2c:null 2d:["$","title",null,{"children":"Hohmann Transfer Orbit | Paul Murray | Observable"}] 32:T962,function create_frames() { const engine = create_engine(); const world = engine.world; const max_time_ms = max_time_seconds * 1e3; const num_frames = Math.floor(max_time_ms / ms_per_frame) + 1; const new_frames = []; const satellite = Matter.Composite.allBodies(world).find( (d) => d.label === `satellite` ); const plans = plan_parsed.map((d) => ({ ...d, used: false })); for (const frame_index of d3.range(num_frames)) { const bodies = Matter.Composite.allBodies(world); const timestamp = engine.timing.timestamp; const plan = plans.filter((d) => !d.used).find((d) => d.time < timestamp); if (plan) { plan.used = true; const { angle, magnitude } = plan; const force = vector_from_angle(angle, magnitude); const flame = Matter.Bodies.circle( satellite.position.x, satellite.position.y, satellite.circleRadius * flame_radius, { label: `flame-${Math.floor(Math.random())}`, plugin: { order: -1, style: `fill: orange; stroke: none;`, beforeUpdate: () => { const flame_shrink_percent = 0.98; Matter.Body.scale( flame, flame_shrink_percent, flame_shrink_percent ); const newArea = flame.area; if (newArea < 0.1) { Matter.Composite.remove(world, flame); } } }, collisionFilter: { mask: 0b0 }, mass: flame_mass * scale_factor, friction: 0, frictionAir: 0, restitution: 0 } ); Matter.Body.applyForce(satellite, satellite.position, force); Matter.Body.applyForce(flame, flame.position, Matter.Vector.neg(force)); Matter.Composite.add(world, flame); } const frame = { bodies: Object.fromEntries( bodies.map((body) => { const { label, position, circleRadius, plugin, speed } = body; return [ label, { ...body, label, position: { ...position }, circleRadius, plugin } ]; }) ), timestamp, index: frame_index, plan }; new_frames.push(frame); Matter.Engine.update(engine, ms_per_frame); } return new_frames; }33:[] 30:{"id":"591d960d18f4f5ff","slug":"hohmann-transfer","title":"Hohmann Transfer Orbit","thumbnail":"bfb1312ee0a83e52ce7e56f345a9e242abbb076573db35a3da99214f2e8662c4","access_level":"public","create_time":"$D2022-05-16T00:54:27.583Z","update_time":"$D2023-07-06T22:48:07.493Z","view_time":null,"first_public_time":"$D2022-05-16T22:38:10.653Z","fork":true,"stars":11,"starred":false,"owner":{"type":"team","id":"77ca23d94884ea46","login":"plmrry","name":"Paul Murray","avatar_url":"https://avatars-next.observableusercontent.com/e55c33ea9568426a80f30a4e3ca4f71e21571d01804bee4b863c3063bd4a62e1","tier":"starter_2024"},"version":1218,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"88a33f32468b0503","login":"plmrry","name":"Paul Murray","avatar_url":"https://avatars-next.observableusercontent.com/e55c33ea9568426a80f30a4e3ca4f71e21571d01804bee4b863c3063bd4a62e1","tier":null}],"members":[{"type":"individual","id":"88a33f32468b0503","login":"plmrry","name":"Paul Murray","avatar_url":"https://avatars-next.observableusercontent.com/e55c33ea9568426a80f30a4e3ca4f71e21571d01804bee4b863c3063bd4a62e1","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":3,"collection":{"id":"de1e16533aad154c","slug":"portfolio","title":"Portfolio","owner":{"id":"77ca23d94884ea46","login":"plmrry","name":"Paul Murray"}},"type":"notebook","body":{"title":"Hohmann Transfer Orbit","cells":[{"id":0,"value":"# Hohmann Transfer Orbit","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":970,"value":"This is a demonstration of a satellite executing a [Hohmann transfer orbit](https://en.wikipedia.org/wiki/Hohmann_transfer_orbit) to move between two approximately circular orbits.\n\nThe forces applied were derived via guess-and-check, as I continue to learn how orbits work.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":239,"value":"viewof current_frame = Scrubber(frames, {\n autoplay: true,\n loop: true,\n format: (d) => d3.format(`,.2f`)(d?.timestamp / 1e3)\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"

\n \n

