27:null 28:["$","title",null,{"children":"ForceLink based Hierarchical Orbits | Antoine Faché | Observable"}] 2d:T58f,forceSim = { const gravity = 0.00005; // Regulates mechanics speed const planet = { id: 'planet', initialState: { y: -height / 4, vx: 0.5 * height * Math.sqrt(gravity) } }; const moon = { id: 'moon', initialState: { y: -height * 3/8, vx: 0.25 * height * Math.sqrt(gravity * 100) } }; const bodies = [{ id: 'sun', initialState: { x: 0, y: 0 } }, planet, moon], links = [ { source: 'planet', target: 'sun-anchor', attraction: gravity }, { source: 'moon', target: 'planet-anchor', attraction: gravity * 100 } // Higher attraction = more revolutions ]; // Generate body anchors const anchors = bodies.map(body => { return { id: body.id + '-anchor', body: body } }); const forceSim = d3.forceSimulation() .alphaDecay(0) .velocityDecay(0) .nodes([...bodies, ...anchors]) .force("gravitate-around", d3.forceLink(links) .id(d => d.id) .distance(0) .strength(link => link.attraction || 0.1) ) .on('tick', () => { mutable planetPos = [planet.x, planet.y]; mutable moonPos = [moon.x, moon.y]; fixAnchors(); }); // Set initial states bodies.forEach(body => { for (let k in body.initialState) { body[k] = body.initialState[k]; } }); function fixAnchors() { anchors.forEach(anchor => { anchor.fx = anchor.body.x; anchor.fy = anchor.body.y; }); } return forceSim; }2e:[] 2b:{"id":"d7ce7f139ac961bb","slug":null,"title":"ForceLink based Hierarchical Orbits","thumbnail":"6f96f24d22ec3732824ab7af48cc33ec35d766349c55b490869e6b2918809f63","access_level":"public","create_time":"$D2026-04-21T04:10:58.914Z","update_time":"$D2026-04-21T04:10:58.914Z","view_time":null,"first_public_time":"$D2026-04-21T04:10:58.914Z","has_unpublished_edits":null,"fork":{"id":"d47bc61dc40be8a3","slug":"forcelink-based-hierarchical-orbits","title":"ForceLink based Hierarchical Orbits","owner":{"id":"dc625de0fe5f3eae","login":"vasturiano","name":"Vasco Asturiano"}},"stars":0,"starred":false,"owner":{"type":"team","id":"ab5c695e0d9f5ed0","login":"anthonyzornig","name":"Antoine Faché","avatar_url":"https://avatars-next.observableusercontent.com/73fe10f97d0449896f1255d6ce2abd09ac0d89a7c87afb645a54faeb67cc288a","tier":"starter_2024"},"version":133,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"a6dae7277d3d666a","login":"anthonyzornig","name":"Antoine Faché","avatar_url":"https://avatars-next.observableusercontent.com/73fe10f97d0449896f1255d6ce2abd09ac0d89a7c87afb645a54faeb67cc288a","tier":null}],"members":[{"type":"individual","id":"a6dae7277d3d666a","login":"anthonyzornig","name":"Antoine Faché","avatar_url":"https://avatars-next.observableusercontent.com/73fe10f97d0449896f1255d6ce2abd09ac0d89a7c87afb645a54faeb67cc288a","tier":null,"role":"editor"},{"type":"team","id":"ab5c695e0d9f5ed0","login":"anthonyzornig","name":"Antoine Faché","avatar_url":"https://avatars-next.observableusercontent.com/73fe10f97d0449896f1255d6ce2abd09ac0d89a7c87afb645a54faeb67cc288a","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"ForceLink based Hierarchical Orbits","cells":[{"id":0,"value":"# ForceLink based Hierarchical Orbits\n\nAttempt at simulation of multiple particles orbitting around each other in a hierarchical system (e.g. sun > planet > moon).\n\nUses [D3 force-directed](https://github.com/d3/d3-force) physics engine's [forceLink](https://github.com/d3/d3-force#links) to connect particles to their moving gravitational centers via fixed position anchor nodes.\n\nThe system fails to reach equilibrium due to the \"spring\" nature of forceLink, in which contrary to gravitational forces the intensity decreases with proximity, causing bodies to inevitably fall onto their attraction center. The [forceMagnetic](https://github.com/vasturiano/d3-force-magnetic) force is a better fit for modelling this type of motion.\n\nCompare with the [forceMagnetic version](forcemagnetic-based-hierarchical-orbits).","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":10,"value":"\n${trailsCanvas}\n","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":20,"value":"mutable planetPos = [0, 0]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"mutable moonPos = [0, 0]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":29,"value":"trailsCanvas = html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":37,"value":"addTrailDot(planetPos)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":110,"value":"addTrailDot(moonPos)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":113,"value":"addTrailDot = pos => {\n d3.select(trailsCanvas).append('circle')\n .attr('id', 'trail')\n .attr('r', 1.5)\n .attr('cx', pos[0])\n .attr('cy', pos[1])\n .transition().duration(5000)\n .style('opacity', 0)\n .remove();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"$2d","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"**Settings**","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":15,"value":"height = 400","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"**Dependencies**","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":7,"value":"d3 = require('d3@7')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W2e","stdlib":"1","titling":"auto"}} 2c:"$2b:body"