Three Body Problem

The Three Body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation.
For the problem, No general closed-form solution exists, as the resulting dynamical system is chaotic for most initial conditions, and numerical methods are generally required.

Code

            

    elem = document.getElementsByClassName("example-container")[0];
    setCanvas(elem);

    w=WIDTH;
    h=HEIGHT;

    
    G=10**1;
    m1=20;
    m2=20;
    m3=20;

    x1=w/2-100;
    y1=150;

    x2=w/2+100;
    y2=150;

    x3=w/2;
    y3=273.2+50;

    v=1;
    vm1={
        x: -v/2,
        y: v*Math.sqrt(3)/2
    };
    vm2={
        x: -v/2,
        y: -v*Math.sqrt(3)/2
    };
    vm3={
        x: v,
        y: 0
    };

    t=0;
    points1=[];
    points2=[];
    points3=[];

    function draw() {
    
        clearCanvas();
        
        new circle(x1,y1,10,'#17D690');
        new circle(x2,y2,10,'#4DE3FF');
        new circle(x3,y3,10,'#FF57B5');
        points1.push([x1,y1]);
        points2.push([x2,y2]);
        points3.push([x3,y3]);

        if(points1.length>200){
            points1.shift();}
            if(points2.length>200){
            points2.shift();}
            if(points3.length>200){
            points3.shift();}


        new polygon(points1,'#17D690',0,'#17D690',2,false);
        new polygon(points2,'#4DE3FF',0,'#4DE3FF',2,false);
        new polygon(points3,'#FF57B5',0,'#FF57B5',2,false);
        

        Fm1m2=Fbetween(x1,y1,x2,y2,m1,m2);
        Fm2m3=Fbetween(x2,y2,x3,y3,m2,m3);
        Fm1m3=Fbetween(x1,y1,x3,y3,m1,m3);

        Fon1={x:Fm1m2.x+Fm1m3.x,y:Fm1m2.y+Fm1m3.y};
        Fon2={x:Fm2m3.x-Fm1m2.x,y:Fm2m3.y-Fm1m2.y};
        Fon3={x:-Fm1m3.x-Fm2m3.x,y:-Fm1m3.y-Fm2m3.y};

        am1={x:Fon1.x/m1,y:Fon1.y/m1};
        am2={x:Fon2.x/m2,y:Fon2.y/m2};
        am3={x:Fon3.x/m3,y:Fon3.y/m3};

        vm1.x+=am1.x;
        vm1.y+=am1.y;
        vm2.x+=am2.x;
        vm2.y+=am2.y;
        vm3.x+=am3.x;
        vm3.y+=am3.y;
        
        x1+=vm1.x;
        y1+=vm1.y;
        x2+=vm2.x;
        y2+=vm2.y;
        x3+=vm3.x;
        y3+=vm3.y;

        requestAnimationFrame(draw);
    
    }

    function Fbetween(x1,y1,x2,y2,m1,m2) {
        r=Math.sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));
        F={
            x:((G*m1*m2)/(r*r*r))*(x2-x1),
            y:((G*m1*m2)/(r*r*r))*(y2-y1)
        }
        return F;
    }
    ///////////////////////////////////////////////////////////////////////////////


    draw();