","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":747,"value":"## Plan","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":415,"value":"viewof plan = Inputs.textarea({\n rows: 6,\n submit: true,\n monospace: true,\n width: 40,\n value: default_plan\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":665,"value":"viewof max_time_seconds = Inputs.range([10, 90], {\n label: `Total Time (seconds)`,\n value: 60,\n step: 1\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":838,"value":"viewof initial_altitude = Inputs.range([1, 7], {\n label: `Initial Altitude`,\n value: 4,\n step: 0.1\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":356,"value":"viewof show_info = Inputs.toggle({ label: `Show Info?`, value: true })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1104,"value":"## Details\n\nA scale factor of ${tex_number(scale_factor)} is applied to masses and forces to produce sensible values on a small scale. The planet's mass is ${tex_number(planet_mass)} and the satellite's mass is ${tex_number(satellite_mass)}\n\nThe satellite produces thrust according to the rows written in `plan`. Each row in the `plan` specifies a `timestamp`, `angle`, and `magnitude` of thrust.\n\nFor example, the plan text: \"`21000 180 10`\" will, after **21** seconds, produce a thrust with an angle of **180** and a magnitude of **10**.\n\nThrust is visualized as a yellow ball of fire emitted from the satellite in the direction of the thrust.\n\nThis simulation uses the [Matter.js physics engine](https://github.com/liabru/matter-js) with a custom gravity attractor applied before each update.\n\nRather than rendering on-demand, frames are pre-computed and stored in an array. This allows for smooth scrubbing.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":251,"value":"## Setup","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":991,"value":"planet_mass = 4e24","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":997,"value":"satellite_mass = 1e4","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"function add_bodies(world) {\n const planet_radius = 50;\n const planet = Matter.Bodies.circle(\n 0.5 * world_size,\n 0.5 * world_size,\n planet_radius,\n {\n label: `planet`,\n plugin: { gravity: true },\n mass: planet_mass * scale_factor,\n friction: 0,\n frictionAir: 0,\n restitution: 0\n }\n );\n Matter.Body.setStatic(planet, true);\n Matter.Composite.add(world, planet);\n const satellite_radius = 5;\n const satellite = Matter.Bodies.circle(\n planet.position.x,\n planet.position.y - planet_radius * initial_altitude,\n satellite_radius,\n {\n label: `satellite`,\n plugin: {\n gravity: true,\n showInfo: true,\n beforeUpdate: () => {\n Matter.Body.setAngularVelocity(satellite, 0);\n }\n },\n mass: satellite_mass * scale_factor,\n friction: 0,\n frictionAir: 0,\n restitution: 0\n }\n );\n Matter.Composite.add(world, satellite);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":432,"value":"## Rendered","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":951,"value":"current_frame","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":644,"value":"plan_parsed = plan\n .split(`\\n`)\n .filter((d) => d.length)\n .map((line) => {\n const [time, angle, magnitude] = line.split(\" \").map((d) => +d);\n return { time, angle, magnitude: +magnitude * scale_factor };\n })\n .filter((d) => d.magnitude > 0)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":437,"value":"frames = create_frames()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":682,"value":"flight_path = path_func(frames.map((d) => d.bodies.satellite.position))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":120,"value":"## Functions","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":945,"value":"function render_bodies(bodies) {\n const rendered = [];\n const render = (body) => {\n const { position, label, plugin, circleRadius } = body;\n // TODO: non-circular bodies, compound bodies...