Initial commit: planetarium

This commit is contained in:
Paul Mathieu 2024-08-15 17:25:56 +02:00
commit ad3925d108
2 changed files with 647 additions and 0 deletions

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planets.ipynb Normal file
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{
"cells": [
{
"cell_type": "code",
"execution_count": 34,
"id": "afcfc049",
"metadata": {},
"outputs": [],
"source": [
"import re\n",
"\n",
"orbits = \"\"\"\n",
"Mercury: 88 days.\n",
"Venus: 225 days.\n",
"Earth: 365 days.\n",
"Mars: 687 days.\n",
"Jupiter: 4333 days.\n",
"Saturn: 10759 days.\n",
"Uranus: 30687 days.\n",
"Neptune: 60190 days.\n",
"\"\"\".splitlines()"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "c0665887",
"metadata": {},
"outputs": [],
"source": [
"ratios = [int((re.findall(r'\\d+', x)[0:1] or [0])[0])/88 for x in orbits][1:]"
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "56eb1e3f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[1.0,\n",
" 6.307132459970888,\n",
" 15.660844250363901,\n",
" 44.66812227074236,\n",
" 87.61280931586609]"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"[x / ratios[3] for x in ratios[3:]]"
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "8401b303",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[1.0,\n",
" 1.5990053726670783,\n",
" 2.036596983383623,\n",
" 2.794068392473273,\n",
" 7.017024751533684,\n",
" 11.0571860632063,\n",
" 18.67393662543892,\n",
" 26.152959158138735]"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import math\n",
"[math.sqrt(x) for x in ratios]"
]
},
{
"cell_type": "code",
"execution_count": 42,
"id": "85f986fc",
"metadata": {},
"outputs": [],
"source": [
"dist = \"\"\"The distance from the Sun to Mercury is 0.39 AU, to Venus is 0.72 AU, to Earth is 1.00 AU, to Mars is 1.52 AU, to Jupiter is 5.20 AU, to Saturn is 9.54 AU, to Uranus is 19.22 AU, and to Neptune is 30.06 AU.\"\"\""
]
},
{
"cell_type": "code",
"execution_count": 56,
"id": "7c321d05",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[5.875871902123325,\n",
" 15.072438995419457,\n",
" 20.0,\n",
" 26.280655022872775,\n",
" 44.729879383810726,\n",
" 53.83240228190293,\n",
" 64.3392710531322,\n",
" 71.04793076487243]"
]
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"[20 + 1.5 * math.log(float(x))*10 for x in re.findall(r'[0-9]+.\\d+', dist)]"
]
},
{
"cell_type": "code",
"execution_count": 60,
"id": "36ce6b46",
"metadata": {},
"outputs": [],
"source": [
"planets = [\n",
" ('mercury', 1.0, 50),\n",
" ('venus', 1.6, 130),\n",
" ('earth', 2.0, 200),\n",
" ('mars', 2.8, 270),\n",
" ('jupiter', 7.0, 450),\n",
" ('saturn', 11, 540),\n",
" ('uranus', 18, 640),\n",
" ('neptune', 26, 710),\n",
"]"
]
},
{
"cell_type": "code",
"execution_count": 64,
"id": "6a36fcb8",
"metadata": {},
"outputs": [],
"source": [
"def b():\n",
" prevp = 1.0\n",
" for n, p, d in planets:\n",
" yield p / prevp\n",
" prevp = p\n",
" \n",
"ratios = list(b())"
]
},
{
"cell_type": "code",
"execution_count": 89,
"id": "5f6e6b6b",
"metadata": {},
"outputs": [],
"source": [
"scale = 5\n",
"\n",
"tooth_width = 0.8;\n",
"tooth_crop = 0.5;\n",
"tooth_thickness = 0.6;\n",
"\n",
"def gear_base_radius(n):\n",
" perimeter = tooth_width * (1 + 0.8*(1-tooth_crop)) * n\n",
" return perimeter / math.pi / 2;\n",
"\n",
"def gear_wheel_radius(n):\n",
" return math.sqrt(gear_base_radius(n)**2 + (tooth_width/2)**2);\n",
"\n",
"def gear_radius(n):\n",
" return scale * (gear_wheel_radius(n) + gear_base_radius(n) + tooth_crop)/2;\n",
"\n",
"def dcenter(n1, n2):\n",
" return gear_radius(n1) + gear_radius(n2)\n",
"\n",
"def search():\n",
" for n1 in range(11, 39):\n",
" n2 = 50 - n1\n",
" yield (n1, n2, n2 / n1, dcenter(n1, n2))\n",
" \n",
"rr = list(search())"
]
},
{
"cell_type": "code",
"execution_count": 92,
"id": "b64daa46",
"metadata": {},
"outputs": [],
"source": [
"def found():\n",
" for r in ratios:\n",
" for n1, n2, tr, _ in rr:\n",
" if tr < r:\n",
