.date = date;\n data.RA_deg = parseFloat((180/Math.PI * ephemeris.getAllPlanets(date,0, 0, 0).observed[planets[i].id].raw.position.apparent.dRA).toFixed(3)) ;\n data.Dec_deg = parseFloat((180/Math.PI * ephemeris.getAllPlanets(date,0, 0, 0).observed[planets[i].id].raw.position.apparent.dDec).toFixed(3));\n\n return data;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":267,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":13,"value":"ephemeris = require(await FileAttachment(\"ephemeris-2.0.0.js\").url())","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W34","stdlib":"1","titling":"auto"}