MMM-PlanetsDance

A MagicMirror² module that draws the planets' real orbits, from today, as figures that look like sacred geometry.

The planets' dance. Real orbits from today, drawn as figures that look like sacred geometry and are nothing but clockwork: the line between Earth and Venus every 4 days for 8 years makes a five-petalled rose; Mars, Jupiter or Saturn seen from Earth loop back each time we overtake them; every meeting of Jupiter and Saturn for 800 years, joined in order, is Kepler's turning triangle. One of eight figures each time the module is shown, drawn in 22 s, then held. Underneath: the figure's arithmetic, a note from its history (the Maya's Venus table, Ptolemy's epicycles, Galileo's moons of Jupiter), and the date the drawing has reached, with the distance between the planets or, for a loop, whether the planet is going backwards.

Built for a Raspberry Pi 3 without GPU acceleration: everything is drawn by the CPU, so the drawing is designed around what that costs (see Performance), and the animation stops completely while the module is hidden.

cd ~/MagicMirror/modules
git clone https://github.com/charleswest775/MMM-PlanetsDance

No npm dependencies: there is nothing to install.

cd ~/MagicMirror/modules/MMM-PlanetsDance
git pull

{
	module: "MMM-PlanetsDance",
	position: "middle_center",
	config: {
		orbitsSeconds: 22,  // drawn in 22 s of a 30 s page, then held
		orbitsDances: [],   // all eight, one per showing
		width: 700,
		height: 700,
		fps: 12
	}
},

With MMM-pages, every page added makes the rotation longer. Modules on the same page can share it instead: with turns: { of: n, at: k }, each of n modules shows on its own one in n showings of the page, the first on showing 0, the next on showing 1, and so on. A module not on its turn takes no room on the page and costs nothing.

On the mirror this module takes turns with two others that draw a figure and hold it, MMM-SacredGeometry and MMM-Tilings:

{
	module: "MMM-SacredGeometry",
	classes: "page-sacred",
	position: "middle_center",
	config: { turns: { of: 3, at: 0 } }
},
{
	module: "MMM-Tilings",
	classes: "page-sacred",
	position: "middle_center",
	config: { turns: { of: 3, at: 1 } }
},
{
	module: "MMM-PlanetsDance",
	classes: "page-sacred",
	position: "middle_center",
	config: { turns: { of: 3, at: 2 } }
},

with the page in MMM-pages' list, e.g. modules: [["page-sacred"], ["page-sky"]].

The module works just as well on a page of its own (leave turns out), or in a normal region without MMM-pages, where it is never hidden and draws a new figure every cycleSeconds.

Each showing draws one of eight figures from today's date, with time running evenly, so a planet lingers where it really moves slowly:

• Earth and Venus, the line between them every 4 days for 8 years: a five-petalled rose, because 8 Earth years (2922.1 days) ≈ 13 Venus years (2921.1) ≈ 5 laps of Earth by Venus (5 × 583.9). Earth and Mercury, every 3 days for 7 years: 22 laps, 29 Mercury years. Jupiter and Saturn, every month for three of Jupiter's laps of Saturn (60 years).
• Venus, Mars, Jupiter or Saturn seen from Earth: the planet's position minus Earth's, with Earth at the centre and the Sun's yearly circle round it. It loops back each time one overtakes the other: Venus 5 times in 8 years, at the corners of a pentagram; Mars 7 times in 15; Jupiter 11 times, Saturn 28, in one of their years. Ptolemy's epicycles were built to reproduce exactly these loops.
• Kepler's trigon: every conjunction of Jupiter and Saturn from the one of 2020 on for 800 years, joined in order on the circle of the zodiac. Each is 243° on from the last, so three make a triangle that turns 9° every 60 years, and after 40 the meetings are back in the same signs. Longitudes are measured from the equinox of each date, which precesses 1.4° a century, as Kepler's were.

The figures are dealt from a shuffled deck, so all eight come round before any repeats.

Positions come from JPL's Keplerian Elements for Approximate Positions of the Major Planets (Standish), in simulations/ephemeris.js: each orbit an ellipse whose elements drift linearly, fitted to JPL's DE ephemeris, good to arcseconds for the inner planets and arcminutes for Saturn from 1800 to 2050 (Table 1), and coarser from 3000 BC to AD 3000 (Table 2, used outside those years). The tests check them against the almanacs: Venus's inferior conjunctions of 2020–2026 and Mars's oppositions of 2018–2027 to the day, Jupiter and Saturn 0.10° apart on 21 December 2020, and the conjunction of December 1603 that Kepler watched. They also check JPL's two tables against each other, Kepler's third law, Venus's 8-year cycle and the 2.4° its pentagram turns in it, Mars going backwards at opposition, and the trigon's 243° steps.

Drawn like sacred geometry: each frame adds only what is new, with lighter compositing so crossings brighten, and the finished figure rests. Measured in a desktop browser by diffing frames, a frame changes on average 15% of the canvas for the line figures and under 1% for the loops.

Measured on a Raspberry Pi 3 B+ (Electron 42, software rendering, 700×700 at 12 fps, seven showings, CPU of the Electron processes plus the cage compositor, in % of one core; the Pi has four, and the mirror without the module uses 0.2%):

What costs what on the Pi:

• There is no GPU acceleration to be had (the Pi 3's GPU does only GLES 2.0), so all canvas drawing is done by the CPU.
• Any frame that changes the canvas costs ~2% of a core per fps, before drawing anything; hence the 12 fps cap.
• On top of that, cost grows with the area that changes: Chromium redraws the bounding box of everything touched in a frame. So each frame draws only the strokes added since the last.
• JavaScript is not the bottleneck: the figure is computed once per showing, and step and draw take a few milliseconds per frame.
• The frame loop sleeps with setTimeout until a frame is due. Once the figure is finished the module rests, and is only polled twice a second. While MagicMirror fades the module out, nothing new is drawn, and once it is hidden (another MMM-pages page, say) the loop stops completely: measured with the same loop in MMM-ChaosTheory, 0.3% of a core against the mirror's 0.2% without it.

node --test                  # the ephemeris against the almanacs, and every figure (no dependencies)
python3 -m http.server       # in the module folder, then open http://localhost:8000/dev/preview.html

dev/preview.html runs the module outside MagicMirror², in a portrait 1200×1920 frame, with hide/show buttons that follow MagicMirror's suspend/resume order. Query options override the config, e.g. ?dance=venus (always this figure), ?dance=trigon&start=1600-01-01 (from another date), ?orbitsDances=mars,jupiter, ?orbitsSeconds=8&fps=20 or ?statsPanel=true (with made-up numbers, as there is no node_helper in the preview).

MIT. Planetary positions from JPL's Keplerian Elements for Approximate Positions of the Major Planets by E. M. Standish (JPL/Caltech).

Part of a family of MagicMirror² modules. Chaos, one simulation each: MMM-LorenzAttractor, MMM-DoublePendulum, MMM-FractalBasins, MMM-LogisticMap, MMM-SymmetricIcons, MMM-ThreeBody, MMM-ChaoticBilliards, MMM-Rule30, MMM-StandardMap, MMM-ChaoticWaterwheel and MMM-Sandpile, or all eleven in one module, MMM-ChaosTheory. And more pages of physics and mathematics: MMM-Atom, MMM-DoubleSlit, MMM-FractalZoom, MMM-Chladni, MMM-SacredGeometry, MMM-Tilings, MMM-Harmonograph, MMM-SnowCrystal, MMM-NightSky and MMM-PhotoDeck.