Make a "heat-seeking" missile work

1

i already know how to create a simple turret / cannon type game wherein the turret will fix its rotation based on where the users mouse is… from there, the user can fire bullets which fly into the direction where the turret was pointed at when it was fired…

however, i want to take it a step further and make the turret fire bullets that can follow the mouse as i move it on stage (sort of like a “heat-seeking” missile) … once i stop moving the mouse around the stage and the bullet catches up / arrives at the mouseX and mouseY, it will remove itself…

below is the code i used for the simple turret / cannon type game…
i was wondering what i should add / modify in the code to make the “heat-seeking” work…

for the main timeline:

stage.addEventListener(Event.ENTER_FRAME, frameEntered);
stage.addEventListener(MouseEvent.MOUSE_DOWN, mouseIsDown);

var radians:Number;
var degrees:Number;

function frameEntered(event:Event):void
{
    radians = Math.atan2(mouseY - turret.y, mouseX - turret.x);
    degrees = radians * 180 / Math.PI;
    turret.rotation = degrees;
}

function mouseIsDown(event:MouseEvent):void
{
    var newBullet:MovieClip = new Bullet();
    newBullet.x = Math.cos(radians) * 43 + turret.x;
    newBullet.y = Math.sin(radians) * 43 + turret.y;
    newBullet.rotation = turret.rotation;
    addChild(newBullet);
}

for the Bullet class:

package
{
    import flash.display.*;
    import flash.events.*;
    
    public class Bullet extends MovieClip
    {
        var xSpeed:Number;
        var ySpeed:Number;
        var bulletAngle:Number;
        var bulletSpeed:Number;
        
        public function Bullet()
        {
            this.addEventListener(Event.ADDED, runInit);
        }
        
        function runInit(event:Event):void
        {
            bulletSpeed = 10;
            bulletAngle = MovieClip(root).degrees * Math.PI / 180;
            xSpeed = Math.cos(bulletAngle) * bulletSpeed;
            ySpeed = Math.sin(bulletAngle) * bulletSpeed;
            
            this.addEventListener(Event.ENTER_FRAME, runEnterFrame);
        }
        
        function runEnterFrame(event:Event):void
        {
            this.x += xSpeed;
            this.y += ySpeed;
        }
    }
}