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Published
Edited
Dec 10, 2018
// Create a Clifford Algebra with 3,0,1 metric.
Algebra({p:3,q:0,r:1,baseType:Float64Array},()=>{
// Basic GA points and vectors. (in KM)
var point = (x,y,z)=>1e123-x*1000e012+y*1000e013+z*1000e023,
vector = (x,y,z)=>-x*1000e012+y*1000e013+z*1000e023;
// Data from https://ssd.jpl.nasa.gov/horizons.cgi on 16/01/2018, mass, x,y,z, vx,vy,vz - units KM/S
var S = {
Sun : [1.988544E30,
point( 2.564294388666002E+05, 9.282480498916068E+05,-1.766238790604926E+04),
vector(-1.032271613682197E-02, 8.506510987745193E-03, 2.500579386306204E-04)],
Mercury : [3.302E23 ,
point(-4.261433008703040E+07,-5.180047961851221E+07,-3.933312499175891E+05),
vector( 2.791200817718316E+01,-2.845907905315504E+01,-4.887507665269149E+00)],
Venus : [48.685E23 ,
point( 5.357396412032661E+07,-9.395832506522638E+07,-4.396021713049673E+06),
vector( 3.028389624261208E+01, 1.704407507992616E+01,-1.514240016876114E+00)],
Earth : [5.97219E24 ,
point(-6.321181522689363E+07, 1.337035149539065E+08,-2.323422257646173E+04),
vector(-2.738214042693713E+01,-1.295254402346621E+01, 1.833826936016081E-03)],
Mars : [6.4185E23 ,
point(-2.261872038770745E+08,-8.456074820817514E+07, 3.748261255788427E+06),
vector( 9.452949401620625E+00,-2.058946931255050E+01,-6.636171336482146E-01)],
Jupiter : [1898.13E24 ,
point(-6.267852905434124E+08,-5.152098357372769E+08, 1.615654184230065E+07),
vector( 8.141900694513106E+00,-9.472185978646950E+00,-1.428289208967608E-01)],
},
G = 6.6723E-11, start = 1516057200000, count=0, scale=.2E-14,
names = Object.keys(S), mass = names.map(x=>S[x][0]),
state = [].concat.apply([],names.map(x=>S[x].slice(1)));
// RK4 integrator. f = derivative function, y = state vector, h = step
// Thanks to ganja.js operator overloading, you can call the code below with scalars, multivectors and arrays.
var RK4 = (f,y,h)=>{
var k1=f(y),
k2=f(y+0.5*h*k1),
k3=f(y+0.5*h*k2),
k4=f(y+h*k3);
return y+(h/3)*(k2+k3+(k1+k4)*0.5);
};
// Acceleration of p1,m1 due to gravity between p1,m1 and p2,m2
var A=(p1,p2,m1,m2)=>{ var v=p2-p1, d=v.VLength; return G*m1*m2/(d*d*m1)*v/d; }
// Derivative function .. returns x' given x
// State contains positions and velocities for each of the planets.
var dFunc = (s)=>s.map((si,i)=>
// the new velocity is the old acceleration.
((i%2==0)?s[i+1]
// the new acceleration is calculated by accumulating attraction from all planets.
:(mass.reduce((F,x,j)=>((i-1)/2==j)?F:F+A(s[i-1],s[j*2],mass[(i-1)/2],x),0)))
);
// Graph the 3D items
return(this.graph(()=>{
state = RK4(dFunc,state,14400);
return [].concat.apply(
// display the current time.
[(new Date(start+(count++)*14400000)).toDateString().replace((/.*? /),'')],
// display points and titles for all the planets
names.map((x,xi)=>[point(state[xi*2].e012*scale,state[xi*2].e013*scale,state[xi*2].e023*scale),0x888888,x,0])
)
},{animate:true}));
})
Algebra = require('ganja.js')
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