Ball Collision, inside of Ball

I am trying to accomplish a rather difficult task - ball collision inside another ball using gravity.

I have one large circle in the middle of the stage (its radius is 150 pixels). I have another circle inside of that one (20 pixels radius), this is the smaller ball that I would like to have bounce around inside of the larger one with gravity. When the small ball hits the edge of the larger circle, I would like it bounce inwards to the center of the larger circle. It keeps doing this until it eventually stops in the center of the larger circle at the bottom.

Can someone please provided some sample code on how to accomplish this, or share their ideas on how to complete this task?

Thank you in advance.