Orbital rotation equation

Question

I am developing a space sandbox (3D). Now I am working on an asteroid belt around a planet. I have an Asteroid class and an AsteroidBelt class that has a collection of the Asteroid instances. Each Asteroid object is placed randomly during initialization.

Asteroid class:

Matrix4 transform;  
double angle;
float x, y, z;
Vector3 initPosition;    

public Asteroid(ModelObject object, Texture diffuseTex){

    initPosition = new Vector3(
            MathUtils.random(-Settings.RingsDepth, Settings.RingsDepth), //x
            MathUtils.random(-.5f, .5f), //y
            MathUtils.random(-Settings.RingsDepth, Settings.RingsDepth)); //z
}

public void update(Camera camera){

    angle += Settings.RingsRotationalSpeed;
    if(angle>360) angle=0;
    if(angle<0) angle = 360;

    double angleRad = angle * MathUtils.degreesToRadians;

    x = (float) (Math.sin(angleRad) * Settings.RingsRadius  + initPosition.x);
    y = initPosition.y;
    z = (float) (Math.cos(angleRad) * Settings.RingsRadius + initPosition.z);

    transform.idt();
    transform.translate(x, y, z);
}

The code above works correctly, but it doesn't allow to rotate the asteroid belt around a planet. How to modify x, y, and z to rotate the asteroid belt around a planet freely? I hope the illustration below will clarify my problem:

Now the asteroid belt looks like below: But I need to rotate it from -90 to 90 degrees by X and Y axis: Any help will be appreciated!

Answer 1

LibGDX allows us to get rid of complex mathematics. I've solved my issue by using Matrix4 class:

Asteroid class:

Vector3 position;
Matrix4 rotationMatrtix;

public void update(Camera camera){

    angle += Settings.RingsRotationalSpeed;
    if(angle>360) angle=0;
    if(angle<0) angle = 360;

    double angleRad = angle * MathUtils.degreesToRadians;

    x = (float) (Math.sin(angleRad) * Settings.RingsRadius  + initPosition.x);
    y = initPosition.y;
    z = (float) (Math.cos(angleRad) * Settings.RingsRadius + initPosition.z);

    position.set(x, y, z);

    //rotate asteroid around X-axis
    rotationMatrtix.setToRotation(Vector3.X, Settings.RingsXRotation);
    position.mul(rotationMatrtix);

    //rotate asteroid around Z-axis
    rotationMatrtix.setToRotation(Vector3.Z, Settings.RingsZRotation);
    position.mul(rotationMatrtix);

    transform.idt();
    transform.translate(position);
}

Don't forget to create instances of the position and rotationMatrtix