" yield (n1, n2, r, tr)\n",
" break"
]
},
{
"cell_type": "code",
"execution_count": 93,
"id": "c587ff67",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[(26, 24, 1.0, 0.9230769230769231),\n",
" (20, 30, 1.6, 1.5),\n",
" (23, 27, 1.25, 1.173913043478261),\n",
" (21, 29, 1.4, 1.380952380952381),\n",
" (15, 35, 2.5, 2.3333333333333335),\n",
" (20, 30, 1.5714285714285714, 1.5),\n",
" (19, 31, 1.6363636363636365, 1.631578947368421),\n",
" (21, 29, 1.4444444444444444, 1.380952380952381)]"
]
},
"execution_count": 93,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"list(found())"
]
},
{
"cell_type": "code",
"execution_count": 81,
"id": "2d7d6f8b",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[(11, 39, 3.5454545454545454, 47.19308954151068),\n",
" (12, 38, 3.1666666666666665, 47.18558098978421),\n",
" (13, 37, 2.8461538461538463, 47.179354476011646),\n",
" (14, 36, 2.5714285714285716, 47.17415487784531),\n",
" (15, 35, 2.3333333333333335, 47.16979419516311),\n",
" (16, 34, 2.125, 47.166131477877656),\n",
" (17, 33, 1.9411764705882353, 47.16305960247725),\n",
" (18, 32, 1.7777777777777777, 47.16049634511566),\n",
" (19, 31, 1.631578947368421, 47.158378230688704),\n",
" (20, 30, 1.5, 47.15665622507779),\n",
" (21, 29, 1.380952380952381, 47.15529268372393),\n",
" (22, 28, 1.2727272727272727, 47.154259179645024),\n",
" (23, 27, 1.173913043478261, 47.15353496521375),\n",
" (24, 26, 1.0833333333333333, 47.15310590655676),\n",
" (25, 25, 1.0, 47.15296378588499),\n",
" (26, 24, 0.9230769230769231, 47.15310590655676),\n",
" (27, 23, 0.8518518518518519, 47.15353496521375),\n",
" (28, 22, 0.7857142857142857, 47.154259179645024),\n",
" (29, 21, 0.7241379310344828, 47.15529268372393),\n",
" (30, 20, 0.6666666666666666, 47.15665622507779),\n",
" (31, 19, 0.6129032258064516, 47.158378230688704),\n",
" (32, 18, 0.5625, 47.16049634511566),\n",
" (33, 17, 0.5151515151515151, 47.16305960247725),\n",
" (34, 16, 0.47058823529411764, 47.166131477877656),\n",
" (35, 15, 0.42857142857142855, 47.16979419516311),\n",
" (36, 14, 0.3888888888888889, 47.17415487784531),\n",
" (37, 13, 0.35135135135135137, 47.179354476011646),\n",
" (38, 12, 0.3157894736842105, 47.18558098978421)]"
]
},
"execution_count": 81,
"metadata": {},
"output_type": "execute_result"
}
],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "8c2dca2a",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
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"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
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},
"nbformat": 4,
"nbformat_minor": 5
}

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tooth_width = 0.8;
tooth_crop = 0.5;
tooth_thickness = 1.0;
module tooth() {
width = tooth_width;
thickness = tooth_thickness;
crop = tooth_crop;
points = [[0, width/2], [0, -width/2], [1, 0]];
intersection() {
// rotate([90, 0, 0])
linear_extrude(height=thickness, center=true)
polygon(points);
cube([crop*2, width, thickness], center=true);
}
}
function gear_base_radius(n) =
let (perimeter = tooth_width * (1 + 0.8*(1-tooth_crop)) * n)
perimeter / PI / 2;
function gear_wheel_radius(n) =
sqrt(gear_base_radius(n)^2 + (tooth_width/2)^2);
function gear_radius(n) =
(gear_wheel_radius(n)
+ gear_base_radius(n) + tooth_crop)/2;
module gear(n) {
radius = gear_base_radius(n);
wheel_radius = gear_wheel_radius(n);
thickness = tooth_thickness;
// rotate([90, 0, 0])
linear_extrude(height=thickness, center=true)
circle(wheel_radius, $fn=50);
for (i=[0:n-1]) {
angle=360 / n;
rotate([0, 0, i * angle])
translate([radius, 0, 0])
tooth();
}
}
gear_scale = 5;
module final_gear(n) {
scale([gear_scale, gear_scale, gear_scale])
gear(n);
}
module orbit_ring(n1, n2) {
difference() {
union() {
cylinder(h=24, r=20, center=true);
translate([22, 0, 0])
rotate([0, 90, 0])
cylinder(h=10, r=5, center=true);
translate([0, 0, 12])
final_gear(n=n1);
translate([0, 0, -12])
final_gear(n=n2);
}
cylinder(h=100, r=14.7, center=true);
