HOW TO ADD GRAVITY TO A OBJECT?

Implement Newton's law of universal gravitation. Wikipedia has a lot of jargon, You can probably find a simpler explanation somewhere else:

Force (F) of gravitational attraction between two objects with Mass1 and Mass2 at distance D is:

  F = G(mass1*mass2)/D squared.

  (G is the gravitational constant, which has the same value throughout our universe.) 

So basically, create a script for your objects that have a Mass and a Velocity. And have another script that will use the formula to calculate the relative forces, you just then update the object's velocity based on the calculated force and direction.

Edit ---

If you're looking for a simpler solution, just for the example that you've provvided. You can probably just have 1 object move towards a point and if the objects get too close, then you change the target that the object moves towards. Psuedo example:

  if (Vector3.Distance(star.transform.position, planet.transform.position) < 1f)
  {
       // objects are within proximity
       targetPosition = star.transform.position; // set targetPosition to the star
  }
  else
  {
       // objects are not close enough to each other
       targetPosition = someOtherPosition; // set targetPosition to some reference
  }
 
  planet.transform.position = Vector3.MoveTowards(planet.transform.position, targetPosition);
         
     

well, this kinda works, maybe you can tweak it. (its for 3d sorry but the principle is the same)

 using UnityEngine;
 using System.Collections;
 
 public class gravityTest : MonoBehaviour {
 
     // Use this for initialization
     public float influence;
     public float mass;
     public bool isPlayable = false;
     float speed = 1; //not sure how you will find this out, it may be easier in 2d?
     Rigidbody body;
 
     void Start () {
         body = gameObject.GetComponent<Rigidbody> ();
     }
     
     // Update is called once per frame
     void Update () {
         if (isPlayable) { //this is for testing purposes however you control the object is up to you.
             if (Input.GetKeyDown (KeyCode.A)) {
                 body.AddForce (new Vector3 (0, 10f, 0));
             }
         }
 
         Collider[] hitColliders = Physics.OverlapSphere(transform.position, influence);
         int i = 0;
         while (i < hitColliders.Length) {
             Debug.Log(hitColliders[i].name);
             if(hitColliders[i].tag == "planet")
             {
                 gravityTest test;
                 test = hitColliders[i].gameObject.GetComponent<gravityTest>();
                 if(test.mass > mass)
                 {
                     body.AddForce((hitColliders[i].transform.position - transform.position) * speed * Time.smoothDeltaTime);
                 }
             }
             i++;
         }
     
     }
 }

this simply attracts an object to another, the one with the smaller mass being attracted to the larger one, you have to tag the objects "planet". see how you get on with it :)