Eu fiz um caminho circular, o centro do caminho circular está no meio da vista. Então, fiz uma bola que pode se mover apenas no caminho do círculo (pelo menos é o que eu quero que seja):

Fiz uma função que move a bola para onde quer que a arraste (apenas no caminho do círculo), mas por alguma razão sempre que a arrasto, ela fica louca e não se move como eu quero.

Este é o meu código até agora:

class ViewController: UIViewController {
    var midViewX = CGFloat()
    var midViewY = CGFloat()

    var circlePath2 = UIBezierPath()
    var shapeLayer2 = CAShapeLayer()
    override func viewDidLoad() {
        super.viewDidLoad()
        midViewX = view.frame.midX
        midViewY = view.frame.midY
        // Do any additional setup after loading the view, typically from a nib.
        let circlePath = UIBezierPath(arcCenter: CGPoint(x: midViewX,y: midViewY), radius: CGFloat(100), startAngle: CGFloat(0), endAngle:CGFloat(M_PI * 2), clockwise: true)
        let shapeLayer = CAShapeLayer()
        shapeLayer.path = circlePath.CGPath
        shapeLayer.fillColor = UIColor.clearColor().CGColor
        shapeLayer.strokeColor = UIColor.redColor().CGColor
        shapeLayer.lineWidth = 3.0
        view.layer.addSublayer(shapeLayer)

        var angleEarth: Double = 180
        var angleEarthAfterCalculate: CGFloat = CGFloat(angleEarth*M_PI/180) - CGFloat(M_PI/2)
        var earthX = midViewX + cos(angleEarthAfterCalculate)*100
        var earthY = midViewY + sin(angleEarthAfterCalculate)*100
        circlePath2 = UIBezierPath(arcCenter: CGPoint(x: earthX,y: earthY), radius: CGFloat(10), startAngle: CGFloat(0), endAngle:CGFloat(M_PI * 2), clockwise: true)
        shapeLayer2.path = circlePath2.CGPath
        shapeLayer2.fillColor = UIColor.blueColor().CGColor
        shapeLayer2.strokeColor = UIColor.clearColor().CGColor
        shapeLayer2.lineWidth = 7
        view.layer.addSublayer(shapeLayer2)

        let dragBall = UIPanGestureRecognizer(target: self, action:#selector(ViewController.dragBall(_:)))
        view.addGestureRecognizer(dragBall)

    }

    @IBAction func dragBall(recognizer: UIPanGestureRecognizer) {
        let point = recognizer.locationInView(self.view);
        let earthX = Double(point.x)
        let earthY = Double(point.y)
        let midViewXDouble = Double(midViewX)
        let midViewYDouble = Double(midViewY)
        let angleX = (earthX - midViewXDouble)
        let angleY = (earthY - midViewYDouble)
        let angle = tan(angleY/angleX)
        let earthX2 = midViewXDouble + cos(angle)*100
        let earthY2 = midViewYDouble + sin(angle)*100
        circlePath2 = UIBezierPath(arcCenter: CGPoint(x: earthX2,y: earthY2), radius: CGFloat(10), startAngle: CGFloat(0), endAngle:CGFloat(M_PI * 2), clockwise: true)
        shapeLayer2.path = circlePath2.CGPath
    }
}

A solução provavelmente está na matemática que fiz nodragBall Func