}
}
module orbit(length, orbit_order, n1, n2=25, planet_size=40) {
// orbit_length = 100;
// orbit_order = 20;
orbit_length = length + 50;
thickness = 2.0;
rotate([0, 90, 0])
translate([0, 0, orbit_length/2])
cylinder(h=orbit_length, r=thickness/2, center=true, $fn=50);
translate([orbit_length, 0, 0])
translate([0, 0, orbit_order/2])
cylinder(h=orbit_order, r=thickness/2, center=true, $fn=50);
translate([orbit_length, 0, orbit_order+planet_size/2])
sphere(planet_size/2);
orbit_ring(n1, n2);
}
module _sidegear_diff(r) {
difference() {
cylinder(h=200, r=r, center=true);
translate([-2.5, 0, -110])
cube([5, 300, 300]);
rotate([0, 0, 120])
translate([-2.5, 0, -110])
cube([5, 300, 300]);
rotate([0, 0, 240])
translate([-2.5, 0, -110])
cube([5, 300, 300]);
cylinder(h=210, r=8, center=true);
}
cube([4, 4, 25], center=true);
}
module sidegear(n) {
difference() {
final_gear(n);
_sidegear_diff(n*0.75);
}
}
module flangebrace() {
translate([0, -30, 0])
cube([14.7, 5, 23], center=true);
difference() {
union() {
translate([0, -12, 10])
cube([14.7, 39, 3], center=true);
translate([0, -12, -10])
cube([14.7, 39, 3], center=true);
}
cylinder(h=50, r=4, center=true);
}
}
module flange(offset) {
difference() {
cylinder(h=5, r=22, center=true);
cylinder(h=10, r=14.4, center=true);
}
difference() {
translate([offset, 0, 0])
cylinder(h=5, r=32, center=true);
translate([offset, -32, 0])
cube([15, 10, 15], center=true);
translate([offset, 0, 0])
_sidegear_diff(25);
translate([offset, 0, 0])
cylinder(h=6, d=6.3, center=true);
}
}
module shaftend() {
difference() {
cylinder(h=3, r=3.9, center=true);
cube([4, 4, 5], center=true);
}
}
module linkage(offset, n1=25, n2) {
color("pink")
translate([offset, 0, 0]) {
cube([4, 4, 25], center=true);
translate([0, 0, 10])
shaftend();
translate([0, 0, -10])
shaftend();
translate([0, 0, 5])
sidegear(n=n1);
translate([0, 0, -5])
sidegear(n=n2);
}
color("white")
flange(offset);
translate([offset, 0, 0])
flangebrace();
}
module sungear(n) {
difference() {
//orbit_ring(n1=25, n2=25);
final_gear(n);
cylinder(h=200, r=14.7, center=true);
}
}
module sunshaft() {
translate([0, 0, -180])
cylinder(h=400, r=15, center=true);
translate([0, 0, -380])
cylinder(h=20, r=150, center=true);
translate([0, 0, 45])
sphere(d=66);
}
/*
inner gears:
-----
25: 9
30: 2
27: 1
29: 2
35: 1
31: 1
-----
16
side gears:
-----
25: 7
20: 2
23: 1
19: 1
21: 2
15: 1
-----
14
*/
sh = 29;
fh = 5;
function sleevez(i) = -i * (sh + fh) - sh/2;
function flangez(i) = sleevez(i) - 17;
function orbitz(i) = 20 - sleevez(i);
gear_offset = 48;
orbit_ring(35, 25);
//color("white") sunshaft();
/*
// mercury
color("grey")
translate([0, 0, sleevez(0)])
orbit(50, orbitz(0), n1=25);
translate([0, 0, flangez(0)])
linkage(offset=gear_offset, n2=20);
/*
// venus
color("yellow")
translate([0, 0, sleevez(1)])
orbit(130, orbitz(1), n1=30);
translate([0, 0, flangez(1)])
linkage(offset=gear_offset, n2=23);
// earth
color("#34a56f")
translate([0, 0, sleevez(2)])
orbit(200, orbitz(2), n1=27);
translate([0, 0, flangez(2)])
linkage(offset=gear_offset, n2=21);
// mars
color("red")
translate([0, 0, sleevez(3)])
orbit(270, orbitz(3), n1=29);
translate([0, 0, flangez(3)])
linkage(offset=50, n2=15);
// jupiter
color("orange")
translate([0, 0, sleevez(4)])
orbit(450, orbitz(4), n1=35);
translate([0, 0, flangez(4)])
linkage(offset=50, n2=20);
// saturn
color("purple")
translate([0, 0, sleevez(5)])
orbit(540, orbitz(5), n1=30);
translate([0, 0, flangez(5)])
linkage(offset=50, n2=19);
// uranus
color("#aaaaff")
translate([0, 0, sleevez(6)])
orbit(640, orbitz(6), n1=31);
translate([0, 0, flangez(6)])
linkage(offset=50, n2=21);
// neptune
color("#3333aa")
translate([0, 0, sleevez(7)])
orbit(710, orbitz(7), n1=29);
/*
*/
/*
gear0 = 7;
gear1 = 7;
spacing = 1.0;
rotate([0, 0, $t*360])
final_gear(gear0);
translate([spacing + (gear_radius(gear0) + gear_radius(gear1)) * gear_scale, 0, 0])
rotate([0, 0, -$t*360 * gear0 / gear1])
final_gear(gear1);
*/