Trying to get missile to home in on player position instead of one fixed position

So right now my missile is homing and tracking just one position but I need it to track the player in real time instead it seems like the missile is only tracking the players starting position.

Here's my code so far:

 public Transform target;
 public float speed;

 void Update()
 {
     Vector3 targetDir = target.position - transform.position;
     float step = speed * Time.deltaTime;
     Vector3 newDir = Vector3.RotateTowards(transform.forward, targetDir, step, 0.0f);
     Debug.DrawRay(transform.position, newDir, Color.red);
     transform.rotation = Quaternion.LookRotation(newDir);
     transform.position = Vector3.MoveTowards(transform.position, target.position, step);
 }

Any help would be greatly appreciated.