Orbiting Billiard Balls

Nrich 4798 Orbiting Billiard Balls. Here's the problem modelled on Geogebra!

At what angle must the billiard ball be struck for it to return to its start position? Your answer will depend on the length and breadth of the table, but does it depend on where the ball is to start with? Don't be too quick to accept this diagram - what assumptions might it be useful to make about the rebound angles? Use point "F" to adjust the angle that the ball (E) is struck.