This javascript appeared on Googles website on February 19, 2013. I wondered, whether the google doodle actually integrates the n body problem as here. The crucial javascript code is below. The part this.W=1/Math.sqrt(Math.pow(this.G,3)) looks like a potential. The code is difficult to read. but it seems that the doodle just animates the world picture at the time of Copernicus without going into any fancy n body dynamics.
The crucial math part of the Javascript is here:
var $a,ab,bb,
    X=function(a,b,c,d){
           this.wa=a;this.O=b;
           this.P="array"==u(b);
           this.G=c;this.va=2*W.getWidth(a);
           this.aa=2*W.getHeight(a);this.V=d||0;
           this.W=1/Math.sqrt(Math.pow(this.G,3))
    },
    W=new V("sprite.png",[
         [85,30,28,28],
         [40,61,42,42],
         [0,0,52,53],
         [55,0,26,26],
         [85,61,36,36],
         [0,61,37,37],
         [84,0,36,27],
         [55,30,27,27]
      ],{ma:0,oa:1,T:2,U:3,qa:4,ra:5,ta:6,ua:7}),
    cb=Math.acos(231/524),
    db=Math.sin(cb),
    eb=Math.cos(cb),
    fb=function(a,b){var c=a.P?a.O:fb(a.O,b);if(0==a.G)return c;
var d=b*a.W+a.V,
    e=a.G*Math.sin(d)+c[0],
    f=a.G*Math.cos(d),
    d=eb*f+c[1],
    c=a.P?db*f:c[2]+(0>f?-1:1);a.P||(d-=a.O.aa/3);return[e,d,c]},
    gb=function(a){var b=fb(a,Y);return{D:a.wa,x:b[0]-a.va/2,y:b[1]-a.aa,ba:b[2]}};
var Z=m,Y=0,hb=0,$=p,
    jb=function(){var a=T(),b=Math.min(a-hb,84);Y+=0.1*b;hb=a;ib();($a=!$)&&Ta(jb)},
    ib=function(){
      Z.clearRect(0,0,1008,458);
      for(var a=W.S,b=[],c=0,d=m,e=0,f;f=bb[e];e++){
        var g=gb(f);b.push(g);g.D==a.U&&(c=Math.cos(Y*f.W+f.V),d=g)
      }
      b.sort(function(a,b){return a.ba-b.ba});
      for(e=0;g=b[e];e++)
        W.J(g.D,Z,g.x,g.y,2),g.D==a.T&&(
             f=Math.min(1,Math.max(0,2*(c+0.5))),1 ≥ f && 0 ≤ f &&
             (Z.globalAlpha=f,W.J(d.D,Z,d.x,d.y,2),Z.globalAlpha=1))
    };
    (function(a,b,c){var d=function(){Xa(a,b,c);Wa(a,b);a()},e=window.google;e&&e.x?e.x({id:"DOODLE"},d):d()})
    (function(){
       var a=document.getElementById("hplogo");if(a){
       var b=document.createElement("canvas");
         if(b&&(Oa(b,"height","229px","left","0","position","absolute","top","-10px","width","504px"),
            b.setAttribute("height",458),
            b.setAttribute("width",1008),
            a.innerHTML="",
            a.appendChild(b),
            a.onclick=Ra,google.doodle&&google.doodle.url&&Oa(b,"cursor","pointer"),
            Z=b.getContext("2d"))){
              var b=W.S,c=[504,239, 0],
                 d=new X(b.T,c,184,2.88);
                 bb=[new X(b.ua,c,64,0.39),
                     new X(b.qa,c,88,-1.73),
                     new X(b.ra,c,272,-0.3),
                     new X(b.oa,c,320,1.86),
                     new X(b.ma,c,382,-0.89),
                     new X(b.U,d,72,-1.585),
                     new X(b.ta,[500,251,0],0),d];
                 Y=0;hb=T();$=p;$a=k;
              var e=new Ya("background.jpg");
              e.s();
              W.s(function(){Za(e,function(){a.style.background="url("+e.h.src+")";jb()})});
            ab=new U(864E5,function(){$=k},function(){$=p;$a||jb()})
           }
      }
  },
  function(){$=k;ab&&ab.H()});
})();