\n // if (parts && parts.length > 1) {\n // const [, ...other_parts] = parts;\n // other_parts.forEach(render);\n // return;\n // }\n // const path_definition = `${path_func(vertices)}z`;\n // if (path_definition.includes(\"NaN\")) return null;\n const style = `\n fill: ${default_fill};\n stroke: ${default_stroke};\n ${plugin?.style ?? ``};\n `;\n const circle = htl.svg`\n \n `;\n rendered.push(circle);\n };\n bodies.forEach(render);\n return rendered;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1114,"value":"function render_info(bodies) {\n return bodies\n .filter((d) => d.plugin?.showInfo)\n .map((body) => {\n const { speed, position } = body;\n return htl.svg`\n \n SPEED: ${d3.format(`.2f`)(speed)}\n `;\n });\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":613,"value":"$32","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":125,"value":"function create_engine() {\n const engine = Matter.Engine.create({ gravity: { y: 0 } });\n\n const world = engine.world;\n\n Matter.Events.on(engine, \"beforeUpdate\", () => {\n const bodies = Matter.Composite.allBodies(world);\n\n d3.pairs(bodies).map(([body_a, body_b]) => {\n // Run beforeUpdate plugin\n if (body_a.plugin.beforeUpdate) {\n body_a.plugin.beforeUpdate();\n }\n gravity_attractor(body_a, body_b);\n });\n });\n\n Matter.Events.on(world, \"afterAdd\", () => {\n world.bodies = d3.sort(world.bodies, (d) => d.plugin?.order ?? 0);\n });\n\n add_bodies(world);\n\n return engine;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1165,"value":"gravitational_constant = 6.67e-11","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":41,"value":"function gravity_attractor(bodyA, bodyB) {\n if (!bodyA.plugin.gravity) return;\n if (!bodyB.plugin.gravity) return;\n const body_a_mass = get_mass(bodyA);\n const body_b_mass = get_mass(bodyB);\n const delta_position = Matter.Vector.sub(bodyB.position, bodyA.position);\n const distance = Matter.Vector.magnitude(delta_position);\n if (distance === 0) return;\n const gravity_constant_scaled = gravitational_constant * scale_factor;\n const magnitude =\n -gravity_constant_scaled * body_a_mass * body_b_mass * distance ** -2;\n const position_normal = Matter.Vector.normalise(delta_position);\n const force = Matter.Vector.mult(position_normal, magnitude);\n Matter.Body.applyForce(bodyA, { x: 0, y: 0 }, Matter.Vector.neg(force));\n Matter.Body.applyForce(bodyB, { x: 0, y: 0 }, force);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":47,"value":"function get_mass(body) {\n const { _original, mass } = body;\n return _original?.mass ?? mass;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":95,"value":"path_func = d3\n .line()\n .x((d) => d.x?.toFixed(2) ?? 0)\n .y((d) => d.y?.toFixed(2) ?? 0)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":881,"value":"function vector_from_angle(angle, magnitude) {\n const radians = angle * Math.PI * 180 ** -1;\n const vector = Matter.Vector.create(magnitude, 0);\n return Matter.Vector.rotate(vector, radians);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1028,"value":"function tex_number(number) {\n const exp = Math.floor(Math.log10(number));\n const base = number / 10 ** exp;\n return tex`${base}^{${exp}}`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":471,"value":"## Config","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":912,"value":"flame_mass = 7e3","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1095,"value":"flame_radius = 5","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":870,"value":"default_plan = `0 0 70\n14000 90 10\n24000 -90 9`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"world_size = 1000","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":771,"value":"scale_factor_exponent = -7","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":223,"value":"scale_factor = 10 ** scale_factor_exponent","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":68,"value":"frames_per_second = 60","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":71,"value":"ms_per_frame = 1000 / frames_per_second","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":101,"value":"default_stroke = `white`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":181,"value":"default_fill = `white`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":234,"value":"## Imports","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":6,"value":"Matter = require(\"matter-js\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":230,"value":"import { Scrubber } from \"@mbostock/scrubber\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W33","stdlib":"1","titling":"auto"}} 31:"$30:body"