Script for auto movement with intersections

Hi,

I am currently working on a game project for my training. It's in 2D top view, and the player doesn't really control the character (a ship). He starts orbitating around a star. He must follow path between planets. We can choose path with arrow key. Also, to simulate gravity, when the player approach a planet, he can choose between a few paths like the picture attached.

I tried Beziers curves and iTween but I can't get the movements as smooth as it has to be... So I would like to know what kind of script would you recommand for this kind of paths ?

PS : I'm a newbie at scripting, and I script in C#. And I'm french, sorry for my poor english.

Thanks !