How to make the bodyParts to follow same places and directions as the player?

Hello! I try to make a game like the classic snake game but on a round ground (Earth). On a plane, the script works well, but when i moved it on a sphere, the bodyparts (prefabs), are not working good as you can see in the picture ( they are going right/left, but they do not sit on the spehre and i tried already to use sphere collider, box collider, rigidbody) and i dont know really how to make it so that they will follow 100% correctly the player. Thanks for help! :/ . Here i put the script for the Player and bodyparts:

using System.Collections;

using System.Collections.Generic;

using UnityEngine; using UnityEngine.UI;

public class PlayerMovementScript : MonoBehaviour {

 protected Joystick joystick;
 public float speed;
 [SerializeField] private float turnFactor;
 [SerializeField] private Transform planet;

 public List<Transform> bodyParts = new List<Transform>();

 public float minDistance = 0.25f;

 public int beginSize;

 public float rotationSpeed = 50;

 public float timeFromLastRetry;

 public GameObject bodyprefabs;
 public Text currentScore;
 public Text scoreText;

 public GameObject deadScreen;

 private float dis;
 private Transform curBodyPart;
 private Transform PrevBodyPart;

 public bool isAlive;

  void Start()
 {
     joystick = FindObjectOfType<Joystick>();
     speed = 3f;
     StartLevel();
 }

 public void StartLevel()
 {
     timeFromLastRetry = Time.deltaTime;
     //deadScreen.SetActive(false);

     for (int i = bodyParts.Count -1; i > beginSize; i++)
     {
         Destroy(bodyParts[i].gameObject);

         bodyParts.Remove(bodyParts[i]);
     }

     bodyParts[0].position = new Vector3(0, 0.5f, 0);

     for (int i = 0; i < beginSize - 1; i++)
     {
         AddBodyPart();
     }

     bodyParts[0].position = new Vector3(0, 0.5f, 0);

     bodyParts[0].rotation = Quaternion.identity;

     currentScore.gameObject.SetActive(true);
     currentScore.text = "Score: 0";

     isAlive = true;
 }

 void Update()
 {
     if (isAlive)
           Move();

     if (Input.GetKey(KeyCode.Q))
         AddBodyPart();
     //RotateAroundPlanet();
     var rb = GetComponent<Rigidbody>();

     //rb.velocity = new Vector3(joystick.Horizontal * 100f, rb.velocity.y, joystick.Vertical * 100f);
 }

 public void Move()
 {

     float curspeed = speed;

     //if (Input.GetKey(KeyCode.W))
     //    curspeed *= 2;

     bodyParts[0].Translate(bodyParts[0].forward * curspeed * Time.smoothDeltaTime, Space.World);


     if (Input.GetAxis("Horizontal") != 0)
         bodyParts[0].Rotate(Vector3.up * rotationSpeed * Time.deltaTime * Input.GetAxis("Horizontal"));

     for (int i = 1; i < bodyParts.Count; i++)
     {

         curBodyPart = bodyParts[i];
         PrevBodyPart = bodyParts[i - 1];

         dis = Vector3.Distance(PrevBodyPart.position, curBodyPart.position);

         Vector3 newpos = PrevBodyPart.position;

         newpos.y = bodyParts[0].position.y;

         float T = Time.deltaTime * dis / minDistance * curspeed;

         if (T > 0.5f)
             T = 0.5f;
         curBodyPart.position = Vector3.Slerp(curBodyPart.position, newpos, T);
         curBodyPart.rotation = Quaternion.Slerp(curBodyPart.rotation, PrevBodyPart.rotation, T);



     }
 }
 public void AddBodyPart()
 {

     Transform newpart = (Instantiate(bodyprefabs, bodyParts[bodyParts.Count - 1].position, bodyParts[bodyParts.Count - 1].rotation) as GameObject).transform;

     newpart.SetParent(transform);

     bodyParts.Add(newpart);

     currentScore.text = "Score: " + (bodyParts.Count - beginSize).ToString();
 }

 public void Die()
 {
     isAlive = false;

     scoreText.text = "Your score was: " + (bodyParts.Count - beginSize).ToString();

     currentScore.gameObject.SetActive(false);

     deadScreen.SetActive(true);
 }