How to make object rotate around target with random height and with option to change the rotation radius?

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class RotateAroundTarget : MonoBehaviour
{
    public Transform target;

    // Start is called before the first frame update
    void Start()
    {
        
    }

    // Update is called once per frame
    void Update()
    {
        transform.RotateAround(target.transform.position, new Vector3(0,1,0), 20 * Time.deltaTime);
        transform.position = new Vector3(0,Random.Range(0,5f),0);
    }
}

the RotateAround was working fine but once i added the Random.Range part the object is no just jumping very fast.

i guess i need somehow to add a delay between the random pickups ? but not sure how to make it smooth so the object will rotate around the target and from time to time randomly will change the height smooth up and down.

and how to add an option to change the rotation around the radius around the target?

tried the code above but it's still far away from what I wanted.

I tried using InvokeRepeating but then the transform is not rotating around anymore.

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class RotateAroundTarget : MonoBehaviour
{
    public Transform target;

    // Start is called before the first frame update
    void Start()
    {
        InvokeRepeating("ChangePosition", 0, 2);
    }

    // Update is called once per frame
    void Update()
    {
        transform.RotateAround(target.transform.position, new Vector3(0,1,0), 20 * Time.deltaTime); 
    }

    private void ChangePosition()
    {
        transform.position = new Vector3(0, Random.Range(0, 5f), 0);
    }
}

There are a couple issues with your code. First, setting the position with:

transform.position = new Vector3(0,Random.Range(0,5f),0);

will completely overwrite any X/Z change caused by the prior RotateAround. That's why your rotation stopped as soon as you introduced this code. To set the position without losing the X/Z values, you could use:

transform.position = new Vector3(
    transform.position.x,
    Random.Range(0,5f),
    transform.position.z);

So now, the rotation works again. But the height changes are still erratic because your code is setting a new random height every frame. What can we do instead?

Let's try constraining the maximum height change to a certain speed, and only set a new height target when the previous one has been reached. So your code might look like:

<!-- language: lang-cs -->

public class RotateAroundTarget : MonoBehaviour
{
    public Transform target;
    public float verticalSpeed = 20;
    public float radius = 10;

    private float targetHeight;

    // Start is called before the first frame update
    void Start()
    {
        // Initialize with a height to start moving toward
        targetHeight = GetNewTargetHeight();

        // If we start at a given distance away from the target, then this
        // will become our radius when we RotateAround it
        transform.position = new Vector3(0, 0, radius);
    }

    // Update is called once per frame
    void Update()
    {
        transform.RotateAround(target.transform.position,
            new Vector3(0,1,0), 20 * Time.deltaTime);

        // Just like your rotation rate, we scale this based on game time
        float maxHeightChange = verticalSpeed * Time.deltaTime;
        float targetHeightDelta = targetHeight - transform.position.y;

        if (maxHeightChange >= Mathf.Abs(targetHeightDelta)){
            // If the current height is close enough to the target, we can move it
            // there and then generate a new height to go towards
            transform.position = new Vector3(
                transform.position.x,
                targetHeight,
                transform.position.z);
            targetHeight = GetNewTargetHeight();
        }
        else{
            // Otherwise, limit the magnitude of the height change by the speed and
            // apply it to the current height
            float allowedHeightChange = Mathf.Clamp(
                targetHeightDelta,
                -maxHeightChange,
                maxHeightChange);
            transform.position = new Vector3(
                transform.position.x,
                transform.position.y + allowedHeightChange,
                transform.position.z);
        }
    }

    private float GetNewTargetHeight()
    {
        return Random.Range(0,5f);
    }
}