Ellipse animation in Unity C#

LerpEllipseExample.cs

using UnityEngine;

// Add this MonoBehaviour to anything on the scene and it will create a prototype comet moving around a pivot
public class LerpEllipseExample : MonoBehaviour
{
    // These are  'a' and 'b' in the ellipse formula, think aphelion and perihelion
    float trajectoryHeight = 4; // y
    float trajectoryWidth = 12; // x

    float timeItTakesToGoAroundTheSun = 6; // 6 seconds, pretty fast

    float timeSinceBeginning = 0;

    GameObject comet;
    GameObject pivotingPoint;

    public void Start()
    {
        // Comet, is going to move around the Sun
        comet = GameObject.CreatePrimitive( PrimitiveType.Sphere );
        comet.name = "Comet";

        // Pivot around which we're going to move the comet
        // Note that the comet is "inside" the Sun GameObject, if you rotate the pivot point, you rotate movement
        pivotingPoint = new GameObject( "Pivoting Point" );
        comet.transform.parent = pivotingPoint.transform;

        // Adding a sun, just because
        var sol = GameObject.CreatePrimitive( PrimitiveType.Sphere );
        sol.name = "Sol";
        sol.transform.localScale = Vector3.one*3;
    }

    public void Update()
    {
        // Increment the time since beginning variable, this is used to know how long it has been since the animation/movement started
        timeSinceBeginning += Time.deltaTime;
        // Calculate and assign the position of the comet
        var positionInEllipse = LerpEllipse( trajectoryWidth, trajectoryHeight, timeSinceBeginning,
            Vector3.zero, timeItTakesToGoAroundTheSun );
        comet.transform.localPosition = positionInEllipse;
    }

    // --- AUXILLIARY FUNCTIONS --- 

    // Lerp Ellipse gives you the x and y position for something moving along an ellipse
    // 'horizontalAxis' and 'verticalAxis' are the 2 axis of the ellipse
    // 'time' is the time that has passed since the animation/movement has started
    // 'center' is the central point around which the ellipse is centered, needs to have x and y
    // 'duration' is the duration of the whole movement/animation
    public Vector2 LerpEllipse( float horizontalAxis, float verticalAxis, float time, Vector2 center, float duration )
    {
        var x = center.x + ( horizontalAxis * Mathf.Cos( ( time / duration ) * Mathf.PI * 2 ) );
        var y = center.y + ( verticalAxis * Mathf.Sin( ( time / duration ) * Mathf.PI * 2 ) );
        return new Vector2( x, y );
    }

    // To draw ellipses with rotation we need more math
    //  x = a* cos( t)*cos( angle) - b* sin( t)*sin( angle)
    //  y = a* cos( t)*sin( angle) + b* sin( t)*cos( angle)
    //
    // To try out in wolfram alpha:
    // having a = 20; b = 120; rotation angle = pi / 8
    // put the line bellow in wolfram alpha and you will see a rotated ellipse
    // x= 20*cos( t)*cos( pi/8)-120*sin( t)*sin( pi/8), y=20*cos( t)*sin( pi/8)+120*sin( t)*cos( pi/8)
}