flying around 3D obj

Question

I'm making a game space simulator. My spacesheep has to fly around the Earth in 3D. I've made a simple controller for spacesheep:

public GameObject objToMove=GameObject.Find("Player");
public GameObject zeroPoint=GameObject.Find("Earth");
public float farFromZero=10;

 void Update(){

    Vector2 Ldirection;
    Ldirection.x = Input.GetAxis ("Horizontal");
    Ldirection.y = Input.GetAxis ("Vertical");


    MoveObj (objToMove, Ldirection.x, Ldirection.y);

}

I also made a separated class just because i want to get control from another class (touchscreen)

public void MoveObj(GameObject LobjToMove, float AxsHoriz, float AxsVert){

    AxsHoriz = AxsHoriz * speed;
    AxsVert = AxsVert * speed; 
    AxsHoriz *= Time.deltaTime;
    AxsVert *= Time.deltaTime;

    LobjToMove.transform.Translate(AxsHoriz, AxsVert, 0);
    //spase has to look at the earth
    LobjToMove.transform.LookAt (zeroPoint.transform.position);

    ZeroPointMagnitude (LobjToMove);
}

//fixing the distance between earth and spacesheep
void ZeroPointMagnitude(GameObject LobjToMove)
{
    Vector3 direction = zeroPoint.transform.position - LobjToMove.transform.position;
    float distance = direction.magnitude;
    if (distance > farFromZero||distance < farFromZero) {
        LobjToMove.transform.position += direction.normalized * (distance - farFromZero);
    }

}

I've put camera in the spacesheep.
It looks good and spacesheep flies around the earth but it looks like it flying around the pivot, just making radius smaller when it reaches poluses and it can't go around if I press up or down - it stops at the bottom and upstairs

I've tried to make my it fly well for 3 months, I used Raycast or Quaternions and it doesn't work as I want it.

Looks like it going to take few months more and I ask you to help me with flying player around the object without stopping on puluses (or camera flipping)

Answer 1

so here we go

   Vector3 rotDir=new Vector3(AxsVert,AxsHoriz,0);
   float gypotenuse=Mathf.Sqrt(AxsHoriz*AxsHoriz+AxsVert*AxsVert);
   gypotenuse=(gypotenuse>1)?1:gypotenuse;

        objToMove.transform.RotateAround (zeroPoint.transform.position,
                                          objToMove.transform.TransformDirection(rotDir), 
                                          gypotenuse
                                          );