Selected Mathematical Actionscript functions used:

function beta( P, A, epsilon ) {
    A*= scalefactor;
    gbeta1 = 2*Math.PI*t/P;
    gbetaV = gbeta1;
    while (Math.abs(gbetaV - (gbeta1 + epsilon*Math.sin(gbetaV)))>=.0000001) {
       gbetaV = gbeta1 + epsilon*Math.sin(gbetaV);
    }
    r = (A*(1 - epsilon*Math.cos(gbetaV)));
    alpha = 2*Math.atan(Math.sqrt((1+epsilon)/(1-epsilon))*Math.tan(gbetaV/2));
}

function coord() {
    if (alpha <= Math.PI/2 && alpha > 0) {
       dY= - Math.sin(alpha)*r;
       dX= Math.sqrt((r*r)-(dY*dY));
    } else if (alpha > Math.PI/2 && alpha <= Math.PI) {
       dY= - Math.sin(Math.PI - alpha)*r;
       dX= -Math.sqrt((r*r)-(dY*dY));
    } else if (- alpha > Math.PI/2 && - alpha <= Math.PI) {
       dY= Math.sin(Math.PI + alpha)*r;
       dX= - Math.sqrt((r*r)-(dY*dY));
    } else if (- alpha <= Math.PI/2 && - alpha > 0) {
       dY= Math.sin(- alpha)*r;
       dX= Math.sqrt((r*r)-(dY*dY));
    }
}

function setup_planets() {
    solar_system = new Array();
    planets = new Array();
    trails = new Array();
    with(planets) {
       push(mercury=new planet( "Mercury", .3871, .3871, .2056, mercury_graphic, 0xE8BE86 )); //color
       push(venus=new planet( "Venus", .7233, .7233, .0068, venus_graphic, 0xE2592C )); //color
       push(earth=new planet( "Earth", 1, 1, .0167, earth_graphic, 0x00CCFF )); //color
       push(mars=new planet( "Mars", 1.5327, 1.5237, .0934, mars_graphic, 0xFF0000 )); //color
       push(jupiter=new planet( "Jupiter", 5.2028, 5.2028, .0484, jupiter_graphic, 0xE8BE86 ));
       push(saturn=new planet( "Saturn", 9.5039, 9.5039, .0557, saturn_graphic, 0xFF8000 ));
       push(uranus=new planet( "Uranus", 19.182, 19.182, .047, uranus_graphic, 0xFFFFFF ));
       push(neptune=new planet( "Neptune", 30.058, 30.058, .009, neptune_graphic, 0x6294E3 ));
       push(pluto=new planet( "Pluto", 39.44, 39.44, .25, pluto_graphic, 0x33FF99 ));
       push(user=new planet("", .3531, 35.71, .8, userplanet_graphic, 0xFFFF00 ));
    }
    reset_planets(0, planets.length-1);
}