Move object around sphere

Hey there I want to achieve something like this:

A character which moves around a sphere. I found quite a lot of Super Mario Galaxy examples which also work fine in my game, however al of them use the unity physics. I would like to achieve this without the need of physics or raycasts etc.

Does anyone know how to calculate something like this ?

Well, I need raycasts to get the normal of the face the character is above. Other than that, it’s just a matter of rotating the character so he is perpendicular to the normal, and set his transform.position to the hit.point of the raycast.

The following was originally for a vehicle script so feel free to play with the mechanics, especially what happens if the character is grounded or not.

private Quaternion rotCur;
private Vector3 posCur;
public bool grounded = true;
public LayerMask terrainLayer;//include the ground layer here and anything else that should act as ground

void Update() {
     if(Physics.Raycast(ray, out hit, 1.5f, terrainLayer) == true) {
			
          Debug.DrawLine(transform.position + transform.up * 1f, hit.point, Color.green);

	  rotCur = Quaternion.FromToRotation(transform.up, hit.normal) * transform.rotation;
	  posCur = new Vector3(transform.position.x, hit.point.y, transform.position.z);
          grounded  = true;
            
     }

     if(grounded == true) {
          //Lerp for smooth transition. transform.rotation and position could be set directly as well 
          transform.position = Vector3.Lerp(transform.position, posCur, Time.deltaTime * 5);
	  transform.rotation = Quaternion.Lerp(transform.rotation, rotCur, Time.deltaTime * 5);
     }
     else {
          rotCur.eulerAngles = Vector3.zero;
	  transform.rotation = Quaternion.Lerp(transform.rotation, rotCur, Time.deltaTime);
     }
}